JP6915117B2 - Transmission device and transmission method - Google Patents

Description

The present invention relates to a transmission device and a transmission method using low density parity check-convolutional codes (LDPC-CC) capable of supporting a plurality of coding rates.

In recent years, low-density parity check (LDPC) codes have been attracting attention as error correction codes that exhibit high error correction capability on a feasible circuit scale. LDPC codes have high error correction capability and are easy to implement, so they are used in error correction coding methods such as IEEE 802.11n high-speed wireless LAN systems and digital broadcasting systems.

The LDPC code is an error correction code defined by the low density parity check matrix H. The LDPC code is a block code having a block length equal to the number of columns N of the check matrix H. For example, Non-Patent Document 1, Non-Patent Document 2, Non-Patent Document 3, and Non-Patent Document 4 propose random LDPC codes, Array LDPC codes, and QC-LDPC codes (QC: Quasi-Cyclic).

However, most of the current communication systems have a feature that transmission information is collectively transmitted for each variable length packet or frame like Ethernet (registered trademark). When an LDPC code, which is a block code, is applied to such a system, there arises a problem of, for example, how to correspond a block of a fixed length LDPC code to a frame of a variable length Ethernet (registered trademark). In IEEE802.11n, the length of the transmission information series and the block length of the LDPC code are adjusted by performing padding processing and puncture processing on the transmission information series, but the coding rate changes depending on the padding and puncture. It is difficult to avoid or send redundant sequences.

For the LDPC code of such a block code (hereinafter, this is referred to as LDPC-BC: Low-Density Parity-Check Block Code), coding / decoding for an information series of arbitrary length can be performed. Possible LDPC-CC (Low-Density Parity-Check Convolutional Codes) are being studied (see, for example, Non-Patent Document 1 and Non-Patent Document 2).

LDPC-CC is a convolutional code defined by a low-density parity check matrix, for example, the coding rate R = 1/2 (= b / c) LDPC-CC parity check matrix ^H T of [0, n] Is shown in FIG. Here, _{the elements h 1} ^{(m) (t) of HT} [0, n] take 0 or 1. Further, _{all the elements other than h 1} ^{(m) and} (t) are 0. M represents the memory length in LDPC-CC, and n represents the length of the codeword of LDPC-CC. As shown in FIG. 1, in the LDPC-CC inspection matrix, 1 is placed only in the diagonal term of the matrix and the elements in the vicinity thereof, the lower left and upper right elements of the matrix are zero, and the parallelogram. It is characterized by being a type matrix.

^{_{Here, h 1 (0) (t}} ) = 1, h 2 (0) (t) = a time 1, the check matrix ^H T [0, n] LDPC-CC encoder defined by T is It is shown in FIG. As shown in FIG. 2, the LDPC-CC encoder is composed of a bit length c shift register M + 1 and a mod2 adder (exclusive OR operation). Therefore, the LDPC-CC encoder can be realized by a very simple circuit as compared with the circuit that performs the multiplication of the generator matrix and the LDPC-BC encoder that performs the operation based on the backward (forward) imputation method. It has the characteristic of being able to do it. Further, since FIG. 2 is a convolutional code encoder, it is not necessary to divide the information sequence into fixed-length blocks and encode the information sequence, and the information sequence of any length can be encoded.

R. G. Gallager, “Low-density parity check codes,” IRE Trans. Inform. Theory, IT-8, pp-21-28, 1962. D. J. C. Mackay, “Good error-correcting codes based on very sparse matrices,” IEEE Trans. Inform. Theory, vol.45, no.2, pp399-431, March 1999. J. L. Fan, “Array codes as low-density parity-check codes,” proc. Of 2nd Int. Symp. On Turbo Codes, pp.543-546, Sep. 2000. M.P.C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inform. Theory, vol.50, no.8, pp.1788-1793, Nov. 2001. MPC Fossorier, M. Mihaljevic, and H. Imai, “Reduced complexity iterative decoding of low density parity check codes based on belief propagation,” IEEE Trans. Commun., Vol.47., No.5, pp.673-680, May 1999. J. Chen, A. Dholakia, E. Eleftheriou, MPC Fossorier, and X.-Yu Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun., Vol.53., no.8, pp.1288 -1299, Aug. 2005. J. Zhang, and M.P.C. Fossorier, “Shuffled iterative decoding,” IEEE Trans. Commun., Vol.53, no.2, pp.209-213, Feb. 2005. S. Lin, D. J. Jr., Costello, “Error control coding: Fundamentals and applications,” Prentice-Hall. Tadashi Wadayama, “Low Density Parity Check Code and Its Decoding Method,” Trikeps.

However, sufficient studies have not been made on LDPC-CC and its encoders and decoders, which have a plurality of coding rates on a low calculation scale and good data reception quality.

For example, Non-Patent Document 8 indicates that a puncture is used to accommodate a plurality of coding rates. When dealing with multiple coding rates using puncture, first prepare the original code, that is, the mother code, create a coding series in the mother code, and do not transmit from that coding series (puncture). Select a bit. Then, by changing the number of bits that are not transmitted, it corresponds to a plurality of coding rates. As a result, both the encoder and the decoder can handle all the coding rates by the encoder and the decoder for the mother code, so that there is an advantage that the calculation scale (circuit scale) can be reduced. ..

On the other hand, as a method of dealing with a plurality of coding rates, there is a method of preparing different codes for each coding rate (Distributed Codes), and in particular, in the case of LDPC codes, as described in Non-Patent Document 9. Since it has the flexibility to easily configure various code lengths and code rates, a method of dealing with a plurality of code rates with a plurality of codes is common. At this time, since multiple codes are used, there is a drawback that the calculation scale (circuit scale) is large, but the data reception quality is very good compared to the case where multiple coding rates are supported by puncture. Has advantages.

Considering the above points, by preparing a plurality of codes to correspond to a plurality of coding rates, the calculation scale of the encoder and the decoder can be ensured while ensuring the data reception quality. There are few documents that discuss the method of generating LDPC codes that can reduce the number of data, and if a method of creating LDPC codes that realizes this can be established, it has been difficult to improve the data reception quality and reduce the calculation scale. Both are possible.

Further, since LDPC-CC is a kind of convolutional code, termination and tail biting are required to ensure reliability in decoding the information bit. However, sufficient studies have not been made on LDPC-CC and its encoder and decoder, which can reduce the number of terminations as much as possible while ensuring the reception quality of data.

An object of the present invention is that in a encoder and a decoder using LDPC-CC, even when termination is performed, the error correction capability is not deteriorated and the decrease in information transmission efficiency can be avoided. It is to provide a transmission device and a transmission method.

In the transmitter of the present invention, a parity bit is applied to an information sequence composed of a plurality of bits and known information added to the information sequence by a coding operation using a low density parity check convolution code (LDPC-CC). The sequence length of the first parity sequence is determined based on the sequence length and coding rate of the information sequence, and based on the determined sequence length of the first parity sequence, The information sequence and the known information are synthesized by a determination unit that determines the sequence length of the known information that generates a part of the parity bit and a coding operation using the low density parity check convolution code (LDPC-CC). A transmission device including a coding unit that encodes a series into the parity bits, a transmission unit that transmits the information series and the parity bits generated by the coding operation is adopted.

In the transmission method of the present invention, a parity bit is applied to an information sequence composed of a plurality of bits and known information added to the information sequence by a coding operation using a low density parity check convolution code (LDPC-CC). Is a transmission method for generating Based on the determination step of determining the sequence length of the known information that generates a part of the parity bit and the determined sequence length of the first parity sequence, the known information is added to the information sequence to obtain the above-mentioned information sequence. A coding step for encoding the information sequence and a composite sequence of the known information into the parity bit by a coding operation using a low density parity check convolution code (LDPC-CC), the information sequence, and the coding. A transmission method configuration including a step of transmitting the parity bit generated by calculation and a step of transmitting the parity bit is adopted.

According to the present invention, it is possible to avoid deterioration of the error correction capability and a decrease in information transmission efficiency even when termination is performed.

The figure which shows the inspection matrix of LDPC-CC The figure which shows the structure of the LDPC-CC encoder The figure which shows an example of the structure of the inspection matrix of LDPC-CC of a time-varying period 4. The figure which shows the structure of the parity check polynomial of LDPC-CC of time-varying period 3 and the check matrix H. The figure which shows the relationship of the reliability propagation between each term about X (D) of "inspection formula # 1" to "inspection formula # 3" of FIG. 4A. The figure which shows the relationship of the reliability propagation between each term about X (D) of "inspection formula # 1" to "inspection formula # 6". (7, 5) The figure which shows the inspection matrix of the convolutional code. The figure which shows an example of the structure of the inspection matrix H of LDPC-CC with a coding rate of 2/3 and a time variation period of 2. The figure which shows an example of the structure of the inspection matrix of LDPC-CC with a coding rate of 2/3 and a time variation period m. The figure which shows an example of the structure of the inspection matrix of LDPC-CC with a coding rate (n-1) / n, and a time variation period m. The figure which shows an example of the structure of the LDPC-CC coding part. Diagram for explaining the method of "Information-zero-termination" A block diagram showing a main configuration of a encoder according to a third embodiment of the present invention. A block diagram showing a configuration of a main part of the first information calculation unit according to the third embodiment. A block diagram showing a configuration of a main part of a parity calculation unit according to a third embodiment. A block diagram showing another main configuration of the encoder according to the third embodiment. A block diagram showing a main configuration of the decoder according to the third embodiment. The figure for demonstrating the operation of the log-likelihood ratio setting part in the case of the coding rate 1/2. The figure for demonstrating the operation of the log-likelihood ratio setting part in the case of the coding rate 2/3. The figure which shows an example of the structure of the communication apparatus which mounts the encoder which concerns on Embodiment 3. Diagram showing an example of transmission format The figure which shows an example of the structure of the communication device which mounts the decoder which concerns on Embodiment 3. A diagram showing an example of the relationship between the information size and the number of terminations. A diagram showing another example of the relationship between the information size and the number of terminations. A diagram showing an example of the relationship between the information size and the number of terminations. A block diagram showing a configuration of a main part of a communication device equipped with a encoder according to a fifth embodiment of the present invention. Diagram for explaining how to determine the termination series length Diagram for explaining how to determine the termination series length Diagram showing an example of transmission format A block diagram showing a configuration of a main part of a communication device equipped with a decoder according to a fifth embodiment. The figure which shows an example of the information flow between the communication device which carries a encoder and the communication device which carries a decoder. The figure which shows an example of the information flow between the communication device which carries a encoder and the communication device which carries a decoder. A diagram showing an example of a correspondence table showing the relationship between the information size and the number of terminations. The figure which shows the BER / BLER characteristic when the termination series is added to the information series whose information size is 512 bits. The figure which shows the BER / BLER characteristic when the termination series is added to the information series whose information size is 1024 bits. The figure which shows the BER / BLER characteristic when the termination series is added to the information series whose information size is 2048 bits. The figure which shows the BER / BLER characteristic when the termination series is added to the information series whose information size is 4096 bits. The figure which shows the correspondence table of information size and support code rate A block diagram showing a configuration of a main part of a communication device equipped with a encoder according to a sixth embodiment of the present invention. The figure which shows an example of the information flow between the communication device which carries a encoder and the communication device which carries a decoder. A block diagram showing a configuration of a main part of a communication device equipped with a decoder according to a sixth embodiment. A block diagram showing a configuration of a main part of the encoder according to the seventh embodiment of the present invention. A block diagram showing a configuration of a main part of the decoder according to the seventh embodiment. A block diagram showing a configuration of a main part of the encoder according to the eighth embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
First, in the present embodiment, the LDPC-CC having good characteristics will be described.

(LDPC-CC with good characteristics)
The LDPC-CC having a time-varying period g having good characteristics will be described below.

First, LDPC-CC having a time-varying period 4 having good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

Consider equations (1-1) to (1-4) as a parity check polynomial of LDPC-CC with a time-varying period of 4. At this time, X (D) is a polynomial representation of data (information), and P (D) is a polynomial representation of parity. Here, in the equations (1-1) to (1-4), a parity check polynomial in which four terms exist in each of X (D) and P (D) is used, but this is good reception quality. This is because it is preferable to have four terms in order to obtain.

In the formula (1-1), a1, a2, a3, and a4 are integers (however, a1 ≠ a2 ≠ a3 ≠ a4, and all of a1 to a4 are different). Hereinafter, when "X ≠ Y ≠ ... ≠ Z" is described, it means that X, Y, ..., Z are all different from each other. Further, b1, b2, b3, and b4 are integers (however, b1 ≠ b2 ≠ b3 ≠ b4). Referred to parity check polynomial of equation (1-1) and "check equation # 1", the sub-matrix based on a parity check polynomial of equation (1-1), the first sub-matrix H _1.

Further, in the equation (1-2), A1, A2, A3, and A4 are integers (where A1 ≠ A2 ≠ A3 ≠ A4). Further, B1, B2, B3, and B4 are integers (however, B1 ≠ B2 ≠ B3 ≠ B4). Referred to parity check polynomial of equation (1-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (1-2), the second sub-matrix H _2.

Further, in the equation (1-3), α1, α2, α3, and α4 are integers (where α1 ≠ α2 ≠ α3 ≠ α4). Further, β1, β2, β3, and β4 are integers (however, β1 ≠ β2 ≠ β3 ≠ β4). Referred to parity check polynomial of equation (1-3) and "check equation # 3", the sub-matrix based on a parity check polynomial of equation (1-3), the third sub-matrix H _3.

Further, in the equation (1-4), E1, E2, E3, and E4 are integers (where E1 ≠ E2 ≠ E3 ≠ E4). Further, F1, F2, F3, and F4 are integers (however, F1 ≠ F2 ≠ F3 ≠ F4). Referred to parity check polynomial of equation (1-4) and "check equation # 4", a sub-matrix based on a parity check polynomial of equation (1-4), the fourth sub-matrix H _4.

Then, from the first sub-matrix H ₁ , the second sub-matrix H ₂ , the third sub-matrix H ₃ , and the fourth sub-matrix H ₄ , the LDPC-CC having a time-varying period 4 in which the inspection matrix is generated as shown in FIG. think.

At this time, in the formulas (1-1) to (1-4), combinations of orders of X (D) and P (D) (a1, a2, a3, a4), (b1, b2, b3, b4), (A1, A2, A3, A4), (B1, B2, B3, B4), (α1, α2, α3, α4), (β1, β2, β3, β4), (E1, E2, E3, E4), When the remainder obtained by dividing each value of (F1, F2, F3, F4) by 4 is k, the remainder is added to the four coefficient sets (for example, (a1, a2, a3, a4)) represented as described above. 0, 1, 2, 3 are included one by one, and all of the above four coefficient sets are satisfied.

For example, if each order (a1, a2, a3, a4) of X (D) of "inspection formula # 1" is (a1, a2, a3, a4) = (8,7,6,5), each order The remainder k obtained by dividing (a1, a2, a3, a4) by 4 is (0,3,2,1), and there is one remainder (k) 0, 1, 2, 3 in each of the four coefficient sets. Will be included. Similarly, if each order (b1, b2, b3, b4) of P (D) of "inspection formula # 1" is (b1, b2, b3, b4) = (4,3,2,1), each The remainder k obtained by dividing the order (b1, b2, b3, b4) by 4 is (0,3,2,1), and 0, 1, 2, 3 are added as the remainder (k) to the four coefficient sets. It will be included one by one. The above "remainder" is also related to each of the four coefficient sets of X (D) and P (D) of the other inspection formulas ("inspection formula # 2", "test formula # 3", "test formula # 4"). It is assumed that the conditions are satisfied.

By doing so, it becomes possible to form a regular LDPC code in which the column weight of the inspection matrix H composed of the equations (1-1) to (1-4) is 4 in all the columns. .. Here, the regular LDPC code is an LDPC code defined by an inspection matrix in which each column weight is constant, and has a feature that the characteristics are stable and an error floor is unlikely to occur. In particular, when the column weight is 4, the characteristics are good. Therefore, by generating the LDPC-CC as described above, it is possible to obtain the LDPC-CC having good reception performance.

Table 1 is an example (LDPC-CC # 1 to # 3) of an LDPC-CC having a time-varying period of 4 and a coding rate of 1/2, in which the above-mentioned condition regarding "remainder" is satisfied. In Table 1, the LDPC-CC having a time-varying period 4 is defined by four parity check polynomials, "check polynomial # 1,""check polynomial # 2,""check polynomial # 3," and "check polynomial # 4." NS.

In the above, the case where the coding rate is 1/2 has been described as an example, but even when the coding rate is (n-1) / n, the information X1 (D), X2 (D), ... Xn- If the above-mentioned "remainder" condition is satisfied in each of the four coefficient sets in 1 (D), the code becomes a regular LDPC code, and good reception quality can be obtained.

It was confirmed that even in the case of the time-varying period 2, a code having good characteristics can be searched by applying the above-mentioned condition regarding "remainder". Hereinafter, the LDPC-CC having a time-varying period 2 having good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

Consider equations (2-1) and (2-2) as parity check polynomials of LDPC-CC with a time-varying period of 2. At this time, X (D) is a polynomial representation of data (information), and P (D) is a polynomial representation of parity. Here, in the equations (2-1) and (2-2), a parity check polynomial in which four terms exist in each of X (D) and P (D) is used, but this is good reception quality. This is because it is preferable to have four terms in order to obtain.

In the formula (2-1), a1, a2, a3, and a4 are integers (where a1 ≠ a2 ≠ a3 ≠ a4). Further, b1, b2, b3, and b4 are integers (however, b1 ≠ b2 ≠ b3 ≠ b4). Referred to parity check polynomial of equation (2-1) and "check equation # 1", the sub-matrix based on a parity check polynomial of equation (2-1), the first sub-matrix H _1.

Further, in the equation (2-2), A1, A2, A3, and A4 are integers (where A1 ≠ A2 ≠ A3 ≠ A4). Further, B1, B2, B3, and B4 are integers (however, B1 ≠ B2 ≠ B3 ≠ B4). Referred to parity check polynomial of equation (2-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (2-2), the second sub-matrix H _2.

Then, consider LDPC-CC having a time-varying period 2 generated from the first sub-matrix H ₁ and the second sub-matrix H _2.

At this time, in the equations (2-1) and (2-2), the combination of the orders of X (D) and P (D) (a1, a2, a3, a4), (b1, b2, b3, b4), Assuming that the remainder of dividing each value of (A1, A2, A3, A4), (B1, B2, B3, B4) by 4 is k, the four coefficient sets represented as described above (for example, (a1, a1,) The remainders 0, 1, 2, 3 are included in a2, a3, a4)) one by one, and all of the above four coefficient sets are satisfied.

For example, if each order (a1, a2, a3, a4) of X (D) of "inspection formula # 1" is (a1, a2, a3, a4) = (8,7,6,5), each order The remainder k obtained by dividing (a1, a2, a3, a4) by 4 is (0,3,2,1), and there is one remainder (k) 0, 1, 2, 3 in each of the four coefficient sets. Will be included. Similarly, if each order (b1, b2, b3, b4) of P (D) of "inspection formula # 1" is (b1, b2, b3, b4) = (4,3,2,1), each The remainder k obtained by dividing the order (b1, b2, b3, b4) by 4 is (0,3,2,1), and 0, 1, 2, 3 are added as the remainder (k) to the four coefficient sets. It will be included one by one. It is assumed that the above-mentioned condition regarding "remainder" is also satisfied for each of the four coefficient sets of X (D) and P (D) of "Inspection formula # 2".

By doing so, it becomes possible to form a regular LDPC code in which the column weight of the inspection matrix H composed of the equations (2-1) and (2-2) is 4 in all the columns. .. Here, the regular LDPC code is an LDPC code defined by an inspection matrix in which each column weight is constant, and has a feature that the characteristics are stable and an error floor is unlikely to occur. In particular, when the row weight is 8, the characteristics are good. Therefore, by generating the LDPC-CC as described above, it is possible to obtain the LDPC-CC capable of further improving the reception performance. Become.

Table 2 shows an example of LDPC-CC (LDPC-CC # 1 and # 2) having a time-varying period of 2 and a coding rate of 1/2 in which the above-mentioned "remainder" condition is satisfied. In Table 2, the LDPC-CC having a time-varying period 2 is defined by two parity check polynomials, “check polynomial # 1” and “check polynomial # 2”.

In the above (LDPC-CC with a time variation period 2), the case where the coding rate is 1/2 has been described as an example, but even when the coding rate is (n-1) / n, the information X1 (D), If the above-mentioned "remainder" condition is satisfied in each of the four coefficient sets of X2 (D) and ... Xn-1 (D), the regular LDPC code can be obtained and good reception quality can be obtained. can.

It was also confirmed that even in the case of the time variation period 3, a code having good characteristics can be searched by applying the following conditions regarding the "remainder". Hereinafter, the LDPC-CC having a time-varying period 3 having good characteristics will be described. In the following, a case where the coding rate is 1/2 will be described as an example.

Consider equations (3-1) to (3-3) as a parity check polynomial of LDPC-CC having a time-varying period of 3. At this time, X (D) is a polynomial representation of data (information), and P (D) is a polynomial representation of parity. Here, in the equations (3-1) to (3-3), it is assumed that the parity check polynomial has three terms in each of X (D) and P (D).

In the formula (3-1), a1, a2, and a3 are integers (where a1 ≠ a2 ≠ a3). Further, b1, b2, and b3 are integers (however, b1 ≠ b2 ≠ b3). Referred to parity check polynomial of equation (3-1) and "check equation # 1", the sub-matrix based on a parity check polynomial of equation (3-1), the first sub-matrix H _1.

Further, in the equation (3-2), A1, A2, and A3 are integers (where A1 ≠ A2 ≠ A3). Further, B1, B2, and B3 are integers (however, B1 ≠ B2 ≠ B3). Referred to parity check polynomial of equation (3-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (3-2), the second sub-matrix H _2.

Further, in the equation (3-3), α1, α2, and α3 are integers (where α1 ≠ α2 ≠ α3). Further, β1, β2, and β3 are integers (however, β1 ≠ β2 ≠ β3). Referred to parity check polynomial of equation (3-3) and "check equation # 3", the sub-matrix based on a parity check polynomial of equation (3-3), the third sub-matrix H _3.

Then, consider LDPC-CC having a time-varying period 3 generated from the first sub-matrix H ₁ , the second sub-matrix H ₂ , and the third sub-matrix H _3.

At this time, in the formulas (3-1) to (3-3), the combination of the order of X (D) and P (D) (a1, a2, a3), (b1, b2, b3), (A1, A2). , A3), (B1, B2, B3), (α1, α2, α3), (β1, β2, β3) divided by 3 and the remainder is k. The coefficient set (for example, (a1, a2, a3)) is set to include one remainder of 0, 1, and 2, and is satisfied with all the above three coefficient sets.

For example, if each order (a1, a2, a3) of X (D) of "inspection formula # 1" is (a1, a2, a3) = (6, 5, 4), each order (a1, a2, a3) ) Divided by 3, the remainder k becomes (0,2,1), and the remainder (k) 0, 1, 2 is included in each of the three coefficient sets. Similarly, if each order (b1, b2, b3) of P (D) of "inspection formula # 1" is (b1, b2, b3) = (3,2,1), each order (b1, b2, The remainder k obtained by dividing b3) by 4 becomes (0,2,1), and 0, 1, 2 are included as the remainder (k) in each of the three coefficient sets. It is assumed that the above-mentioned condition regarding "remainder" is also satisfied for each of the three coefficient sets of X (D) and P (D) of "inspection formula # 2" and "inspection formula # 3".

By generating LDPC-CC in this way, with some exceptions, it is possible to generate a regular LDPC-CC code in which row weights are equal in all rows and column weights are equal in all rows. can. The exception means that the row weights and column weights are not equal to the other row weights and column weights in the first part and the last part of the check matrix. Further, when BP decoding is performed, the reliability in "inspection formula # 2" and the reliability in "inspection formula # 3" are accurately propagated to "inspection formula # 1", and "inspection formula # 1" The reliability in "Inspection formula # 3" and the reliability in "Inspection formula # 3" are accurately propagated to "Inspection formula # 2", and the reliability in "Inspection formula # 1" and the reliability in "Inspection formula # 2" are Accurately propagates to "inspection formula # 3". Therefore, it is possible to obtain LDPC-CC with better reception quality. This is because, when considered in column units, the position where "1" exists is arranged so as to accurately propagate the reliability as described above.

Hereinafter, the above-mentioned reliability propagation will be described with reference to the figures. FIG. 4A shows the configuration of the parity check polynomial and the check matrix H of the LDPC-CC having the time variation period 3.

"Check formula # 1" is the parity check polynomial of formula (3-1), in which (a1, a2, a3) = (2,1,0), (b1, b2, b3) = (2,1,0). ), And the remainder after dividing each coefficient by 3 is (a1% 3, a2% 3, a3% 3) = (2,1,0), (b1% 3, b2% 3, b3% 3). ) = (2,1,0). In addition, "Z% 3" represents the remainder obtained by dividing Z by 3 (the same applies hereinafter).

"Check formula # 2" is the parity check polynomial of formula (3-2), in which (A1, A2, A3) = (5,1,0), (B1, B2, B3) = (5,1,0). ), And the remainder after dividing each coefficient by 3 is (A1% 3, A2% 3, A3% 3) = (2,1,0), (B1% 3, B2% 3, B3% 3). ) = (2,1,0).

"Check formula # 3" is the parity check polypoly of formula (3-3), in which (α1, α2, α3) = (4,2,0), (β1, β2, β3) = (4,2,0). ), And the remainder after dividing each coefficient by 3 is (α1% 3, α2% 3, α3% 3) = (1,2,0), (β1% 3, β2% 3, β3% 3). ) = (1,2,0).

Therefore, the example of LDPC-CC having a time variation period 3 shown in FIG. 4A is based on the above-mentioned condition regarding "remainder", that is,
(A1% 3, a2% 3, a3% 3),
(B1% 3, b2% 3, b3% 3),
(A1% 3, A2% 3, A3% 3),
(B1% 3, B2% 3, B3% 3),
(Α1% 3, α2% 3, α3% 3),
(Β1% 3, β2% 3, β3% 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) It meets the condition of becoming.

Returning to FIG. 4A again, reliability propagation will be described. By the column operation of column 6506 in BP decoding, the "1" in the area 6501 of "inspection matrix # 1" becomes the "1" in the area 6504 of the "inspection matrix # 2" and the "1" in the area 6505 of the "inspection matrix # 3". The reliability is propagated from "1". As described above, "1" in the region 6501 of "inspection formula # 1" is a coefficient in which the remainder divided by 3 is 0 (a3% 3 = 0 (a3 = 0) or b3% 3 =. 0 (b3 = 0)). Further, "1" in the area 6504 of "inspection matrix # 2" is a coefficient in which the remainder divided by 3 is 1 (A2% 3 = 1 (A2 = 1) or B2% 3 = 1 (B2). = 1)). Further, "1" in the region 6505 of "inspection formula # 3" is a coefficient in which the remainder divided by 3 is 2 (α2% 3 = 2 (α2 = 2) or β2% 3 = 2 (β2). = 2)).

As described above, "1" in the region 6501 where the coefficient of "inspection formula # 1" has a remainder of 0 has a remainder of 1 in the coefficient of "inspection formula # 2" in the column operation of column 6506 in BP decoding. The reliability is propagated from "1" in region 6504 and "1" in region 6505 where the coefficient of "inspection formula # 3" has a remainder of 2.

Similarly, "1" in the region 6502 having a remainder of 1 in the coefficient of "inspection formula # 1" is a region in which the remainder is 2 in the coefficient of "inspection formula # 2" in the column operation of column 6509 in BP decoding. The reliability is propagated from "1" of 6507 and "1" of the region 6508 where the remainder is 0 in the coefficient of "inspection formula # 3".

Similarly, the "1" in the region 6503 where the coefficient of the "check formula # 1" is 2 is the region where the remainder is 0 in the coefficient of the "check formula # 2" in the column operation of the column 6512 in the BP decoding. The reliability is propagated from the "1" of 6510 and the "1" of the region 6511 where the remainder is 1 in the coefficient of "inspection formula # 3".

A supplementary explanation will be given about reliability propagation with reference to FIG. 4B. FIG. 4B shows the relationship of reliability propagation between each term regarding X (D) of “inspection formula # 1” to “inspection formula # 3” of FIG. 4A. “Inspection formula # 1” to “Inspection formula # 3” in FIG. 4A are described in the section relating to X (D) of formulas (3-1) to (3-3), wherein (a1, a2, a3) = (2, 1,0), (A1, A2, A3) = (5,1,0), (α1, α2, α3) = (4,2,0).

In FIG. 4B, the squared terms (a3, A3, α3) indicate the coefficients with a remainder of 0 divided by 3. The circled terms (a2, A2, α1) indicate a coefficient with a remainder of 1 divided by 3. In addition, the terms (a1, A1, α2) surrounded by diamonds indicate a coefficient in which the remainder divided by 3 is 2.

As can be seen from FIG. 4B, the reliability of a1 of "inspection formula # 1" is propagated from A3 of "inspection formula # 2" and α1 of "inspection formula # 3" having different remainders divided by 3. The reliability of a2 of "inspection formula # 1" is propagated from A1 of "inspection formula # 2" and α3 of "inspection formula # 3" having different remainders divided by 3. The reliability of a3 of "inspection formula # 1" is propagated from A2 of "inspection formula # 2" and α2 of "inspection formula # 3" having different remainders divided by 3. FIG. 4B shows the relationship of reliability propagation between the terms related to X (D) of “Inspection formula # 1” to “Inspection formula # 3”, but the same applies to each term related to P (D). It can be said.

In this way, the reliability is propagated to the "inspection formula # 1" from the coefficient of the coefficient of the "inspection formula # 2" in which the remainder obtained by dividing by 3 is 0, 1, or 2. That is, the reliability is propagated to the "inspection formula # 1" from the coefficients of the "inspection formula # 2" in which the remainders divided by 3 are all different. Therefore, all the reliabilitys with low correlation are propagated to "inspection formula # 1".

Similarly, in "inspection formula # 2", the reliability is propagated from the coefficient of "inspection formula # 1" in which the remainder divided by 3 is 0, 1, or 2. That is, the reliability is propagated to the "inspection formula # 2" from the coefficients of the "inspection formula # 1" in which the remainders divided by 3 are all different. Further, in the "inspection formula # 2", the reliability is propagated from the coefficient of the coefficient of the "inspection formula # 3" in which the remainder obtained by dividing by 3 is 0, 1, or 2. That is, the reliability is propagated to the "inspection formula # 2" from the coefficients of the "inspection formula # 3" in which the remainders divided by 3 are all different.

Similarly, in "inspection formula # 3", the reliability is propagated from the coefficients of "inspection formula # 1" in which the remainder divided by 3 is 0, 1, or 2. That is, the reliability is propagated to the "inspection formula # 3" from the coefficients of the "inspection formula # 1" in which the remainders divided by 3 are all different. Further, in the "inspection formula # 3", the reliability is propagated from the coefficient of the coefficient of the "inspection formula # 2" in which the remainder obtained by dividing by 3 is 0, 1, or 2. That is, the reliability is propagated to the "inspection formula # 3" from the coefficients of the "inspection formula # 2" in which the remainders divided by 3 are all different.

In this way, by ensuring that each degree of the parity check polynomials in equations (3-1) to (3-3) satisfies the above-mentioned "remainder" condition, the reliability is guaranteed in all column operations. Since it is propagated, the reliability can be efficiently propagated in all the inspection formulas, and the error correction capability can be further improved.

The LDPC-CC having a time variation period of 3 has been described above by taking the case where the coding rate is 1/2 as an example, but the coding rate is not limited to 1/2. In the case of coding rate (n-1) / n (n is an integer of 2 or more), each of the three coefficients in the information X1 (D), X2 (D), ... Xn-1 (D). If the above-mentioned condition regarding "remainder" is satisfied in the set, the code becomes a regular LDPC code, and good reception quality can be obtained.

Hereinafter, the case where the coding rate (n-1) / n (n is an integer of 2 or more) will be described.

Consider equations (4-1) to (4-3) as a parity check polynomial of LDPC-CC having a time-varying period of 3. At this time, X ₁ (D), X ₂ (D), ... X _n-1 (D) are polynomial representations of data (information) X ₁ , X ₂ , ... X _{n-1, and P.} (D) is a polynomial representation of parity. Here, in the equations (4-1) to (4-3), _{there are three terms for each of X 1} (D), X ₂ (D), ... X _n-1 (D), and P (D). Let it be a parity check polynomial that exists.

In equation (4-1), a _{i, 1} , a _{i, 2} , a _{i, 3} (i = 1, 2, ..., N-1) are integers (where a _{i, 1} ≠ a _{i, 2} ≠ _{ai, 3} ). Further, b1, b2, and b3 are integers (however, b1 ≠ b2 ≠ b3). Referred to parity check polynomial of equation (4-1) and "check equation # 1", the sub-matrix based on a parity check polynomial of equation (4-1), the first sub-matrix H _1.

Further, in the equation (4-2), A _{i, 1} , A _{i, 2} , A _{i, 3} (i = 1, 2, ..., N-1 are integers (however, A _{i, 1} ≠ A _{i). , 2} ≠ _{Ai, 3} ). Also, B1, B2, and B3 are integers (where B1 ≠ B2 ≠ B3). Let the sub-matrix based on the parity check polynomial of Eq. (4-2) be the second sub-matrix H ₂ .

Further, in the equation (4-3), α _{i, 1} , α _{i, 2} , α _{i, 3} (i = 1, 2, ..., N-1 are integers (where α _{i, 1} ≠ α _{i). , 2} ≠ α _{i, 3} ). Also, β1, β2, β3 are integers (where β1 ≠ β2 ≠ β3). call, the sub-matrix based on a parity check polynomial of equation (4-3), the third sub-matrix _{H 3.}

Then, consider LDPC-CC having a time-varying period 3 generated from the first sub-matrix H ₁ , the second sub-matrix H ₂ , and the third sub-matrix H _3.

At this time, in the equations (4-1) to (4-3), _{the combination of the orders of X 1} (D), X ₂ (D), ... X _n-1 (D) and P (D) (a). _1,1 , a _1,2 , a _1,3 ),
(A ₂ , 1, a ₂ , _{2, a 2, 3} ), ...,
( _An-1,1 , _ann-1,2 , an _-1,3 ),
(B1, b2, b3),
(A ₁ , 1, A ₁ , _{2, A 1, 3} ),
(A ₂ , 1, A ₂ , _{2, A 2, 3} ), ...,
( _An-1,1 , _An-1,2 , _An-1,3 ),
(B1, B2, B3),
(Α ₁ , 1, α ₁ , _{2, α 1, 3} ),
(Α ₂ , 1, α ₂ , _{2, α 2, 3} ), ...
(Α _n-1 , 1, α _n-1 , 2, α _n-1 , 3),
(Β1, β2, β3)
When the remainder obtained by dividing each value of 3 by 3 is k, the remainder 0 _{is added to the three coefficient sets (for example, (a 1} , 1, a ₁ , 2, a _{1, 3)) expressed as described above.} 1 and 2 are included one by one, and all of the above three coefficient sets are satisfied.

in short,
(A _1,1 % 3, a _1,2 % 3, a _1,3 % 3),
(A _2,1 % 3, a _2,2 % 3, a _2,3 % 3), ...
( _An-1,1 % 3, _ann-1,2 % 3, _ann-1,3 % 3),
(B1% 3, b2% 3, b3% 3),
(A _1,1 % 3, A _1,2 % 3, A _1,3 % 3),
(A _2,1 % 3, A _2,2 % 3, A _2,3 % 3), ...
( _An-1,1 % 3, _An-1,2 % 3, _An-1,3 % 3),
(B1% 3, B2% 3, B3% 3),
(Α _1,1 % 3, α _1,2 % 3, α _1,3 % 3),
(Α _2,1 % 3, α _2,2 % 3, α _2,3 % 3), ...
(Α _n-1,1 % 3, α _n-1,2 % 3, α _n-1,3 % 3),
(Β1% 3, β2% 3, β3% 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) To be.

By generating the LDPC-CC in this way, the regular LDPC-CC code can be generated. Further, when BP decoding is performed, the reliability in "inspection formula # 2" and the reliability in "inspection formula # 3" are accurately propagated to "inspection formula # 1", and "inspection formula # 1" The reliability in "Inspection formula # 3" and the reliability in "Inspection formula # 3" are accurately propagated to "Inspection formula # 2", and the reliability in "Inspection formula # 1" and the reliability in "Inspection formula # 2" are Accurately propagates to "inspection formula # 3". Therefore, as in the case of the coding rate of 1/2, an LDPC-CC having better reception quality can be obtained.

In Table 3, an example of LDPC-CC having a time-varying period of 3 and a coding rate of 1/2 (LDPC-CC # 1, # 2, # 3, # 4, # 5) in which the above-mentioned "remainder" condition is satisfied. ) Is shown. In Table 3, the LDPC-CC having a time-varying period 3 is based on the three parity check polynomials of "inspection (multinomial) equation # 1,""inspection (multinomial) equation # 2", and "inspection (multinomial) equation # 3". Defined.

Further, similarly to the time-varying cycle 3, the following conditions regarding the "remainder" are applied to the LDPC-CC having the time-varying period that is a multiple of 3 (for example, the time-varying period is 6, 9, 12, ...). Then, it was confirmed that a code having good characteristics could be searched for. Hereinafter, LDPC-CC, which is a multiple of the time-varying period 3 having good characteristics, will be described. In the following, the case of LDPC-CC having a coding rate of 1/2 and a time variation period of 6 will be described as an example.

Consider equations (5-1) to (5-6) as parity check polynomials of LDPC-CC with a time-varying period of 6.

At this time, X (D) is a polynomial representation of data (information), and P (D) is a polynomial representation of parity. In the LDPC-CC having a time-varying period 6, if the parity Pi and the information Xi at time i are i% 6 = k (k = 0, 1, 2, 3, 4, 5), the equation (5- (k + 1)) ) Parity check polynomial is established. For example, if i = 1, then i% 6 = 1 (k = 1), so that equation (6) holds.

Here, in the equations (5-1) to (5-6), it is assumed that the parity check polynomial has three terms in each of X (D) and P (D).

In the formula (5-1), a1,1, a1,2, a1,3 are integers (where a1,1 ≠ a1,2 ≠ a1,3). Further, b1,1, b1,2, b1,3 are integers (however, b1,1 ≠ b1, ≠ b1,3). Referred to parity check polynomial of equation (5-1) and "check equation # 1", the sub-matrix based on a parity check polynomial of equation (5-1), the first sub-matrix H _1.

Further, in the equation (5-2), a2,1, a2,2, a2,3 are integers (however, a2,1 ≠ a2,2 ≠ a2,3). Further, b2,1, b2,2, b2,3 are integers (however, b2,1 ≠ b2,2 ≠ b2,3). Referred to parity check polynomial of equation (5-2) and "check equation # 2", the sub-matrix based on a parity check polynomial of equation (5-2), the second sub-matrix H _2.

Further, in the equation (5-3), a3,1, a3,2, a3,3 are integers (however, a3,1 ≠ a3,2 ≠ a3,3). Further, b3,1, b3,2, b3,3 are integers (however, b3,1 ≠ b3,2 ≠ b3,3). Referred to parity check polynomial of equation (5-3) and "check equation # 3", the sub-matrix based on a parity check polynomial of equation (5-3), the third sub-matrix H _3.

Further, in the equation (5-4), a4,1, a4,2, a4,3 are integers (however, a4,1 ≠ a4,2 ≠ a4,3). Further, b4, 1, b4, 2, b4, 3 are integers (however, b4, 1 ≠ b4, 2 ≠ b4, 3). Referred to parity check polynomial of equation (5-4) and "check equation # 4", a sub-matrix based on a parity check polynomial of equation (5-4), the fourth sub-matrix H _4.

Further, in the equation (5-5), a5,1, a5,2, a5,3 are integers (however, a5,1 ≠ a5,2 ≠ a5,3). Further, b5,1, b5,2, b5,3 are integers (however, b5,1 ≠ b5,2 ≠ b5,3). Referred to parity check polynomial of equation (5-5) and "check equation # 5", a sub-matrix based on a parity check polynomial of equation (5-5), the fifth sub-matrix H _5.

Further, in the equation (5-6), a6,1, a6,2, a6,3 are integers (where a6,1 ≠ a6,2 ≠ a6,3). Further, b6, 1, b6, 2, b6, 3 are integers (however, b6, 1 ≠ b6, 2 ≠ b6, 3). Referred to parity check polynomial of equation (5-6) and "check equation # 6", the sub-matrix based on a parity check polynomial of equation (5-6), and the sixth sub-matrix H _6.

The first sub-matrix _{H 1,} second sub-matrix _{H 2,} third sub-matrix _{H 3,} fourth sub-matrix _{H 4,} fifth sub-matrix _{H 5,} varying period 6 when generating the sixth sub-matrix _{H 6} Consider the LDPC-CC of.

At this time, in the formulas (5-1) to (5-6), the combination of orders of X (D) and P (D) (a1, 1, a1, 2, a1, 3),
(B1,1, b1,2, b1,3),
(A2,1, a2,2, a2,3),
(B2,1, b2,2, b2,3),
(A3,1, a3,2, a3,3),
(B3,1, b3,2, b3,3),
(A4,1, a4,2, a4,3),
(B4, 1, b4, 2, b4, 3),
(A5,1, a5,2, a5,3),
(B5,1, b5,2, b5,3),
(A6,1, a6,2, a6,3),
(B6, 1, b6, 2, b6, 3)
Assuming that the remainder k when each value of is divided by 3, the remainder 0, 1, 2 is included one by one, and all of the above three coefficient sets are satisfied. in short,
(A1,1% 3, a1,2%3, a1,3%3),
(B1, 1% 3, b1, 2% 3, b1, 3% 3),
(A2, 1% 3, a2, 2% 3, a2, 3% 3),
(B2, 1% 3, b2, 2% 3, b2, 3% 3),
(A3, 1% 3, a3, 2% 3, a3, 3% 3),
(B3, 1% 3, b3, 2% 3, b3, 3% 3),
(A4, 1% 3, a4, 2% 3, a4, 3% 3),
(B4, 1% 3, b4, 2% 3, b4, 3% 3),
(A5, 1% 3, a5, 2% 3, a5, 3% 3),
(B5, 1% 3, b5, 2% 3, b5, 3% 3),
(A6, 1% 3, a6, 2% 3, a6, 3% 3),
(B6, 1% 3, b6, 2% 3, b6, 3% 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.

By generating LDPC-CC in this way, when an edge is drawn when a tanner graph is drawn for "inspection formula # 1", if an edge exists, "inspection formula # 2 or inspection formula # 5" is accurately obtained. The reliability in "Inspection formula # 3 or inspection formula # 6" is accurately propagated.

In addition, when an edge is present when a tanner graph is drawn for "inspection formula # 2", the reliability in "inspection formula # 1 or inspection formula # 4", "inspection formula # 3," Alternatively, the reliability in "Inspection formula # 6" is accurately propagated.

In addition, when an edge is present when a tanner graph is drawn for "inspection formula # 3", the reliability in "inspection formula # 1 or inspection formula # 4", "inspection formula # 2," Alternatively, the reliability in "Inspection formula # 5" is accurately propagated. When an edge is present when drawing a tanner graph for "inspection formula # 4", the reliability in "inspection formula # 2 or inspection formula # 5", "inspection formula # 3 or" The reliability in "Inspection formula # 6" is accurately propagated.

In addition, when an edge is present when drawing a tanner graph, the reliability of "inspection formula # 1 or inspection formula # 4" is accurately compared to "inspection formula # 5", and "inspection formula # 3," Alternatively, the reliability in "Inspection formula # 6" is accurately propagated. In addition, when an edge is present when a tanner graph is drawn for "inspection formula # 6", the reliability in "inspection formula # 1 or inspection formula # 4", "inspection formula # 2," Alternatively, the reliability in "Inspection formula # 5" is accurately propagated.

Therefore, the LDPC-CC having the time-varying period 6 retains a better error correction capability as in the case where the time-varying period is 3.

Regarding this, reliability propagation will be described with reference to FIG. 4C. FIG. 4C shows the relationship of reliability propagation between each term regarding X (D) of “inspection formula # 1” to “inspection formula # 6”. In FIG. 4C, the square indicates a coefficient with a remainder of 0 divided by 3 in ax, y (x = 1,2,3,4,5,6; y = 1,2,3).

Further, the circle indicates a coefficient in which the remainder obtained by dividing by 3 in ax, y (x = 1,2,3,4,5,6; y = 1,2,3) is 1. Further, the rhombus shows a coefficient of 2 in ax, y (x = 1,2,3,4,5,6; y = 1,2,3), and the remainder divided by 3 is 2.

As can be seen from FIG. 4C, when an edge is present when the tanner graph is drawn, a1 and 1 of "inspection formula # 1" have different remainders divided by 3 "inspection formula # 2 or # 5" and "inspection formula # 1" and "inspection formula # 1". The reliability is propagated from the inspection formula # 3 or # 6. Similarly, when an edge is present when drawing a tanner graph, a1 and 2 of "inspection formula # 1" are different in the remainder divided by 3 "inspection formula # 2 or # 5" and "inspection formula # 3". Or the reliability is propagated from "# 6".

Similarly, when an edge is present when drawing a tanner graph, a1 and 3 of "inspection formula # 1" are different in the remainder divided by 3 "inspection formula # 2 or # 5" and "inspection formula # 3". Or the reliability is propagated from "# 6". FIG. 4C shows the relationship of reliability propagation between the terms related to X (D) of “Inspection formula # 1” to “Inspection formula # 6”, but the same applies to each term related to P (D). It can be said.

In this way, the reliability is propagated to each node in the tanner graph of "inspection formula # 1" from the coefficient nodes other than "inspection formula # 1". Therefore, it is considered that the error correction capability is improved because all the reliabilitys having low correlations are propagated to "inspection formula # 1".

In FIG. 4C, attention was paid to "inspection formula # 1", but a tanner graph can be drawn for "inspection formula # 2" to "inspection formula # 6" in the same manner, and in the tanner graph of "inspection formula # K". The reliability is propagated to each node from coefficient nodes other than "inspection formula #K". Therefore, it is considered that the error correction capability is improved because all the reliabilitys having low correlations are propagated to the “inspection formula #K”. (K = 2,3,4,5,6)

In this way, by making each degree of the parity check polynomials of the equations (5-1) to (5-6) satisfy the condition regarding the above-mentioned "remainder", the reliability is efficiently obtained in all the inspection equations. Will be able to propagate, and the possibility that the error correction capability can be further increased will increase.

The LDPC-CC having a time variation period of 6 has been described above by taking the case where the coding rate is 1/2 as an example, but the coding rate is not limited to 1/2. In the case of the coding rate (n-1) / n (n is an integer of 2 or more), the respective information X ₁ (D), X ₂ (D), ... X _n-1 (D) If the above-mentioned "remainder" condition is satisfied in the three coefficient sets, the possibility that good reception quality can be obtained is also increased.

Hereinafter, the case where the coding rate (n-1) / n (n is an integer of 2 or more) will be described.

Consider equations (7-1) to (7-6) as a parity check polynomial of LDPC-CC having a time-varying period of 6.

At this time, X ₁ (D), X ₂ (D), ... X _n-1 (D) are polynomial representations of the data (information) X1, X2, ... Xn-1, and P (D). Is a polynomial representation of parity. Here, in the equations (7-1) to (7-6), _{there are three terms for each of X 1} (D), X ₂ (D), ... X _n-1 (D), and P (D). Let it be a parity check polynomial that exists. Considering the same as when the coding rate is 1/2 and when the time-varying period is 3, the time-varying period 6 represented by the parity check polynomials in Eqs. (7-1) to (7-6), the code. In LDPC-CC with a conversion rate (n-1) / n (n is an integer of 2 or more), if the following conditions (<condition # 1>) are satisfied, there is a possibility that higher error correction capability can be obtained. Increase.

However, in the LDPC-CC having a time variation period of 6 and a coding rate (n-1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , and so on. ..., X _{i, n-1} . At this time, if i% 6 = k (k = 0, 1, 2, 3, 4, 5), the parity check polynomial of the equation (7- (k + 1)) is established. For example, if i = 8, then i% 6 = 2 (k = 2), so that equation (8) holds.

<Condition # 1>
In the formulas (7-1) to (7-6), _{the combination of the orders of X 1} (D), X ₂ (D), ... X _n-1 (D) and P (D) satisfies the following conditions. Fulfill.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, k, 1} % 3, a _{# 1, k, 2} % 3, a _{# 1, k, 3} % 3), ...
(A _{# 1, n-1, 1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, k, 1} % 3, a _{# 2, k, 2} % 3, a _{# 2, k, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, k, 1} % 3, a _{# 3, k, 2} % 3, a _{# 3, k, 3} % 3), ...
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3, a _{# 3, n-1,3} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3, b _{# 3,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)
And,
(A _{# 4,1,1} % 3, a _{# 4,1,2} % 3, a _{# 4,1,3} % 3),
(A _{# 4,2,1} % 3, a _{# 4,2,2} % 3, a _{# 4,2,3} % 3), ...,
(A _{# 4, k, 1} % 3, a _{# 4, k, 2} % 3, a _{# 4, k, 3} % 3), ...
(A _{# 4, n-1,1} % 3, a _{# 4, n-1,2} % 3, a _{# 4, n-1,3} % 3),
(B _{# 4,1} % 3, b _{# 4,2} % 3, b _{# 4,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)
And,
(A _{# 5,1,1} % 3, a _{# 5,1,2} % 3, a _{# 5,1,3} % 3),
(A _{# 5,2,1} % 3, a _{# 5,2,2} % 3, a _{# 5,2,3} % 3), ...
(A _{# 5, k, 1} % 3, a _{# 5, k, 2} % 3, a _{# 5, k, 3} % 3), ...
(A _{# 5, n-1,1} % 3, a _{# 5, n-1,2} % 3, a _{# 5, n-1,3} % 3),
(B _{# 5,1} % 3, b _{# 5,2} % 3, b _{# 5,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)
And,
(A _{# 6,1,1} % 3, a _{# 6,1,2} % 3, a _{# 6,1,3} % 3),
(A _{# 6,2,1} % 3, a _{# 6,2,2} % 3, a _{# 6,2,3} % 3), ...,
(A _{# 6, k, 1} % 3, a _{# 6, k, 2} % 3, a _{# 6, k, 3} % 3), ...
(A _{# 6, n-1,1} % 3, a _{# 6, n-1,2} % 3, a _{# 6, n-1,3} % 3),
(B _{# 6,1} % 3, b _{# 6,2} % 3, b _{# 6,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (K = 1, 2, 3, ..., n-1)

In the above, the code having a high error correction capability in the LDPC-CC having the time-varying period 6 has been described, but the time-varying period 3g (g = 1) is the same as the design method of the LDPC-CC having the time-varying period 3 and 6. When an LDPC-CC (that is, an LDPC-CC having a time variation period that is a multiple of 3) of 2, 3, 4, ...) Is created, a code having a high error correction capability can be generated. The method of constructing the code will be described in detail below.

The equation is used as a parity check polynomial of LDPC-CC with a time-varying period of 3 g (g = 1, 2, 3, 4, ...) And a coding rate (n-1) / n (n is an integer of 2 or more). Consider (9-1) to (9-3 g).

At this time, X ₁ (D), X ₂ (D), ... X _n-1 (D) are polynomial representations of data (information) X ₁ , X ₂ , ... X _{n-1, and P.} (D) is a polynomial representation of parity. Here, in the formulas (9-1) to (9-3g), _{there are three terms for each of X 1} (D), X ₂ (D), ... X _n-1 (D), and P (D). Let it be a parity check polynomial that exists.

Considering the same as LDPC-CC with time-varying period 3 and LDPC-CC with time-varying period 6, time-varying period 3g and coding rate represented by the parity check polynomials of equations (9-1) to (9-3g). In the LDPC-CC of (n-1) / n (n is an integer of 2 or more), if the following conditions (<condition # 2>) are satisfied, the possibility that a higher error correction capability can be obtained increases.

However, in the LDPC-CC having a time variation period of 3 g and a coding rate (n-1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., X _{i, n-1} . At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (9- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (10) holds.

Further, in equations (9-1) to (9-3g), a _{# k, p, 1} , a _{# k, p, 2} , a _{# k, p, 3} are integers (however, a _{# k, p). , 1} ≠ a _{# k, p, 2} ≠ a _{# k, p, 3} ) (k = 1, 2, 3, ..., 3g: p = 1, 2, 3, ..., n- 1). Further, b _{# k, 1} , b _{# k, 2} , b _{# k, and 3} are integers (where b _{# k, 1} ≠ b _{# k, 2} ≠ b _{# k, 3} ). The parity check polynomial (k = 1, 2, 3, ..., 3 g) of the formula (9-k) is called "check formula #k", and the submatrix based on the parity check polynomial of the formula (9-k) is called. , Kth sub-matrix H _k . Then, consider LDPC-CC having a time variation period of 3 g generated from the first sub-matrix H ₁ , the second sub-matrix H ₂ , the third sub-matrix H ₃ , ..., And the third g sub-matrix H _{3 g.}

<Condition # 2>
In the formulas (9-1) to (9-3g), the combination of the orders of X ₁ (D), X ₂ (D), ... X _n-1 (D) and P (D) satisfies the following conditions. Fulfill.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3, a _{# 1, p, 3} % 3), ...
(A _{# 1, n-1, 1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3, a _{# 2, p, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3, a _{# 3, p, 3} % 3), ...
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3, a _{# 3, n-1,3} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3, b _{# 3,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3} % 3), ...
(A _{# k, n-1, 1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3} % 3),
(B _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3) is
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1) (Therefore, k = 1, 2, 3, ..., 3 g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3, a _{# 3g-2,2,3} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3, a _{# 3g-2, p, 3} % 3), ...
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3, a _{# 3g-2, n-1,3} % 3),
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3, b _{# 3g-2,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3, a _{# 3g-1,2,3} % 3), ...
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3, a _{# 3g-1, p, 3} % 3), ...
(A _{# 3g-1, n-1,1} % 3, a _{# 3g-1, n-1,2} % 3, a _{# 3g-1, n-1,3} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3, b _{# 3g-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3, a _{# 3g, 2,3} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3, a _{# 3g, p, 3} % 3), ...
(A _{# 3g, n-1, 1} % 3, a _{# 3g, n-1,2} % 3, a _{# 3g, n-1,3} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3, b _{# 3g, 3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)

However, in consideration of easy coding, in the equations (9-1) to (9-3g),
It is _{preferable that one "0" exists out of the three (b # k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3) (however, k = 1, 2, ... 3g). At this time, if D ⁰ = 1 exists and b _{# k, 1} , b _{# k, 2} , b _{# k, and 3} are integers of 0 or more, the parity P can be sequentially obtained. Because it has.

In addition, in order to make the parity bit and the data bit at the same time related to each other and to easily search for a code having a high correction capability,
There is one "0" out of the three (a _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3% 3).}
There is one "0" out of the three (a _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3% 3).}
・
・
・
There is one "0" out of the three (a _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3% 3).}
・
・
・
It is preferable that one "0" exists out of the three _{(a # k, n-1, 1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3% 3).} (However, k = 1, 2, ... 3 g).

Next, consider an LDPC-CC having a time-varying period of 3 g (g = 2, 3, 4, 5, ...) Considering that coding can be easily performed. At this time, assuming that the coding rate is (n-1) / n (n is an integer of 2 or more), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X ₁ (D), X ₂ (D), ... X _n-1 (D) are polynomial representations of data (information) X ₁ , X ₂ , ... X _{n-1, and P.} (D) is a polynomial representation of parity. Here, in the formulas (11-1) to (11-3g), _{there are three terms for each of X 1} (D), X ₂ (D), ... X _n-1 (D), and P (D). Let it be a parity check polynomial that exists. However, in the LDPC-CC having a time variation period of 3 g and a coding rate (n-1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., X _{i, n-1} . At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (11- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (12) holds.

At this time, if <Condition # 3> and <Condition # 4> are satisfied, the possibility that a code having a higher error correction capability can be created increases.

<Condition # 3>
In the formulas (11-1) to (11-3g), the combination of orders of X1 (D), X2 (D), ... Xn-1 (D) satisfies the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3, a _{# 1,2,3} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3, a _{# 1, p, 3} % 3), ...
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3, a _{# 1, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3, a _{# 2,2,3} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3, a _{# 2, p, 3} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3, a _{# 2, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3, a _{# 3,2,3} % 3), ...
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3, a _{# 3, p, 3} % 3), ...
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3, a _{# 3, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3, a _{# k, 2,3} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3, a _{# k, p, 3} % 3), ...
(A _{# k, n-1, 1} % 3, a _{# k, n-1,2} % 3, a _{# k, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1) (Therefore, k = 1, 2, 3, ..., 3 g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3, a _{# 3g-2,2,3} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3, a _{# 3g-2, p, 3} % 3), ...
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3, a _{# 3g-2, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3, a _{# 3g-1,2,3} % 3), ...
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3, a _{# 3g-1, p, 3} % 3), ...
(A _{# 3g-1, n-1,1} % 3, a _{# 3g-1, n-1,2} % 3, a _{# 3g-1, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3, a _{# 3g, 2,3} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3, a _{# 3g, p, 3} % 3), ...
(A _{# 3g, n-1, 1} % 3, a _{# 3g, n-1,2} % 3, a _{# 3g, n-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (P = 1, 2, 3, ..., n-1)

In addition, in the formulas (11-1) to (11-3g), the combination of orders of P (D) satisfies the following conditions.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3)
It is one of (1, 2) and (2, 1) (k = 1, 2, 3, ..., 3 g).

<Condition # 3> for equations (11-1) to (11-3g) has the same relationship as <condition # 2> for equations (9-1) to (9-3g). By adding the following conditions (<condition # 4>) in addition to <condition # 3> to equations (11-1) to (11-3g), an LDPC-CC having higher error correction capability is created. The chances of being able to do it increase.

<Condition # 4>
The following conditions are satisfied in the order of P (D) of the formulas (11-1) to (11-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
(B _{# 3g, 1} % 3g, b _{# 3g, 2} % 3g) has 6g orders (since the two orders form one set, there are 6g orders that make up the 3g set). Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist.

By the way, in the inspection matrix, if the position where "1" exists has regularity but randomness, there is a high possibility that good error correction capability can be obtained. It has a time-varying period of 3 g (g = 2, 3, 4, 5, ...) With a parity check polynomial of equations (11-1) to (11-3 g), and the coding rate is (n-1) / n (n-1) / n (. In LDPC-CC with (n is an integer of 2 or more), if a code is created by adding the condition of <condition # 4> in addition to <condition # 3>, the position where "1" exists has regularity in the check matrix. However, since it is possible to give randomness, the possibility of obtaining good error correction ability increases.

Next, a time-varying period of 3 g (g = 2, 3, 4, 5, ...) That can be easily coded and has a relation between the parity bit and the data bit at the same time point. Consider LDPC-CC. At this time, assuming that the coding rate is (n-1) / n (n is an integer of 2 or more), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X ₁ (D), X ₂ (D), ... X _n-1 (D) are polynomial representations of data (information) X ₁ , X ₂ , ... X _{n-1, and P.} (D) is a polynomial representation of parity. Then, in the formulas (13-1) to (13-3g), _{there are three terms in each of X 1} (D), X ₂ (D), ... X _n-1 (D), and P (D). The parity check polynomial is such that X ₁ (D), X ₂ (D), ... X _n-1 (D), P (D) have a term ^{of D 0.} (K = 1, 2, 3, ..., 3g)

However, in the LDPC-CC having a time variation period of 3 g and a coding rate (n-1) / n (n is an integer of 2 or more), the parity at time i is Pi and the information is X _{i, 1} , X _{i, 2} , ..., X _{i, n-1} . At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (13- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (14) holds.

At this time, if the following conditions (<condition # 5> and <condition # 6>) are satisfied, there is a high possibility that a code having a higher error correction capability can be created.

<Condition # 5>
In the formulas (13-1) to (13-3g), the combination of the orders of X ₁ (D), X ₂ (D), ... X _n-1 (D) satisfies the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3),
(A _{# 1,2,1} % 3, a _{# 1,2,2} % 3), ...
(A _{# 1, p, 1} % 3, a _{# 1, p, 2} % 3), ...
(A _{# 1, n-1,1} % 3, a _{# 1, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3),
(A _{# 2,2,1} % 3, a _{# 2,2,2} % 3), ...
(A _{# 2, p, 1} % 3, a _{# 2, p, 2} % 3), ...
(A _{# 2, n-1,1} % 3, a _{# 2, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3),
(A _{# 3,2,1} % 3, a _{# 3,2,2} % 3), ...
(A _{# 3, p, 1} % 3, a _{# 3, p, 2} % 3), ...
(A _{# 3, n-1,1} % 3, a _{# 3, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3),
(A _{# k, 2,1} % 3, a _{# k, 2,2} % 3), ...
(A _{# k, p, 1} % 3, a _{# k, p, 2} % 3), ...
(A _{# k, n-1, 1} % 3, a _{# k, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1) (Therefore, k = 1, 2, 3, ..., 3 g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3),
(A _{# 3g-2,2,1} % 3, a _{# 3g-2,2,2} % 3), ...
(A _{# 3g-2, p, 1} % 3, a _{# 3g-2, p, 2} % 3), ...,
(A _{# 3g-2, n-1,1} % 3, a _{# 3g-2, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3),
(A _{# 3g-1,2,1} % 3, a _{# 3g-1,2,2} % 3), ...
(A _{# 3g-1, p, 1} % 3, a _{# 3g-1, p, 2} % 3), ...,
(A _{# 3g-1, n-1, 1} % 3, a _{# 3g-1, n-1,2} % 3) is
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3),
(A _{# 3g, 2,1} % 3, a _{# 3g, 2,2} % 3), ...
(A _{# 3g, p, 1} % 3, a _{# 3g, p, 2} % 3), ...
(A _{# 3g, n-1,1} % 3, a _{# 3g, n-1,2} % 3)
It is either (1, 2) or (2, 1). (P = 1, 2, 3, ..., n-1)

In addition, in the formulas (13-1) to (13-3g), the combination of orders of P (D) satisfies the following conditions.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3)
It is one of (1, 2) and (2, 1) (k = 1, 2, 3, ..., 3 g).

<Condition # 5> for equations (13-1) to (13-3g) has the same relationship as <condition # 2> for equations (9-1) to (9-3g). By adding the following conditions (<condition # 6>) in addition to <condition # 5> to the formulas (13-1) to (13-3g), an LDPC-CC having high error correction capability can be created. The possibility is high.

<Condition # 6>
The following conditions are satisfied in the order of _{X 1} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
The 6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
And,
The following conditions are satisfied in the order of _{X 2} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1,2,1} % 3g, a _{# 1,2,2} % 3g),
(A _{# 2,2,1} % 3g, a _{# 2,2,2} % 3g), ...
(A _{# p, 2,1} % 3g, a _{#p, 2,2} % 3g), ...
The 6g values of (a _{# 3g, 2,1} % 3g, a _{# 3g, 2,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3g)
And,
The following conditions are satisfied in the order of _{X 3} (D) of the formulas (13-1) to (13-3 g).
_{(A # 1,3,1% 3g, a} # 1,3,2% 3g),
_{(A # 2,3,1% 3g, a} # 2,3,2% 3g), ···,
(A _{# p, 3.1} % 3g, a _{# p, 3,2} % 3g), ...
The 6g values of (a _{# 3g, 3.1} % 3g, a _{# 3g, 3,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
And,
・
・
・
And,
The following conditions are satisfied in the order of _{X k} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1, k, 1} % 3g, a _{# 1, k, 2} % 3g),
(A _{# 2, k, 1} % 3g, a _{# 2, k, 2} % 3g), ...
(A _{# p, k, 1} % 3g, a _{# p, k, 2} % 3g), ...
The 6g values of (a _{# 3g, k, 1} % 3g, a _{# 3g, k, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
(K = 1, 2, 3, ..., n-1)
And,
・
・
・
And,
The following conditions are satisfied in the order of _{X n-1} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1, n-1,1} % 3g, a _{# 1, n-1,2} % 3g),
(A _{# 2, n-1,1} % 3g, a _{# 2, n-1,2} % 3g), ...
(A _{# p, n-1, 1} % 3g, a _{# p, n-1,2} % 3g), ...
The 6g values of (a _{# 3g, n-1, 1} % 3g, a _{# 3g, n-1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
And,
The following conditions are satisfied in the order of P (D) of the formulas (13-1) to (13-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
The 6g values of (b _{# 3g, 1} % 3g, b _{# 3g, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

By the way, in the inspection matrix, if the position where "1" exists has regularity but randomness, there is a high possibility that good error correction capability can be obtained. It has a time-varying period of 3 g (g = 2, 3, 4, 5, ...) With a parity check polynomial of equations (13-1) to (13-3 g), and the coding rate is (n-1) / n (n-1) / n (. In LDPC-CC in which n is an integer of 2 or more), when a code is created by adding the condition of <condition # 6> in addition to <condition # 5>, regularity occurs at the position where "1" exists in the check matrix. Since it is possible to give randomness while having the above, there is a high possibility that better error correction ability can be obtained.

Further, even if <condition # 6'> is used instead of <condition # 6>, that is, <condition # 6'> is added in addition to <condition # 5> to create a code, higher error correction is performed. There is a high possibility that an LDPC-CC with the ability can be created.

<Condition # 6'>
The following conditions are satisfied in the order of _{X 1} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
The 6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
Or
The following conditions are satisfied in the order of _{X 2} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1,2,1} % 3g, a _{# 1,2,2} % 3g),
(A _{# 2,2,1} % 3g, a _{# 2,2,2} % 3g), ...
(A _{# p, 2,1} % 3g, a _{#p, 2,2} % 3g), ...
The 6g values of (a _{# 3g, 2,1} % 3g, a _{# 3g, 2,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
Or
The following conditions are satisfied in the order of _{X 3} (D) of the formulas (13-1) to (13-3 g).
_{(A # 1,3,1% 3g, a} # 1,3,2% 3g),
_{(A # 2,3,1% 3g, a} # 2,3,2% 3g), ···,
(A _{# p, 3.1} % 3g, a _{# p, 3,2} % 3g), ...
The 6g values of (a _{# 3g, 3.1} % 3g, a _{# 3g, 3,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
Or
・
・
・
Or
The following conditions are satisfied in the order of _{X k} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1, k, 1} % 3g, a _{# 1, k, 2} % 3g),
(A _{# 2, k, 1} % 3g, a _{# 2, k, 2} % 3g), ...
(A _{# p, k, 1} % 3g, a _{# p, k, 2} % 3g), ...
The 6g values of (a _{# 3g, k, 1} % 3g, a _{# 3g, k, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
(K = 1, 2, 3, ..., n-1)
Or
・
・
・
Or
The following conditions are satisfied in the order of _{X n-1} (D) of the formulas (13-1) to (13-3 g).
(A _{# 1, n-1,1} % 3g, a _{# 1, n-1,2} % 3g),
(A _{# 2, n-1,1} % 3g, a _{# 2, n-1,2} % 3g), ...
(A _{# p, n-1, 1} % 3g, a _{# p, n-1,2} % 3g), ...
The 6g values of (a _{# 3g, n-1, 1} % 3g, a _{# 3g, n-1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
Or
The following conditions are satisfied in the order of P (D) of the formulas (13-1) to (13-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
The 6g values of (b _{# 3g, 1} % 3g, b _{# 3g, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

The LDPC-CC having a time-varying period of 3 g and a coding rate (n-1) / n (n is an integer of 2 or more) has been described above. Hereinafter, the conditions of the degree of the parity check polynomial of the LDPC-CC having a time variation period of 3 g and a coding rate of 1/2 (n = 2) will be described.

Equations (15-1) to (15-1) as a parity check polynomial of LDPC-CC having a time-varying period of 3 g (g = 1, 2, 3, 4, ...) And a coding rate of 1/2 (n = 2). 15-3g) is considered.

At this time, X (D) is a polynomial representation of the data (information) X, and P (D) is a polynomial representation of the parity. Here, in the equations (15-1) to (15-3g), it is assumed that the parity check polynomial has three terms in each of X (D) and P (D).

Considering the same as LDPC-CC with time-varying period 3 and LDPC-CC with time-varying period 6, time-varying period 3g and coding rate represented by the parity check polynomials of equations (15-1) to (15-3g). In the LDPC-CC of 1/2 (n = 2), if the following conditions (<condition # 2-1>) are satisfied, the possibility that a higher error correction capability can be obtained increases.

However, in the LDPC-CC having a time variation period of 3 g and a coding rate of 1/2 (n = 2), the parity at time i is represented _{by Pi and the information is represented by X i and 1.} At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (15- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (16) holds.

Further, in equations (15-1) to (15-3g), a _{# k, 1,1} , a _{# k, 1} , 2, a _{# k, 1,3} are integers (however, a _{# k, 1). , 1} ≠ a _{# k, 1, 2,} ≠ a _{# k, 1, 3} ) (k = 1, 2, 3, ..., 3 g). Further, b _{# k, 1} , b _{# k, 2} , b _{# k, and 3} are integers (where b _{# k, 1} ≠ b _{# k, 2} ≠ b _{# k, 3} ). The parity check polynomial (k = 1, 2, 3, ..., 3 g) of the formula (15-k) is called "check formula #k", and the submatrix based on the parity check polynomial of the formula (15-k) is called. , Kth sub-matrix H _k . Then, consider LDPC-CC having a time variation period of 3 g generated from the first sub-matrix H ₁ , the second sub-matrix H ₂ , the third sub-matrix H ₃ , ..., And the third g sub-matrix H _{3 g.}

<Condition # 2-1>
In formulas (15-1) to (15-3g), the combination of orders of X (D) and P (D) satisfies the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3),
(B _{# 1,1} % 3, b _{# 1,2} % 3, b _{# 1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3, b _{# 2,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3, a # 3,1,3% 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3, b _{# 3,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3),
(B _{# k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3) is
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become. (Therefore, k = 1, 2, 3, ..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3),
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3, b _{# 3g-2,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3, b _{# 3g-1,3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3, b _{# 3g, 3} % 3)
With any of (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0) Become.

However, in consideration of easy coding, in the equations (15-1) to (15-3g),
It is _{preferable that one "0" exists out of the three (b # k, 1} % 3, b _{# k, 2} % 3, b _{# k, 3} % 3) (however, k = 1, 2, ... 3g). At this time, if D ⁰ = 1 exists and b _{# k, 1} , b _{# k, 2} , b _{# k, and 3} are integers of 0 or more, the parity P can be sequentially obtained. Because it has.

Further, in order to make the parity bit and the data bit at the same time related to each other and to easily search for a code having a high correction capability, (a _{# k, 1,1} % 3, a _{# k, 1, It is} preferable that one "0" is present out of the three (2% 3, a _{# k, 1,3} % 3) (however, k = 1, 2, ... 3 g).

Next, consider an LDPC-CC having a time-varying period of 3 g (g = 2, 3, 4, 5, ...) Considering that coding can be easily performed. At this time, assuming that the coding rate is 1/2 (n = 2), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X (D) is a polynomial representation of the data (information) X, and P (D) is a polynomial representation of the parity. Here, in the equations (17-1) to (17-3g), it is assumed that the parity check polynomial has three terms in each of X and P (D). However, in the LDPC-CC having a time variation period of 3 g and a coding rate of 1/2 (n = 2), the parity at time i is represented _{by Pi and the information is represented by X i and 1.} At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (17- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (18) holds.

At this time, if <Condition # 3-1> and <Condition # 4-1> are satisfied, the possibility that a code having a higher error correction capability can be created increases.

<Condition # 3-1>
In formulas (17-1) to (17-3g), the combination of orders of X (D) satisfies the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3, a _{# 1,1,3} % 3) are (0,1,2), (0,2,1), ( It is one of 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3, a # 2,1,3% 3) is (0,1,2), (0,2,1), ( It is one of 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3,1,1} % 3, a # 3,1,2% 3, a _{# 3,1,3} % 3) are (0,1,2), (0,2,1), ( It is one of 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3, a _{# k, 1,3} % 3) is (0, 1, 2), (0, 2, 1), ( It is one of 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0). (Therefore, k = 1, 2, 3, ..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3, a # 3g-2,1,3% 3) is (0,1,2), (0, It is one of 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3, a _{# 3g-1,1,3} % 3) is (0,1,2), (0, It is one of 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3, a _{# 3g, 1,3} % 3) is (0, 1, 2), (0, 2, 1), ( It is one of 1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0).

In addition, in the formulas (17-1) to (17-3g), the combination of orders of P (D) satisfies the following conditions.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3)
It is one of (1, 2) and (2, 1) (k = 1, 2, 3, ..., 3 g).

The <condition # 3-1> for the formulas (17-1) to (17-3g) has the same relationship as the <condition # 2-1> for the formulas (15-1) to (15-3g). LDPC with higher error correction capability by adding the following conditions (<condition # 4-1>) in addition to <condition # 3-1> to equations (17-1) to (17-3g). -It is more likely that you can create a CC.

<Condition # 4-1>
The following conditions are satisfied in the order of P (D) of the formulas (17-1) to (17-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
The 6g values of (b _{# 3g, 1} % 3g, b _{# 3g, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist.

By the way, in the inspection matrix, if the position where "1" exists has regularity but randomness, there is a high possibility that good error correction capability can be obtained. With a time-varying period of 3 g (g = 2, 3, 4, 5, ...) With a parity check polynomial of equations (17-1) to (17-3 g), a coding rate of 1/2 (n = 2). In LDPC-CC, if a code is created by adding the condition of <condition # 4-1> in addition to <condition # 3-1>, the position where "1" exists in the check matrix has regularity but randomness. Therefore, there is a high possibility that a better error correction ability can be obtained.

Next, a time-varying period of 3 g (g = 2, 3, 4, 5, ...) That can be easily coded and has a relation between the parity bit and the data bit at the same time point. Consider LDPC-CC. At this time, assuming that the coding rate is 1/2 (n = 2), the parity check polynomial of LDPC-CC can be expressed as follows.

At this time, X (D) is a polynomial representation of the data (information) X, and P (D) is a polynomial representation of the parity. Then, in the equations (19-1) to (19-3g), a parity check polynomial in which three terms exist in each of X (D) and P (D) is used, and X (D) and P (D) are set. Will have a term of D ^0. (K = 1, 2, 3, ..., 3g)

However, in the LDPC-CC having a time variation period of 3 g and a coding rate of 1/2 (n = 2), the parity at time i is represented _{by Pi and the information is represented by X i and 1.} At this time, if i% 3g = k (k = 0, 1, 2, ..., 3g-1), the parity check polynomial of the equation (19- (k + 1)) is established. For example, if i = 2, then i% 3g = 2 (k = 2), so that equation (20) holds.

At this time, if the following conditions (<Condition # 5-1> and <Condition # 6-1>) are satisfied, the possibility that a code having a higher error correction capability can be created increases.

<Condition # 5-1>
In the formulas (19-1) to (19-3g), the combination of orders of X (D) satisfies the following conditions.
(A _{# 1,1,1} % 3, a _{# 1,1,2} % 3) is one of (1,2) and (2,1).
And,
_{(A # 2,1,1% 3, a} # 2,1,2% 3) is a one of the (1,2), (2,1).
And,
_{(A # 3,1,1% 3, a} # 3,1,2% 3) is a one of the (1,2), (2,1).
And,
・
・
・
And,
(A _{# k, 1,1} % 3, a _{# k, 1,2} % 3) is one of (1, 2) and (2, 1). (Therefore, k = 1, 2, 3, ..., 3g)
And,
・
・
・
And,
_{(A # 3g-2,1,1% 3} , a # 3g-2,1,2% 3) is a one of the (1,2), (2,1).
And,
(A _{# 3g-1,1,1} % 3, a _{# 3g-1,1,2} % 3) is one of (1, 2) and (2, 1).
And,
(A _{# 3g, 1,1} % 3, a _{# 3g, 1,2} % 3) is one of (1, 2) and (2, 1).

In addition, in the formulas (19-1) to (19-3g), the combination of orders of P (D) satisfies the following conditions.
(B _{# 1,1} % 3, b _{# 1,2} % 3),
(B _{# 2,1} % 3, b _{# 2,2} % 3),
(B _{# 3,1} % 3, b _{# 3,2} % 3), ...
(B _{# k, 1} % 3, b _{# k, 2} % 3), ...
(B _{# 3g-2,1} % 3, b _{# 3g-2,2} % 3),
(B _{# 3g-1,1} % 3, b _{# 3g-1,2} % 3),
(B _{# 3g, 1} % 3, b _{# 3g, 2} % 3)
It is one of (1, 2) and (2, 1) (k = 1, 2, 3, ..., 3 g).

The <condition # 5-1> for the formulas (19-1) to (19-3g) has the same relationship as the <condition # 2-1> for the formulas (15-1) to (15-3g). LDPC with higher error correction capability by adding the following conditions (<condition # 6-1>) in addition to <condition # 5-1> to equations (19-1) to (19-3g). -It is more likely that you can create a CC.

<Condition # 6-1>
The following conditions are satisfied in the order of X (D) of the formulas (19-1) to (19-3 g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
The 6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
And,
The following conditions are satisfied in the order of P (D) of the formulas (19-1) to (19-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
6g (3g x 2) values of (b _{# 3g, 1} % 3g, b _{# 3g, 2% 3g)}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

By the way, in the inspection matrix, if the position where "1" exists has regularity but randomness, there is a high possibility that good error correction capability can be obtained. In LDPC-CC having a time-varying period of 3 g (g = 2, 3, 4, 5, ...) With a parity check polynomial of equations (19-1) to (19-3 g) and a coding rate of 1/2, When the code is created by adding the condition of <Condition # 6-1> in addition to <Condition # 5-1>, randomness is given to the position where "1" exists in the check matrix while having regularity. Therefore, it is more likely that better error correction capability can be obtained.

Further, <condition # 6'-1> is used instead of <condition # 6-1>, that is, <condition # 6'-1> is added in addition to <condition # 5-1> to create a code. Even so, the possibility of creating an LDPC-CC with higher error correction capability increases.

<Condition # 6'-1>
The following conditions are satisfied in the order of X (D) of the formulas (19-1) to (19-3 g).
(A _{# 1,1,1} % 3g, a _{# 1,1,2} % 3g),
_{(A # 2,1,1% 3g, a} # 2,1,2% 3g), ···,
(A _{# p, 1,1} % 3g, a _{# p, 1,2} % 3g), ...
The 6g values of (a _{# 3g, 1,1} % 3g, a _{# 3g, 1,2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (P = 1, 2, 3, ..., 3 g)
Or
The following conditions are satisfied in the order of P (D) of the formulas (19-1) to (19-3 g).
(B _{# 1,1} % 3g, b _{# 1,2} % 3g),
(B _{# 2,1} % 3g, b _{# 2,2} % 3g),
(B _{# 3,1} % 3g, b _{# 3,2} % 3g), ...
(B _{# k, 1} % 3g, b _{# k, 2} % 3g), ...
(B _{# 3g-2,1} % 3g, b _{# 3g-2,2} % 3g),
(B _{# 3g-1,1} % 3g, b _{# 3g-1,2} % 3g),
The 6g values of (b _{# 3g, 1} % 3g, b _{# 3g, 2% 3g) include}
Of the integers from 0 to 3g-1 (0, 1, 2, 3, 4, ..., 3g-2, 3g-1), multiples of 3 (that is, 0, 3, 6, ..., 3g) All values other than -3) exist. (K = 1, 2, 3, ..., 3g)

As an example, Table 4 lists LDPC-CCs having a coding rate of 1/2 and a time variation period of 6 having good error correction capability.

The LDPC-CC having a time-varying period g having good characteristics has been described above. The LDPC-CC can obtain coded data (codewords) by multiplying the information vector n by the generator matrix G. That is, the coded data (codeword) c can be represented as c = n × G. Here, the generator matrix G is obtained corresponding to the pre-designed inspection matrix H. Specifically, the generator matrix G is a matrix satisfying G × H ^{T =} 0.

ここで、Ｄは、遅延演算子である。 For example, consider a convolutional code having a coding rate of 1/2 and a generation polynomial G = [1 G ₁ (D) / G _{0 (D)].} At this time, G ₁ represents a feedforward polynomial and G ₀ represents a feedback polynomial. Assuming that the polynomial representation of the information series (data) is X (D) and the polynomial representation of the parity series is P (D), the parity check polynomial is represented by the following equation (21).

Here, D is a delay operator.

FIG. 5 shows information regarding the convolutional code of (7, 5). (7, 5) The convolutional code generation matrix is expressed as G = [1 (D ² + 1) / (D ² + D + 1)]. Therefore, the parity check polynomial is given by the following equation (22).

Here, represents a data at the time point i _{X i,} parity and _{P i,} indicating transmission sequence _{W i = (X i, P} i) and. Then, the transmission vector w = (X ₁ , P ₁ , X ₂ , P ₂ , ..., X _i , _Pi ...) ^T. Then, from the equation (22), the inspection matrix H can be represented as shown in FIG. At this time, the relational expression of the following expression (23) is established.

Therefore, on the decoding side, the inspection matrix H is used to perform BP (Belief Propagation) (reliability propagation) decoding as shown in Non-Patent Documents 5 to 7, and min-sum decoding that approximates BP decoding. Decoding using reliability propagation such as offset BP decoding, Normalized BP decoding, and shuffled BP decoding can be performed.

(Time-invariant / time-variable LDPC-CC based on convolutional code (coding rate (n-1) / n) (n: natural number))
The outline of the time-invariant / time-variable LDPC-CC based on the convolutional code will be described below.

Information of coding rate R = (n-1) / n X ₁ , X ₂ , ..., X _n-1 polynomial representations of X ₁ (D), X ₂ (D), ..., X _{n Let} P (D) be the polynomial representation of parity P, and consider a parity check polynomial expressed as in Eq. (24).

In equation (24), at this time, _{ap, p} (p = 1,2, ···, n-1; q = 1,2, ···, rp) is, for example, a natural number, and _ap, Satisfy ₁ ≠ a _{p, 2} ≠ ... ≠ a _{p, rp.} Further, b _q (q = 1, 2, ..., S) is a natural number and satisfies _{b 1} ≠ b ₂ ≠ ... ≠ b _s. At this time, the code defined by the check matrix based on the parity check polynomial of the equation (24) is referred to as a time-invariant LDPC-CC here.

ここで、ｉ＝０，１，・・・，ｍ−１である。 Prepare m different parity check polynomials based on the equation (24) (m is an integer of 2 or more). The parity check polynomial is expressed as follows.

Here, i = 0, 1, ..., M-1.

ここで、「ｊ ｍｏｄ ｍ」は、ｊをｍで除算した余りである。 Then, the information X ₁ , X ₂ , ..., X _n-1 at _{the time point j is represented as X 1, j} , X _{2, j} , ..., X _{n-1, j,} and the parity P at the time point j is expressed. It is expressed as Pj, and u _j = (X _{1, j} , X _{2, j} , ..., X _{n-1, j} , Pj) ^T. At this time, the information X _{1, j} , X _{2, j} , ..., X _{n-1, j} and the parity P _j at the time point j satisfy the parity check polynomial of the equation (26).

Here, "j mod m" is the remainder obtained by dividing j by m.

The code defined by the check matrix based on the parity check polynomial of the equation (26) is referred to as a time-varying LDPC-CC here. At this time, the time-invariant LDPC-CC defined by the parity check polynomial of the equation (24) and the time-variable LDPC-CC defined by the parity check polynomial of the equation (26) sequentially register and exclusive the parity. It has the characteristic that it can be easily obtained by exclusive-or-logic sum.

For example, FIG. 6 shows the configuration of the inspection matrix H of the LDPC-CC having the time variation period 2 based on the equations (24) to (26) with a coding rate of 2/3. Two inspection polynomials with different time variation periods 2 based on equation (26) are named "inspection equation # 1" and "inspection equation # 2". In FIG. 6, (Ha, 111) is a part corresponding to “inspection formula # 1”, and (Hc, 111) is a part corresponding to “inspection formula # 2”. Hereinafter, (Ha, 111) and (Hc, 111) are defined as sub-matrix.

In this way, the check matrix H of the LDPC-CC having the time variation period 2 of the present proposal is the first sub-matrix representing the parity check polynomial of "check formula # 1" and the parity check polynomial of "check formula # 2". It can be defined by the second sub-matrix represented. Specifically, in the inspection matrix H, the first sub-matrix and the second sub-matrix are arranged alternately in the row direction. When the coding rate is 2/3, as shown in FIG. 6, the sub-matrix is shifted to the right by 3 columns in the i-th row and the i + 1-th row.

Further, in the case of the time-varying LDPC-CC having the time-varying period 2, the sub-matrix in the i-th row and the sub-matrix in the i + 1-th row are different sub-matrix. That is, either one of the sub-matrix (Ha, 11) or (Hc, 11) becomes the first sub-matrix, and the other becomes the second sub-matrix. The transmission vector u is u = (X _1,0 , X _2,0 , P ₀ , X ₁ , 1, X ₂ , 1, P ₁ , ..., X _{1, k} , X _{2, k} , P _k. , ...) If ^T , Hu = 0 holds (see equation (23)).

Next, consider LDPC-CC in which the time variation period is m when the coding rate is 2/3. As in the case of the time-varying period 2, m parity check polynomials represented by the equation (24) are prepared. Then, the "inspection formula # 1" represented by the formula (24) is prepared. Similarly, "inspection formula # 2" to "inspection formula # m" represented by the formula (24) are prepared. _{The data X and the parity P at the time point mi + 1 are represented as X mi + 1} and P mi + 1, respectively, and the data X and the parity P at the time point mi + 2 are represented as X _{mi + 2} and P _{mi + 2, respectively. Are expressed as X mi + m} and P _{mi + m} , respectively (i: integer).

At this time, the parity P _{mi + 1} at the time point mi + 1 is obtained by using "inspection formula # 1", the parity P _{mi + 2} at the time point mi + 2 is obtained by using "inspection formula # 2", and ..., the parity P _{mi + m} at the time point mi + m is obtained. Consider LDPC-CC obtained using "inspection formula #m". Such an LDPC-CC code is
-The encoder can be easily configured and the parity can be obtained sequentially.-It has the advantages of reducing the end bits and improving the reception quality at the time of puncture at the end.

FIG. 7 shows the configuration of the LDPC-CC inspection matrix having the above-mentioned coding rate of 2/3 and the time variation period m. In FIG. 7, (H ₁ , 111) is a part corresponding to “inspection formula # 1”, (H ₂ , 111) is a part corresponding to “inspection formula # 2”, ..., (H). _m , 111) is a part corresponding to "inspection formula #m". Hereinafter, (H ₁ , 111) is defined as the first sub-matrix, (H ₂ , 111) is defined as the second sub-matrix, ..., (H _m , 111) is defined as the m-th sub-matrix. do.

As described above, the inspection matrix H of the LDPC-CC having the time variation period m of the present proposal represents the first sub-matrix representing the parity check polynomial of "check formula # 1" and the parity check polynomial of "check formula # 2". It can be defined by the second sub-matrix, ..., And the m-th sub-matrix representing the parity check polynomial of "check formula #m". Specifically, in the inspection matrix H, the first sub-matrix to the m-th sub-matrix are periodically arranged in the row direction (see FIG. 7). When the coding rate is 2/3, the sub-matrix is shifted to the right by 3 columns in the i-th row and the i + 1-th row (see FIG. 7).

The transmission vector u is u = (X _1,0 , X _2,0 , P ₀ , X ₁ , 1, X ₂ , 1, P ₁ , ..., X _{1, k} , X _{2, k} , P _k. , ...) If ^T , Hu = 0 holds (see equation (23)).

In the above description, as an example of the time-invariant / time-variable LDPC-CC based on the convolutional code of the code rate (n-1) / n, the case of the code rate 2/3 has been described as an example. Therefore, it is possible to create a parity check matrix of the time-invariant / time-variable LDPC-CC based on the convolutional code of the code rate (n-1) / n.

That is, in the case of a coding rate of 2/3, in FIG. 7, (H ₁ , 111) is a part (first sub-matrix) corresponding to “inspection formula # 1”, and (H ₂ , 111) is “inspection”. The part corresponding to "Equation # 2" (second sub-matrix), ..., (H _m , 111) is the part corresponding to "Inspection formula # m" (m-th sub-matrix). When the coding rate is (n-1) / n, it is as shown in FIG. In other words, the portion corresponding to "check equation # 1" (the first sub-matrix) _is, (H 1, 11 · · · 1) is represented by "check equation #k" (k = 2,3, · · · , M _{) is represented by (H k} , 11 ... 1). At this time, in the k-th sub-matrix, the number of "1" s except for _{H k is n-1.} Then, in the inspection matrix H, the sub-matrix is shifted to the right by n-1 columns in the i-th row and the i + 1-th row (see FIG. 8).

The transmission vector u is set to u = (X _1,0 , X _2,0 , ..., X _n-1,0 , P ₀ , X _1,1 , X ₂ , 1, ..., X _{n-1. , 1} , P ₁ , ..., X _{1, k} , X _{2, k} , ..., X _{n-1, k} , P _k , ...) If ^T , Hu = 0 holds (Hu = 0). See equation (23)).

Note that FIG. 9 shows, as an example, a configuration example of the LDPC-CC encoder when the coding rate R = 1/2. As shown in FIG. 9, the LDPC-CC encoder 100 mainly includes a data calculation unit 110, a parity calculation unit 120, a weight control unit 130, and a mod2 addition (exclusive OR calculation) device 140.

The data calculation unit 110 includes shift registers 111-1 to 111-M and weight multipliers 112-0-1112-M.

The parity calculation unit 120 includes shift registers 121-1 to 121-M and weight multipliers 122-0 to 122-M.

Shift register 111-1 to 111-M and 121-1 to 121-M, respectively _{v 1, t-i, v} 2, t-i (i = 0, ..., M) is a register holding the next At the timing when the input of is input, the held value is output to the shift register on the right side, and the value output from the shift register on the left side is newly held. The initial state of the shift register is all 0.

The weight multipliers 112-0 to 112-M and 122-0 to 122-M set the values of _{h 1} ^(m) and h ₂ ^{(m) to 0/1 according to the control signal output from the weight control unit 130.} Switch to.

_{The weight control unit 130 outputs the values of h 1} ^(m) and h ₂ ^(m) at that timing based on the inspection matrix held internally, and the weight multipliers 112-0 to 112-M, 122-0. Supply toward ~ 122-M.

mod2 adder 140, weight multipliers 112-0~112-M, by adding all the calculated results of the mod2 to the output of 122-0~122-M, and calculates the _{p i.}

By adopting such a configuration, the LDPC-CC encoder 100 can encode the LDPC-CC according to the inspection matrix.

When the arrangement of each row of the inspection matrix held by the weight control unit 130 is different for each row, the LDPC-CC encoder 100 becomes a time varying convolutional encoder. Further, in the case of LDPC-CC having a coding rate (q-1) / q, (q-1) data calculation units 110 are provided, and the mod2 adder 140 adds mod2 to the output of each weight multiplier (). The configuration may be such that the exclusive OR operation) is performed.

(Embodiment 2)
Next, in the present embodiment, a method of searching for an LDPC-CC capable of dealing with a plurality of coding rates on a low calculation scale in a encoder / decoder will be described. By using the LDPC-CC searched by the method described below, the decoder can realize high data reception quality.

The LDPC-CC search method in the present embodiment is, for example, based on the LDPC-CC having a coding rate of 1/2 among the LDPC-CCs having good characteristics as described above, and has a coding rate of 2/3. The LDPC-CCs of 3/4, 4/5, ..., (Q-1) / q are sequentially searched. As a result, in the coding and decoding processing, by preparing a encoder and a decoder when the coding rate is the highest (q-1) / q, the coding rate is the highest (q-1). ) / Q, It is possible to encode and decode the coding rate (s-1) / s (s = 2, 3, ..., Q-1).

In the following, as an example, LDPC-CC having a time variation period of 3 will be described. As mentioned above, the LDPC-CC having a time variation period of 3 has a very good error correction capability.

(Search method for LDPC-CC)
(1) Code rate 1/2
First, LDPC-CC having a coding rate of 1/2 is selected as the basic LDPC-CC. As the basic LDPC-CC having a coding rate of 1/2, the LDPC-CC having good characteristics as described above is selected.

Hereinafter, a case where the parity check polynomials represented by the equations (27-1) to (27-3) are selected as the parity check polynomial of the LDPC-CC having a coding rate of 1/2 as the basis will be described. (In the examples of equations (27-1) to (27-3), the LDPC-CC having a time variation period of 3 is 3 because it is expressed in the same format as the above-mentioned (LDPC-CC having good characteristics). It can be defined by one parity check polynomial.)

As shown in Table 3, Equations (27-1) to (27-3) are examples of LDPC-CC parity check polynomials having a time-varying period of 3 and a coding rate of 1/2 with good characteristics. .. Then, as described above (LDPC-CC having good characteristics), the information X ₁ at _{the time point j is represented as X 1, j} , the parity P at the time point j is represented as Pj, and u _j = (X _{1). , J} , Pj) Let ^T be. At this time, the information X _{1, j} and the parity P _j at the time point j are
"When j mod 3 = 0, the parity check polynomial of Eq. (27-1) is satisfied."
"When j mod 3 = 1, the parity check polynomial in Eq. (27-2) is satisfied."
"When j mod 3 = 2, the parity check polynomial in Eq. (27-3) is satisfied."
At this time, the relationship between the parity check polynomial and the check matrix is the same as the case described above (LDPC-CC having good characteristics).

(2) Code rate 2/3
Next, a parity check polynomial of LDPC-CC having a coding rate of 2/3 is created based on a parity check polynomial having a coding rate of 1/2 having good characteristics. Specifically, the LDPC-CC parity check polynomial having a coding rate of 2/3 includes the basic parity checking polynomial with a coding rate of 1/2.

For LDPC-CC with a base coding rate of 1/2, the parity check polynomial of LDPC-CC with a coding rate of 2/3 when equations (27-1) to (27-3) are used is given by equation (28-). It can be expressed as 1) to equation (28-3).

The parity check polynomials shown in Eqs. (28-1) to (28-3) have a configuration in which the terms of _{X 2 (D) are added to Eqs. (27-1) to (27-3), respectively.} .. The LDPC-CC parity check polynomial having a code rate of 2/3 using the equations (28-1) to (28-3) is the basis of the parity check polynomial having a code rate of 3/4, which will be described later.

In the formulas (28-1) to (28-3), _{the respective orders of X 2} (D), (α1, β1), (α2, β2), and (α3, β3) are the above-mentioned conditions (<. When the conditions # 1> to <condition # 6> and the like are set to be satisfied, LDPC-CC having good characteristics can be obtained even when the coding rate is 2/3.

Then, as described above (LDPC-CC having good characteristics), the information X _{1 and} X ₂ at _{the time point j are represented as X 1, j and} X _{2, j,} and the parity P at the time point j is referred to as Pj. Representation, u _j = (X _{1, j} , X _{2, j} , Pj) ^T. At this time, the information X _{1, j,} X _{2, j} and the parity P _j at the time point j are
"When j mod 3 = 0, the parity check polynomial of Eq. (28-1) is satisfied."
"When j mod 3 = 1, the parity check polynomial of Eq. (28-2) is satisfied."
"When j mod 3 = 2, the parity check polynomial of Eq. (28-3) is satisfied."
At this time, the relationship between the parity check polynomial and the check matrix is the same as the case described above (LDPC-CC having good characteristics).

(3) Code rate 3/4
Next, a parity check polynomial of LDPC-CC having a code rate of 3/4 is created based on the above-mentioned parity check polynomial having a code rate of 2/3. Specifically, the parity check polynomial of the LDPC-CC having a code rate of 3/4 includes the parity check polynomial having the base code rate of 2/3.

When equations (28-1) to (28-3) are used for the base LDPC-CC with a coding rate of 2/3, the parity check polynomial of the LDPC-CC with a coding rate of 3/4 is given by equation (29-). 1)-Equation (29-3).

A parity check polynomial represented by formula (29-1) to (29-3), the formula (28-1) to Formula (28-3), a configuration obtained by adding the term of _X 3 (D), respectively .. In equations (29-1) to (29-3), the _{orders of X 3} (D), (γ1, δ1,), (γ2, δ2), and (γ3, δ3) are LDPCs having good characteristics. By setting so as to satisfy the conditions of the order of −CC (<condition # 1> to <condition # 6>, etc.), LDPC-CC having good characteristics can be obtained even when the coding rate is 3/4. ..

Then, as described in the above (LDPC-CC with good characteristics), represent information _{X 1, X} 2, _{X 3} at the time point _{j X 1, j, X 2} , j, and _{X 3, j,} The parity P at the time point j is represented as Pj, and u _j = (X _{1, j} , X _{2, j} , X _{3, j} , Pj) ^T. At this time, the information X _{1, j,} X _{2, j,} X _{3, j} and the parity P _j at the time point j are
"When j mod 3 = 0, the parity check polynomial of Eq. (29-1) is satisfied."
"When j mod 3 = 1, the parity check polynomial of Eq. (29-2) is satisfied."
"When j mod 3 = 2, the parity check polynomial of Eq. (29-3) is satisfied."
At this time, the relationship between the parity check polynomial and the check matrix is the same as the case described above (LDPC-CC having good characteristics).

Equations (30-1) to (30- (q-1)) show general equations of the parity check polynomial of the LDPC-CC having the time variation period g when the search is performed as described above.

However, since the formula (30-1) is expressed by a general formula, it is expressed like the formula (30-1), but as described above (LDPC-CC having good characteristics). In fact, since the time-varying period is g, the equation (30-1) is expressed by g parity check polynomials. (As described in the present embodiment, for example, in the case of the time-varying period 3, it is represented by three parity check polynomials as in Eqs. (27-1) to (27-3).) Similar to the equation (30-1), each of the equations (30-2) to (30- (q-1)) is expressed by g parity check polynomials because the time variation period is g.

Here, the g parity check polynomials of the equation (30-1) are expressed in the equations (30-1-0), equations (30-1-1), equations (30-1-2), ..., Equations (30-1). It will be expressed as 30-1- (g-2)) and the formula (30-1- (g-1)).

Similarly, equation (30-w) is represented by g parity check polynomials (w = 2, 3, ..., Q-1). Here, the g parity check polynomials of the equation (30-w) are the equations (30-w-0), the equations (30-w-1), the equations (30-w-2), ..., The equations (30-w-1), ... It will be expressed as 30-w- (g-2)) and the formula (30-w- (g-1)).

In equations (30-1) to (30- (q-1)), X _{1, i} , X _{2, i} , ..., X _{q-1, i are information X 1} , at time point i. X _2, ···, shows a _{X q-1, P i} denotes a parity P at point in time i. Further, A _{Xr, k} (D) is the time i of the coding rate (r-1) / r (r = 2,3, ..., Q (q is a natural number of 3 or more)), and k = i mod g. It is a term _{of X r} (D) in the parity check polynomial of k obtained as. Further, B _k (D) is a term of P (D) in the parity check polynomial of k obtained by setting the time i at the coding rate (r-1) / r and k = i mod g. Further, "i mod g" is the remainder obtained by dividing i by g.

That is, equation (30-1) is a parity check polynomial of LDPC-CC having a time variation period g corresponding to a coding rate of 1/2, and equation (30-2) corresponds to a coding rate of 2/3. It is a parity check polynomial of the LDPC-CC of the time-varying period g, and ..., Equation (30- (q-1)) is the LDPC- of the time-varying period g corresponding to the coding rate (q-1) / q. It is a parity check polynomial of CC.

In this way, based on the equation (30-1) which is the parity check polynomial of the LDPC-CC having a good coding rate of 1/2, the parity check polynomial of the LDPC-CC having a coding rate of 2/3 (30-1). 30-2) is generated.

Further, a parity check polynomial (30-3) of LDPC-CC having a code rate of 3/4 is generated based on the parity check polynomial (30-2) of LDPC-CC having a code rate of 2/3. Hereinafter, in the same manner, a parity check polynomial of the LDPC-CC having the coding rate r / (r + 1) is generated based on the LDPC-CC having the coding rate (r-1) / r. (R = 2, 3, ..., q-2, q-1)

Another expression is given about the above-mentioned construction method of the parity check polynomial. Consider an LDPC-CC having a time-varying period g having a coding rate (y-1) / y and an LDPC-CC having a time-varying period g having a coding rate (z-1) / z. However, the maximum coding rate among the coding rates for sharing the circuit of the encoder and the circuit of the decoder is (q-1) / q, and g is 2 or more. It is assumed that an integer, y is an integer of 2 or more, z is an integer of 2 or more, and the relationship of y <z ≦ q is established. Note that the sharing of the circuit of the encoder is the sharing of the circuit inside the encoder, not the sharing of the circuit between the encoder and the decoder.

At this time, the equations (30-w-0) and the equations (30-w) expressing the g parity check polynomials described in the explanation of the equations (30-1) to (30- (q-1)) are given. -1), Equation (30-w-2), ..., Equation (30-w- (g-2)), Equation (30-w- (g-1)), w = y-1 The g parity check polynomials at this time are represented by equations (31-1) to (31-g).

In the formulas (31-1) to (31-g), the formula (31-w) and the formula (31-w') are equivalent formulas, and are described below as the formula (31-w). May be replaced with the equation (31-w') (w = 1, 2, ..., G).

Then, as described above (LDPC-CC having good characteristics), the information X _1, X _2, ..., X _y-1 at the time point j is changed to X _{1, j,} X _{2, j, ...} ..., X _{y-1, j,} and the parity P at the time point _{j is represented as Pj, u j} = (X _{1, j} , X _{2, j,} ..., X _{y-1, j} , Pj) ^T And. At this time, the information X _{1, j,} X _{2, j,} ..., X _{y-1, j} and the parity P _j at the time point j are
"When j mod g = 0, the parity check polynomial of Eq. (31-1) is satisfied."
"When j mod g = 1, the parity check polynomial of Eq. (31-2) is satisfied."
"When j mod g = 2, the parity check polynomial of Eq. (31-3) is satisfied."
・
・
・
"When j mod g = k, the parity check polynomial of Eq. (31- (k + 1)) is satisfied."
・
・
・
"When j mod g = g-1, the parity check polynomial of equation (31-g) is satisfied."
At this time, the relationship between the parity check polynomial and the check matrix is the same as the case described above (LDPC-CC having good characteristics).

Next, the equations (30-w-0) and the equations (30-w) expressing the g parity check polynomials described when the equations (30-1) to (30- (q-1)) are explained. -1), Equation (30-w-2), ..., Equation (30-w- (g-2)), Equation (30-w- (g-1)), w = z-1 The g parity check polynomials at this time are represented by equations (32-1) to (32-g). (From the relationship of y <z ≤ q, it can be expressed as equations (32-1) to (32-g).)

In the formulas (32-1) to (32-g), the formula (32-w) and the formula (32-w') are equivalent formulas, and are described below as the formula (32-w). May be replaced with the equation (32-w') (w = 1, 2, ..., G).

Then, as described above (LDPC-CC having good characteristics), the information X _1, X _2, ..., X _y-1, ..., X _s, ..., At the time point j. X _z-1 is represented as X _{1, j,} X _{2, j,} ..., X _{y-1, j,} ..., X _{s, j,} ..., X _{z-1, j,} and the time point j Parity P in is expressed as Pj, and u _j = (X _{1, j} , X _{2, j,} ..., X _{y-1, j,} ..., X _{s, j,} ..., X _{z-1. , J} , Pj) ^T (Therefore, from the relationship of y <z≤q, s = y, y + 1, y + 2, y + 3, ..., Z-3, z-2, z-1). At this time, the information at the time point j, X _{1, j,} X _{2, j,} ..., X _{y-1, j,} ..., X _{s, j,} ..., X _{z-1, j} and the parity P. _j is
"When j mod g = 0, the parity check polynomial of Eq. (32-1) is satisfied."
"When j mod g = 1, the parity check polynomial of Eq. (32-2) is satisfied."
"When j mod g = 2, the parity check polynomial of Eq. (32-3) is satisfied."
・
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"When j mod g = k, the parity check polynomial of Eq. (32- (k + 1)) is satisfied."
・
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"When j mod g = g-1, the parity check polynomial of the equation (32-g) is satisfied." At this time, the relationship between the parity check polynomial and the check matrix is as described above (LDPC-CC having good characteristics). It is the same as the case explained in.

When the above relationship is established, the LDPC-CC having a time-varying period g at a coding rate (y-1) / y and the LDPC-CC having a time-varying period g at a coding rate (z-1) / z When the following conditions are satisfied, the LDPC-CC encoder having a time-varying period g at a coding rate (y-1) / y and the time-varying period g at a coding rate (z-1) / z The LDPC-CC encoder can share the circuit, and the LDPC-CC decoder with a time-varying period g at the coding rate (y-1) / y and the coding rate (z-). 1) The circuit can be shared with the LDPC-CC decoder having the time-varying period g at / z. The conditions are as follows.

First, the following relationship is established between the equation (31-1) and the equation (32-1).
"The equal sign holds for _AX1,0 (D) in equation (31-1) and _AX1,0 (D) in equation (32-1)."
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・
"The equal sign holds for _{AXf, 0} (D) in equation (31-1) and _{AXf, 0} (D) in equation (32-1)."
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"Equation (31-1) of _{A Xy-1, 0} (D) and _{A Xy-1, 0} (D) of the formula (32-1), the equality is satisfied."
That is, the above relationship is established when f = 1, 2, 3, ..., Y-1.

In addition, the following relationship holds for parity.
_"B 0 and (D) is of formula (31-1) _B 0 of (D) and Formula (32-1), equality is established."

Similarly, the following relationship holds between the equation (31-2) and the equation (32-2).
"The equal sign holds for _AX1,1 (D) in equation (31-2) and _AX1,1 (D) in equation (32-2)."
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"The equal sign holds for _{AXf, 1} (D) in equation (31-2) and _{AXf, 1} (D) in equation (32-2)."
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"Equation (31-2) of _{A Xy-1, 1} (D) and _{A Xy-1, 1} (D) of the formula (32-2), the equality is satisfied."
That is, the above relationship is established when f = 1, 2, 3, ..., Y-1.

In addition, the following relationship holds for parity.
_"B 1 and (D) is of formula (31-2) _B 1 of (D) and Formula (32-2), equality is established."

(Omitted)

Similarly, the following relationship is established between the equation (31-h) and the equation (32-h).
"The equal sign holds for _{AX1, h-1} (D) of equation (31-h) and _{AX1, h-1} (D) of equation (32-h)."
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・
"The equal sign holds for _{AXf, h-1} (D) of equation (31-h) and _{AXf, h-1} (D) of equation (32-h)."
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・
_{"The equal sign holds for A Xy-1, h-1} (D) of the formula (31-h) and A _{Xy-1, h-1} (D) of the formula (32-h)."
That is, the above relationship is established when f = 1, 2, 3, ..., Y-1.

In addition, the following relationship holds for parity.
_{"The equal sign holds for B h-1} (D) of equation (31-h) and B _h-1 (D) of equation (32-h)."

(Omitted)

Similarly, the following relationship is established between the equation (31-g) and the equation (32-g).
"The equal sign holds for _{AX1, g-1} (D) of formula (31-g) and _{AX1, g-1} (D) of formula (32-g)."
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"The equal sign holds for _{AXf, g-1} (D) of formula (31-g) and _{AXf, g-1} (D) of formula (32-g)."
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・
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_{"The equal sign holds for A Xy-1, g-1} (D) of the formula (31-g) and A _{Xy-1, g-1} (D) of the formula (32-g)."
That is, the above relationship is established when f = 1, 2, 3, ..., Y-1.

In addition, the following relationship holds for parity.
_{"The equal sign holds for B g-1} (D) of the formula (31-g) and B _g-1 (D) of the formula (32-g)."
(Therefore, h = 1, 2, 3, ..., G-2, g-1, g.)

When the above relationship is established, the LDPC-CC encoder and the time-varying period g at the coding rate (z-1) / z of the time-varying period g at the coding rate (y-1) / y The LDPC-CC encoder can share the circuit, and the LDPC-CC decoder and coding rate (z-1) with a time-varying period g at a coding rate (y-1) / y. ) / Z The circuit can be shared with the LDPC-CC decoder having the time-varying period g. However, the method of sharing the circuit of the encoder and the method of sharing the circuit of the decoder will be described in detail in the following (configuration of the encoder and the decoder).

Table 5 shows an example of a parity check polynomial of LDPC-CC that satisfies the above conditions, has a time variation period of 3, and has a corresponding coding rate of 1/2, 2/3, 3/4, and 5/6. However, the format of the parity check polynomial is the same as the format shown in Table 3. As a result, when the transmitting device and the receiving device correspond to a coding rate of 1/2, 2/3, 3/4, 5/6 (or two or more of the four coding rates are coded). When the rate is supported by the transmitter and receiver) The calculation scale (circuit scale) can be reduced (Distributed codes, but the encoder circuit can be shared and the decoder circuit can be shared. , The circuit scale can be reduced), and the receiving device can obtain high data reception quality.

It will be described that the LDPC-CC having the time variation period 3 in Table 5 satisfies the above conditions. For example, consider an LDPC-CC having a time-varying period of 3 at a coding rate of 1/2 in Table 5 and an LDPC-CC having a time-varying period of 3 at a coding rate of 2/3 in Table 5. That is, y = 2 in (31-1) to (31-g), and z = 3 in (32-1) to (32-g).

Then, from the LDPC-CC of the time-varying period 3 at the coding rate 1/2 of Table 5, _AX1,0 (D) ^{of the equation (31-1) becomes D 373} + D ⁵⁶ + 1, and the coding rate of Table 5 is obtained. From the LDPC-CC with the time variation period 3 in 2/3, _AX1,0 (D) ^{in equation (32-1) becomes D 373} + D ⁵⁶ + 1, and " _AX1,0 (D) in equation (31-1)). _{And AX1,0} (D) in equation (32-1) have an equal sign. "

Further, from the LDPC-CC having the time variation period 3 at the coding rate 1/2 in Table 5, B ₀ (D) ^{in Eq. (31-1) becomes D 406} + D ²¹⁸ + 1, and the coding rate 2 / in Table 5 From the LDPC-CC of the time-varying period 3 in 3, B ₀ (D) = D ⁴⁰⁶ + D ²¹⁸ + 1 of the equation (32-1), and "B ₀ (D) of the equation (31-1) and the equation (32-)". An equal sign holds with _{B 0} (D) in 1). "

Similarly, from LDPC-CC having a time-varying period 3 at a coding rate of 1/2 in Table 5, _AX1,1 (D) = D ⁴⁵⁷ + D ¹⁹⁷ + 1 in Eq. (31-2), and the coding in Table 5 From LDPC-CC with a time variation period of 3 at a rate of 2/3, _AX1,1 (D) ^{of equation (32-2) = D 457} + D ¹⁹⁷ _{+ 1, and "AX1,1} (D) of equation (31-2)". _{) And AX1,1} (D) of equation (32-2) have equal signs. "

Further, from the LDPC-CC having the time variation period 3 at the coding rate 1/2 in Table 5, B ₁ (D) ^{in Eq. (31-2) becomes D 491} + D ²² + 1, and the coding rate 2 / in Table 5 is obtained. From the LDPC-CC of the time-varying period 3 in 3, B ₁ (D) ^{of equation (32-2) = D 491} + D ²² + 1, and "B ₁ (D) of equation (31-2) and equation (32-)" An equal sign holds with _{B 1} (D) of 2). "

Similarly, from the LDPC-CC having the time variation period 3 at the coding rate 1/2 in Table 5, _{AX1, 2} (D) ^{in Eq. (31-3) becomes D 485} + D ⁷⁰ + 1, and the coding in Table 5 From LDPC-CC with a time-varying period of 3 at a rate of 2/3, _{AX1, 2} (D) = D ⁴⁸⁵ + D ⁷⁰ _{+1 in Eq. (32-3), and "AX1, 2 in} Eq. (31-3) ( The equal sign holds between D) and _AX1 , 2 (D) in equation (32-3). "

Further, from the LDPC-CC having the time variation period 3 at the coding rate 1/2 in Table 5, B ₂ (D) in ^{the equation (31-3) becomes D 236} + D ¹⁸¹ + 1, and the coding rate 2 / in Table 5 From the LDPC-CC of the time-varying period 3 in 3, the B ₂ (D) ^{of the equation (32-3) becomes D 236} + D ¹⁸¹ + 1, and "B ₂ (D) of the equation (31-3) and the equation (32-)". An equal sign holds with _{B 2} (D) in 3). "

As can be seen from the above, the LDPC-CC having a time-varying period of 3 at a coding rate of 1/2 in Table 5 and the LDPC-CC having a time-varying period of 3 at a coding rate of 2/3 in Table 5 have the above-mentioned conditions. It can be confirmed that the above is satisfied.

Similarly to the above, in the LDPC-CC having the time-varying period 3 in Table 5, the time-varying period 3 having two different coding rates out of the coding rates of 1/2, 2/3, 3/4, and 5/6 When LDPC-CC is selected and it is verified whether the above conditions are satisfied, it can be confirmed that the above conditions are satisfied in any of the selection patterns.

Since LDPC-CC is a kind of convolutional code, termination and tail biting are required to ensure reliability in decoding the information bit. Here, a case where a method of setting the state of data (information) X to zero (hereinafter referred to as "Information-zero-termination") is performed will be considered.

FIG. 10 is a diagram showing a method of “Information-zero-termination”. As shown in FIG. 10, the information bit (final transmission bit) to be transmitted last in the information series to be transmitted is Xn (110). If the transmitting device transmits data only up to the parity bit generated by the encoder with the final information bit Xn (110) and the receiving device decodes the data, the reception quality of the information is significantly deteriorated. .. In order to solve this problem, the information bits (called "virtual information bits") after the final information bit Xn (110) are encoded assuming "0" to generate the parity bit (130). do.

At this time, since the receiving device knows that the virtual information bit (120) is "0", the transmitting device does not transmit the virtual information bit (120) and is generated by the virtual information bit (120). Only the parity bit (130) is transmitted (this parity bit becomes a redundant bit that must be transmitted. Therefore, this parity bit is referred to as a redundant bit). Then, as a new issue, in order to improve the data transmission efficiency and secure the data reception quality at the same time, the parity bit generated by the virtual information bit (120) while ensuring the data reception quality (120). It is necessary to reduce the number of 130) as much as possible.

At this time, in order to minimize the number of parity bits generated by the virtual information bits while ensuring the reception quality of the data, the term related to the parity of the parity check polynomial plays an important role. Confirmed by simulation.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）。 As an example, LDPC-CC when the time-varying period m (m is an integer and m ≧ 2) and the coding rate is 1/2 will be described as an example. When the time-varying period m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1, ..., M-1. Further, _{the order of D existing in AX1 , i} (D) is only an integer of 0 or more (for example, the order existing for D such as AX1,1 (D) = D ¹⁵ + D ³ + D ^0). the as 15,3,0, all composed of zero or more _degrees), only and shall not exist order algebraic equation in the zero or more D present in _B i (D) _{(e.g., B} i ( The orders that exist for D, such as D) = D 18 + D ⁴ + D ⁰ , are all composed of 0 or higher orders, such as ^{18, 4, 0).}

At this time, at time j, the parity check polynomial of the following equation is established.

_Then, in _X 1 _(D), the highest order of D in _{A X1,1} (D) _{α 1 (e.g.,} when ^{A X1,1 (D) = D 15} + D 3 + D 0, the order 15 for D, There are 3 and 0 degrees, and the highest order of D is α ₁ = 15.), and the highest order of D in _{AX1, 2 (D) is α 2} , ..., _{AX1, i} (D). ), The highest order of D is α _i , ···, _{AX1, m-1.} The highest order of D in (D) is α _m-1 . Then, let α be _{the largest value in α i} (i = 0, 1, 2, ..., M-1).

On the other hand, in P (D), the highest order of D in _{B 1 (D) is β 1} , the _{highest order of D in B 2} (D) is β ₂ , ..., _{D in Bi} (D). The highest order is β _i , ..., The highest order of D in _{B m-1 (D) is β m-1} . Then, in β _i (i = 0, 1, 2, ..., M-1), the largest value is β.

Then, in order to reduce the number of parity bits generated by the virtual information bits as much as possible while ensuring the data reception quality, β should be 1/2 or less of α.

Here, the case where the coding rate is 1/2 has been described, but the case where the coding rate is higher than that can be considered in the same manner. At this time, particularly when the coding rate is 4/5 or more, the necessary redundancy is required to satisfy the condition that the number of parity bits generated by the virtual information bits is reduced as much as possible while ensuring the data reception quality. Bits tend to be very large, and the conditions considered above are to minimize the number of parity bits generated by virtual information bits while ensuring data reception quality. It becomes important.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、同様に、Ａ_Ｘ２，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ３，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ４，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）。 As an example, LDPC-CC when the time variation period m (m is an integer and m ≧ 2) and the coding rate is 4/5 will be described as an example. When the time-varying period m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1, ..., M-1. Further, _{the order of D existing in AX1 , i} (D) is only an integer of 0 or more (for example, the order existing for D such as AX1,1 (D) = D ¹⁵ + D ³ + D ^0). Is composed of all orders of 0 or more, such as 15, 3, 0). Similarly, _{the order of D existing in AX2, i} (D) is only an integer of 0 or more, and _{AX3 ,} the order of D existing in the i (D) is not only there integer of 0 or _more, orders of D present in _{a X4,} i (D) is absent only an integer of 0 or _more, the _B i (D) only and shall not exist order algebraic equation in the zero or more existing D _(e.g., as in ^{B i (D) = D 18} + D 4 + D 0, orders exist for D is as 18,4,0, All consist of orders of 0 or higher).

At this time, at time j, the parity check polynomial of the following equation is established.

Then, in X ₁ (D), if the highest order of D in _{AX 1, 1 (D) is α 1, 1} (for example, _AX 1, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order for D is There are 15, order 3 and order 0, and the highest order α _{1, 1} = 15 of D), and the highest order of D in _{AX1, 2 (D) is α 1} , 2, ..., The highest order of D in _{AX1, i (D) is α 1, i} , ..., And the highest order of D in _{AX1, m-1 (D) is α 1, m-1} . Then, in α _{1, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₁ .

In X 2 (D), if the highest order of D in _{AX 2, 1 (D) is α 2, 1} (for example, _AX 2, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order 15 for D, degree 3, there is order 0, the highest order alpha _2,1 = 15 of _D.), the highest order of D in _{a x2,2 (D) α 2,2,} ···, a X2 _{, I} The highest order of D in (D) is α _{2, i} , ···, _{AX2, m-1} The highest order of D in (D) is α _{2, m-1} . Then, in α _{2, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₂ .

In X 3 (D), if the highest order of D in _{AX 3, 1 (D) is α 3, 1} (for example, _AX 3, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order 15 for D, degree 3, there is order 0, the highest order alpha _{3, 1} = 15 in _D.), the highest order of D in _{a X3,2 (D) α 3,2,} ···, a X3 _{, I} The highest order of D in (D) is α _{3, i} , ···, _{AX3, m-1} The highest order of D in (D) is α _{3, m-1} . Then, in α _{3, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₃ .

In X 4 (D), if the highest order of D in _{AX 4, 1 (D) is α 4, 1} (for example, _AX 4, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order 15 for D, degree 3, there is order 0, the highest order alpha _{4, 1} = 15 in _D.), the highest order of D in _{a X4,2 (D) α 4,2,} ···, a X4 _{, I} The highest order of D in (D) is α _{4, i} , ···, _{AX4, m-1} The highest order of D in (D) is α _{4, m-1} . Then, in α _{4, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₄ .

In P (D), the highest order of D in _{B 1 (D) is β 1} , the _{highest order of D in B 2 (D) is β 2} , ..., The highest order of D in _Bi (D). The order is β _i , ..., The highest order of D in _{B m-1 (D) is β m-1} . Then, in β _i (i = 0, 1, 2, ..., M-1), the largest value is β.

Then, in order to minimize the number of parity bits generated by the virtual information bits while ensuring the reception quality of the data,
"Β is 1/2 or less of _{α 1 , β is 1/2 or less of α 2} , β is 1/2 or less of α ₃ , and β is 1/2 or less of _{α 4."}
In particular, there is a high possibility that good data reception quality can be ensured.

also,
"Β is 1/2 or less of _{α 1} , or β is 1/2 or less of _{α 2} , or β is 1/2 or less of _{α 3} , or β is 1/2 or less of _{α 4."}
Even so, the number of parity bits generated by the virtual information bits can be reduced as much as possible while ensuring the data reception quality, but it may cause a slight deterioration in the data reception quality (however). However, it does not necessarily lead to deterioration of data reception quality.)

Therefore, in the case of LDPC-CC when the time variation period m (m is an integer and m ≧ 2) and the coding rate is (n-1) / n, it can be considered as follows.

ただし、ｉ＝０、１、・・・、ｍ−１とする。また、Ａ_Ｘ１，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず（例えば、Ａ_Ｘ１，１（Ｄ）＝Ｄ^１５＋Ｄ^３＋Ｄ^０のように、Ｄについて存在する次数は１５、３、０のように、全てが０以上の次数で構成される）、同様に、Ａ_Ｘ２，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ３，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ａ_Ｘ４，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、・・・、Ａ_Ｘｕ，ｉ（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、・・・、Ａ_{Ｘｎ−１，ｉ}（Ｄ）に存在するＤの次数は０以上の整数しか存在せず、Ｂ_ｉ（Ｄ）に存在するＤの次数も０以上の次数しか存在しないものとする（例えば、Ｂ_ｉ（Ｄ）＝Ｄ^１８＋Ｄ^４＋Ｄ^０のように、Ｄについて存在する次数は１８、４、０のように、全てが０以上の次数で構成される）（ｕ＝１、２、３、・・・、ｎ−２、ｎ−１）。 When the time-varying period m, the required m parity check polynomials are expressed by the following equations.

However, i = 0, 1, ..., M-1. Further, _{the order of D existing in AX1 , i} (D) is only an integer of 0 or more (for example, the order existing for D such as AX1,1 (D) = D ¹⁵ + D ³ + D ^0). Is composed of all orders of 0 or more, such as 15, 3, 0). Similarly, _{the order of D existing in AX2, i} (D) is only an integer of 0 or more, and _{AX3 ,} the order of D existing in the i (D) is not only there integer of 0 or _more, orders of D present in _{a X4,} i (D) is absent only integer of 0 or more, · · _{·, a Xu ,} The order of D existing in i (D) exists only an integer of 0 or more, ..., _{The order of D existing in AXn-1, i} (D) exists only an integer of 0 or more. also the order of D present in B _i (D) is assumed there is only 0 or more orders _(e.g., as in ^{B i (D) = D 18} + D 4 + D 0, orders exist for D is 18,4 , 0, all of which are of order 0 or higher) (u = 1, 2, 3, ..., N-2, n-1).

At this time, at time j, the parity check polynomial of the following equation is established.

Then, in X ₁ (D), if the highest order of D in _{AX 1, 1 (D) is α 1, 1} (for example, _AX 1, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order for D is There are 15, order 3 and order 0, and the highest order α _{1, 1} = 15 of D), and the highest order of D in _{AX1, 2 (D) is α 1} , 2, ..., The highest order of D in _{AX1, i (D) is α 1, i} , ..., And the highest order of D in _{AX1, m-1 (D) is α 1, m-1} . Then, in α _{1, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₁ .

In X 2 (D), if the highest order of D in _{AX 2, 1 (D) is α 2, 1} (for example, _AX 2, 1 (D) = D ¹⁵ + D ³ + D ⁰ , then the order 15 for D, degree 3, there is order 0, the highest order alpha _2,1 = 15 of _D.), the highest order of D in _{a x2,2 (D) α 2,2,} ···, a X2 _{, I} The highest order of D in (D) is α _{2, i} , ···, _{AX2, m-1} The highest order of D in (D) is α _{2, m-1} . Then, in α _{2, i} (i = 0, 1, 2, ..., M-1), the largest value is set to α ₂ .
・
・
・

In X _u (D), if the highest order of D in _{AX u, 1 (D) is α u, 1} (for example, _{AX u, 1} (D) = D ¹⁵ + D ³ + D ⁰ , then the order 15 for D, There are 3 and 0 degrees, and the highest order of D is α _{u, 1} = 15.), The highest order of D in _{AXu, 2 (D) is α u, 2} , ..., _{AXu. , I} The highest order of D in (D) is α _{u, i} , ···, _{AXu, m-1} The highest order of D in (D) is α _{u, m-1} . Then, in α _{u, i} (i = 0, 1, 2, ..., M-1), the largest value is α _u . (U = 1, 2, 3, ..., n-2, n-1)
・
・
・

In _{X n-1 (D),} A Xn-1,1 highest order of D in (D) α _{n-1,1 ^{(e.g., A Xn-1,1 (D)}} = D 15 + D 3 + D 0 Then, there are a degree 15, a degree 3, and a degree 0 for D, and the highest order α _n-1,1 = 15 of D), and the highest order of D in _{AXn-1,2 (D).} The highest order of D in α _n-1 , 2, ..., A _{Xn-1, i (D) is α n-1, i} , ..., A _{Xn-1, m-1} (D). The highest order of D in is α _{n-1, m-1} . Then, in α _{n-1, i} (i = 0, 1, 2, ..., M-1), the largest value is α _n-1 .

In P (D), the highest order of D in _{B 1 (D) is β 1} , the _{highest order of D in B 2 (D) is β 2} , ..., The highest order of D in _Bi (D). The order is β _i , ..., The highest order of D in _{B m-1 (D) is β m-1} . Then, in β _i (i = 0, 1, 2, ..., M-1), the largest value is β.

Then, in order to minimize the number of parity bits generated by the virtual information bits while ensuring the reception quality of the data,
"Β is 1/2 or less of _{α 1 , and β is 1/2 or less of α 2} , and ..., and β is _{1/2 or less of α u} , and ..., and β Is _{1/2 or less of α n-1} (u = 1, 2, 3, ..., N-2, n-1) "
In particular, there is a high possibility that good data reception quality can be ensured.

also,
"Β is 1/2 or less of _{α 1 , or β is 1/2 or less of α 2} , or ..., Or β is _{1/2 or less of α u} , or ..., or β Is _{1/2 or less of α n-1} (u = 1, 2, 3, ..., N-2, n-1) "
Even so, the number of parity bits generated by the virtual information bits can be reduced as much as possible while ensuring the data reception quality, but it may cause a slight deterioration in the data reception quality (however). However, it does not necessarily lead to deterioration of data reception quality.)

Table 6 shows LDPC-CCs with a time-varying period 3 that can reduce redundant bits while ensuring data reception quality, and a coding rate of 1/2, 2/3, 3/4, 4/5. An example of a parity check polynomial is shown. In the LDPC-CC having a time-varying period 3 in Table 6, the LDPC-CC having a time-varying period 3 having two different coding rates out of the coding rates 1/2, 2/3, 3/4, and 4/5 are used. When it is selected, it is verified whether or not the conditions that can be shared by the encoder and the decoder described above are satisfied. In any of the selection patterns, the same as the LDPC-CC having the time variation period 3 in Table 5 In addition, it can be confirmed that the condition that the encoder and the decoder can be shared is satisfied.

When the coding rate of Table 5 was 5/6, 1000 or more redundant bits were required, but when the coding rate of Table 6 was 4/5, it was confirmed that the redundant bits were 500 bits or less. ing.

Further, in the reference numerals in Table 6, a different number of redundant bits (redundant bits added for "Information-zero-termination") are used for each coding rate. At this time, the number of redundant bits tends to increase as the coding rate increases. However, this is not always the case. Further, when the coding rate is large and the information size is large, the number of redundant bits tends to increase. That is, when the codes are created as shown in Tables 5 and 6, when there is a code having a code rate (n-1) / n and a code having a code rate (m-1) / m (n> m). , The number of redundant bits (redundant bits added for "Information-zero-termination") required for the code rate (n-1) / n is the code rate (m-1) / m. It tends to be larger than the number of redundant bits required for the code (redundant bits added for "Information-zero-termination"), and the redundancy required for the code rate (n-1) / n. The number of bits tends to be greater than the number of redundant bits required for a code rate (m-1) / m when the information size is small. However, this is not always the case.

As described above, the maximum coding rate among the coding rates for sharing the encoder circuit and the decoder circuit is (q-1) / q, and the coding rate (r-) is set. The parity check polypoly of LDPC-CC having a time variation period g of 1) / r (r = 2,3, ..., Q (q is a natural number of 3 or more)) has been described (g is an integer of 2 or more).

Here, an LDPC-CC having a time-varying period g of at least a coding rate (y-1) / y and an LDPC-CC having a time-varying period g of a coding rate (z-1) / z are provided. The transmitter (y ≠ z) and the LDPC-CC having a time-varying period g of at least the coding rate (y-1) / y and the LDPC-CC having a time-varying period g of the coding rate (z-1) / z. The receiving device provided with the decoder, the method of generating the parity check polymorphism of the LDPC-CC having the time variation period g that can reduce the calculation scale (circuit scale), and the features of the parity check polymorphism have been described.

Here, the transmission device is a modulated signal for transmitting a coded sequence of the LDPC-CC having a time variation period g of at least a code rate (y-1) / y, or a code rate (z-1) /. It is a transmission device capable of generating a modulated signal of any of the modulated signals for transmitting the coded sequence of LDPC-CC having a time-varying period g of z.

Further, when the receiving device is a received signal including a coding sequence of LDPC-CC having a time variation period g of at least a coding rate (y-1) / y, or a coding rate (z-1) / z. It is a receiving device that demolishes and decodes any received signal of the received signal including the coded sequence of LDPC-CC having a variable period g.

By using the LDPC-CC having a time variation period g proposed in the present invention, it is possible to reduce the calculation scale (circuit scale) of the transmitting device including the encoder and the receiving device including the decoder (circuit scale). The circuit can be standardized).

Further, by using the LDPC-CC having the time variation period g proposed in the present invention, the receiving device has an effect that high data reception quality can be obtained at any coding rate. The configuration of the encoder, the configuration of the decoder, and its operation will be described in detail below.

Further, in the equations (30-1) to (30- (q-1)), when the coding rates are 1/2, 2/3, 3/4, ..., (Q-1) / q. Although the LDPC-CC having a time-varying period g has been described, the transmitting device provided with the encoder and the receiving device provided with the decoder have a coding rate of 1/2, 2/3, 3/4, ... -It is not necessary to support all of (q-1) / q, and if at least two or more different coding rates are supported, the calculation scale (circuit scale) of the transmitting device and the receiving device is reduced (code). It is possible to obtain the effect that the circuit of the converter and the decoder is standardized) and that the receiving device can obtain high data reception quality.

Further, when all the coding rates supported by the transmitter / receiver (encoder / decoder) are codes based on the method described in the present embodiment, the highest coding rate among the supported coding rates is obtained. By having a rate encoder / decoder, it is possible to easily support coding and decoding of all coding rates, and at this time, the effect of reducing the calculation scale is very large.

Further, in the present embodiment, the description has been made based on the reference numeral of (LDPC-CC having good characteristics) described in the first embodiment, but it is not necessarily explained by the above-mentioned (LDPC-CC having good characteristics). It is not necessary to satisfy the above-mentioned conditions, and if the LDPC-CC has a time-varying period g based on the parity check polynomial of the form described in the above (LDPC-CC having good characteristics), the present embodiment is similarly implemented. (G is an integer greater than or equal to 2). This is clear from the relationship between (31-1) to (31-g) and (32-1) to (32-g).

Naturally, for example, the transmitter / receiver (encoder / decoder) corresponds to a coding rate of 1/2, 2/3, 3/4, 5/6, and a coding rate of 1/2, 2/3 and 3/4 use LDPC-CC based on the above rule, and code rate 5/6 is a coder / decoder when a code not based on the above rule is used. The circuit can be shared for the coding rates of 1/2, 2/3, and 3/4, and it is difficult to share the circuit for the coding rate of 5/6.

(Embodiment 3)
In the present embodiment, a method of sharing the circuit of the LDPC-CC encoder and a method of sharing the circuit of the decoder formed by using the search method described in the second embodiment will be described in detail.

First, the highest coding rate among the coding rates for sharing the encoder circuit and the decoder circuit according to the present invention is set to (q-1) / q (for example,). When the coding rate corresponding to the transmitter / receiver is 1/2, 2/3, 3/4, 5/6, the code of the coding rate 1/2, 2/3, 3/4 is the encoder / The circuit is standardized in the decoder, and the coding rate of 5/6 does not make the circuit common in the encoder / decoder. At this time, the highest coding rate (q-) described above is used. 1) / q is 3/4), LDPC with a time-varying period g (g is a natural number) that can handle multiple coding rates (r-1) / r (r is an integer of 2 or more and q or less) The encoder that creates -CC will be described.

FIG. 11 is a block diagram showing an example of the main configuration of the encoder according to the present embodiment. The encoder 200 shown in FIG. 11 is an encoder that can handle coding rates of 1/2, 2/3, and 3/4. The encoder 200 of FIG. 11 includes an information generation unit 210, a first information calculation unit 220-1, a second information calculation unit 220-2, a third information calculation unit 220-3, a parity calculation unit 230, and an addition unit 240. It mainly includes a coding rate setting unit 250 and a weight control unit 260.

_{The information generation unit 210 sets the information X 1, i} , the information X _{2, i} , and the information X _{3, i} at the time point i according to the coding rate designated by the coding rate setting unit 250. For example, if the coding rate setting unit 250 sets the coding rate to 1/2, information generating section 210 sets the input information data _{S j} to information _{X 1, i} of point in time i, the time point i Information X _2. Set 0 to _{the information X3, i} of i and the time point i.

When the coding rate is 2/3, the information generation unit 210 sets the input information data S _{j in the information X 1 and i} at the time point i, and sets the input information data S _{j + 1} in _{the information X 2 and i at the time point i.} set, sets information _{X 3,} 0 to _i of point-in-time i.

When the coding rate is 3/4, the information generation unit 210 sets the input information data S _{j in the information X 1 and i} at the time point i, and sets the input information data S _{j + 1} in _{the information X 2 and i at the time point i.} set, sets the input information data _{S j + 2} to the information _{X 3, i} of point-in-time i.

_{In this way, the information generation unit 210 transfers the input information data to the information X 1, i} , the information X _{2, i} , and the information X ₃ at the time point i according to the coding rate set by the coding rate setting unit 250. _{, I} are set, the set information X _{1, i} is output to the first information calculation unit 220-1, and the set information X _{2, i} is output to the second information calculation unit 220-2. Then, the set information X3 _{and i} are output to the third information calculation unit 220-3.

The first information calculation unit 220-1 calculates _{X 1} (D) according to AX _{1, k (D) of the equation (30-1).} Similarly, second information computing section 220-2, according to _{A X2,} k (D) of the formula _(30-2) to calculate _X 2 and (D). Similarly, third information computing section 220-3, according to _{A X3,} k (D) of the formula _(30-3) to calculate _X 3 and (D).

At this time, as described in the second embodiment, it is assumed that the coding rate is switched from the conditions that satisfy the conditions (31-1) to (31-g) and (32-1) to (32-g). Also, it is not necessary to change the configuration of the first information calculation unit 220-1, and similarly, it is not necessary to change the configuration of the second information calculation unit 220-2, and the third information calculation unit 220- There is no need to change the configuration of 3.

Therefore, when dealing with a plurality of code rates, the operation as described above is performed based on the configuration of the coder having the highest code rate among the code rates that can be shared by the coder circuits. , Other code rates can be accommodated. That is, the first information calculation unit 220-1, the second information calculation unit 220-2, and the third information calculation unit 220-3, which are the main parts of the encoder, are common regardless of the coding rate. The LDPC-CC described in the second embodiment will have the advantage of being able to do so. Then, for example, the LDPC-CC shown in Table 5 has an advantage of providing good data reception quality regardless of the coding rate.

FIG. 12 shows the internal configuration of the first information calculation unit 220-1. The first information calculation unit 220-1 of FIG. 12 includes a shift register 221-1 to 221-M, a weight multiplier 222-0 to 222-M, and an addition unit 223.

The shift registers 221-1 to 221-M are registers that hold X _{1, it} (t = 0, ..., M-1), respectively, and hold them at the timing when the next input comes in. The value being sent is sent to the shift register on the right side, and the value output from the shift register on the left side is held.

The weight multipliers 222 to 222-M switch the value of _{h 1} ^(m) to 0 or 1 according to the control signal output from the weight control unit 260.

The addition unit 223 performs an exclusive OR operation on the outputs of the weight multipliers 222 to 222-M, calculates the calculation results Y _{1, i,} and displays the calculated Y _{1, i} in FIG. Output toward the addition unit 240.

Since the internal configurations of the second information calculation unit 220-2 and the third information calculation unit 220-3 are the same as those of the first information calculation unit 220-1, the description thereof will be omitted. The second information calculation unit 220-2 calculates the calculation results Y _{2, i} in the same manner as the first information calculation unit 220-1, and outputs the calculated Y _{2, i} to the addition unit 240. The third information calculation unit 220-3 calculates the calculation results Y _{3, i} in the same _{manner as the first information calculation unit 220-1, and directs the calculated Y 3, i} toward the addition unit 240 in FIG. Output.

The parity calculation unit 230 of FIG. 11 calculates P (D) according to _{B k} (D) of the formulas (30-1) to (30-3).

FIG. 13 shows the internal configuration of the parity calculation unit 230 of FIG. The parity calculation unit 230 of FIG. 13 includes shift registers 231 to 231-M, weight multipliers 232 to 232-M, and addition unit 233.

Shift register 231-1~231-M, _{respectively, P i-t (t =} 0, ···, M-1) is a register that holds the, at the timing at which the next input comes in, holding The current value is sent to the shift register on the right side, and the value output from the shift register on the left side is held.

The weight multipliers 232-0 to 232-M switch the value of _{h 2} ^(m) to 0 or 1 according to the control signal output from the weight control unit 260.

The addition unit 233 performs an exclusive OR operation on the outputs of the weight multipliers 232 to 232-M, calculates the calculation result Z _i, and directs the calculated Z _i to the addition unit 240 in FIG. Output.

Returning to FIG. 11 again, the addition unit 240 performs operations output from the first information calculation unit 220-1, the second information calculation unit 220-2, the third information calculation unit 220-3, and the parity calculation unit 230. Result _{The exclusive OR operation of Y 1, i} , Y _{2, i} , Y _{3, i} , and Z _i is performed, and the parity Pi at time _i is obtained and output. Adding section 240 also outputs toward parity _{P i} at time i to parity computing section 230.

The coding rate setting unit 250 sets the coding rate of the encoder 200 and outputs the information of the coding rate to the information generation unit 210.

The weight control unit 260 is of the equations (30-1) to (30-3) based on the inspection matrix corresponding to the equations (30-1) to (30-3) held in the weight control unit 260. _{The value of h 1} ^(m) at time i based on the parity check polynomial is directed to the first information calculation unit 220-1, the second information calculation unit 220-2, the third information calculation unit 220-3, and the parity calculation unit 230. And output. Further, the weight control unit 260 sets the value _{of h 2} ^(m) at that timing to 232 based on the inspection matrix corresponding to the equations (30-1) to (30-3) held in the weight control unit 260. Outputs to -0 to 232-M.

Note that FIG. 14 shows another configuration example of the encoder according to the present embodiment. In the encoder of FIG. 14, the components common to the encoder of FIG. 11 are designated by the same reference numerals as those of FIG. In the encoder 200 of FIG. 14, the coding rate setting unit 250 transfers the coding rate information to the first information calculation unit 220-1, the second information calculation unit 220-2, and the third information calculation unit 220-3. It is different from the encoder 200 of FIG. 11 in that it outputs to the parity calculation unit 230.

When the coding rate is 1/2, the second information calculation unit 220-2 _{outputs 0 as the calculation results Y 2 and i} toward the addition unit 240 without performing the calculation process. Further, when the coding rate is 1/2 or 2/3, the third information calculation unit 220-3 directs 0 to the addition unit 240 as the _{calculation results Y3 and i without performing the calculation processing.} Output.

In the encoder 200 of FIG. 11, the information generation unit 210 _{sets the information X 2, i} and the information X _{3, i} at the time point i to 0 according to the coding rate, whereas the information X 3, i of FIG. 14 is shown in FIG. In the encoder 200, the second information calculation unit 220-2 and the third information calculation unit 220-3 stop the calculation processing according to the coding rate, and set the calculation results as Y _{2, i} , Y _{3, i.} Since 0 is output, the obtained calculation result is the same as that of the encoder 200 of FIG.

As described above, in the encoder 200 of FIG. 14, the second information calculation unit 220-2 and the third information calculation unit 220-3 stop the calculation processing according to the coding rate. The arithmetic processing can be reduced as compared with the chemical device 200.

Next, the method of sharing the circuit of the decoder of the LDPC-CC described in the second embodiment will be described in detail.

FIG. 15 is a block diagram showing a configuration of a main part of the decoder according to the present embodiment. The decoder 300 shown in FIG. 15 is a decoder capable of handling coding rates of 1/2, 2/3, and 3/4. The decoder 300 of FIG. 14 mainly includes a log-likelihood ratio setting unit 310 and a matrix processing calculation unit 320.

The log-likelihood ratio setting unit 310 inputs a received log-likelihood ratio and a coding rate calculated by a log-likelihood-ratio calculation unit (not shown), and is known as a received log-likelihood ratio according to the coding rate. Insert the log-likelihood ratio.

For example, when the coding rate is 1/2, it _{corresponds to transmitting "0" as X 2, i} , X _{3, i in} the encoder 200, so that the log-likelihood ratio setting unit 310 is used. , The fixed log-likelihood ratio corresponding to the known bit “0” is _{inserted as the log-likelihood ratio of X 2, i} , X _{3, i} , and the log-likelihood ratio after insertion is directed to the matrix processing calculation unit 320. Output. Hereinafter, a description will be given with reference to FIG.

As shown in FIG. 16, the case of a coding rate 1/2, log likelihood ratio setting section _{310, X 1, i} and the reception log likelihood ratios _LLR X1 corresponding to _{P i,} i, and inputs the _{LLR Pi} do. Therefore, the log-likelihood ratio setting unit 310 inserts the received log-likelihood ratios LLR _{X2, i} , LLR _{3, i corresponding to X 2, i} , X _{3, i.} In FIG. 16, the received log-likelihood ratio circled by a dotted line indicates the received log-likelihood ratio LLR _{X2, i} , LLR _{3, i} inserted by the log-likelihood ratio setting unit 310. The log-likelihood ratio setting unit 310 inserts a fixed value log-likelihood ratio as the received log-likelihood ratios LLR _{X2, i} , LLR _{3, i.}

Further, when the coding rate is 2/3, the encoder 200 _{corresponds to transmitting "0" as X3 and i} , so that the log-likelihood ratio setting unit 310 has a known bit "0". The fixed log-likelihood ratio corresponding to "" is _{inserted as the log-likelihood ratio of X3 and i} , and the log-likelihood ratio after insertion is output to the matrix processing calculation unit 320. Hereinafter, a description will be given with reference to FIG.

As shown in FIG. 17, when the coding rate 2/3, log likelihood ratio setting section _{310, X 1, i, X 2} , i and _{P i} corresponding to the received log-likelihood ratio _{LLR X1,} i, Input LLR _{X2, i} and LLR _Pi. Therefore, the log-likelihood ratio setting unit 310 inserts the received log-likelihood ratio LLR _{3, i corresponding to X 3, i.} In FIG. 17, the received log-likelihood ratio circled by the dotted line indicates _{the received log-likelihood ratio LLR 3, i inserted by the log-likelihood ratio setting unit 310.} The log-likelihood ratio setting unit 310 inserts a fixed value log-likelihood ratio as the received log-likelihood ratio LLR _{3, i.}

The matrix processing calculation unit 320 of FIG. 15 includes a storage unit 321, a row processing calculation unit 322, and a column processing calculation unit 323.

The storage unit 321 holds a received log-likelihood ratio, an external value α _mn obtained by row processing, and a prior value β _mn obtained by column processing.

The row processing calculation unit 322 holds a weight pattern in the row direction of the check matrix H of the LDPC-CC having the maximum coding rate of 3/4 of the coding rates supported by the encoder 200. _{The row processing calculation unit 322 reads the necessary prior value β mn} from the storage unit 321 according to the weight pattern in the row direction, and performs the row processing calculation.

In row processing computation, row processing computation section 322, using a priori value beta _mn, performs decoding of a single parity check codes, obtains external value alpha _mn.

ここで、Φ（ｘ）は、Ｇａｌｌａｇｅｒのｆ関数と呼ばれ、次式で定義される。

The mth line processing will be described. However, the binary MxN matrix H = {H _mn } is used as the inspection matrix of the LDPC code to be decoded. The _{external value α mn} is updated by using the following update formula for all the sets (m, n) satisfying _{H mn = 1.}

Here, Φ (x) is called Gallager's f function and is defined by the following equation.

The column processing calculation unit 323 holds a weight pattern in the column direction of the check matrix H of the LDPC-CC having the maximum coding rate of 3/4 of the coding rates supported by the encoder 200. _{The column processing calculation unit 323 reads the necessary external value α mn} from the storage unit 321 according to the weight pattern in the column direction, and obtains the prior value β _mn.

In the column processing calculation, the column processing calculation unit 323 obtains the _{prior value β mn} by iterative decoding using _{the input log-likelihood ratio λ n} and the external value α _mn.

The mth column processing will be described.
For all sets (m, n) satisfying _{H mn = 1, β mn} is updated using the following update formula. However, only when q = 1, the calculation is made with _{α mn = 0.}

The decoder 300 obtains the log-likelihood ratio after the fact by repeating the above-mentioned row processing and column processing a predetermined number of times.

As described above, in the present embodiment, the highest coding rate among the available coding rates is (q-1) / q, and the coding rate setting unit 250 sets the coding rate to (s−). 1) When set to / s, the information generation unit 210 sets the information _{from the information X s, i} to the information X _{q-1, i} to zero. For example, when the corresponding coding rate is 1/2, 2/3, 3/4 (q = 4), the first information calculation unit 220-1 _{inputs the information X 1, i} at the time point i, and the formula _{Calculate the X 1} (D) term of (30-1). Further, the second information calculation unit 220-2 _{inputs the information X 2 and i at the time point i and calculates the X 2} (D) term of the equation (30-2). The third information computing section 220-3 receives the information _{X 3, i} at the time i, and calculates the _X 3 (D) term of formula (30-3). Further, the parity calculation unit 230 _{inputs the parity P i-1} at the time point i-1, and calculates the P (D) term of the equations (30-1) to (30-3). Further, the addition unit 240 exclusively ORs the calculation results of the first information calculation unit 220-1, the second information calculation unit 220-2, and the third information calculation unit 220-3 and the calculation results of the parity calculation unit 230. , was to be as a parity P _i of the time i.

According to this configuration, even when LDPC-CCs corresponding to different coding rates are created, the configuration of the information calculation unit in this description can be shared, so that a plurality of coding rates can be used on a low calculation scale. It is possible to provide an LDPC-CC encoder and a decoder that are compatible with the above.

Further, _{AX1, k} (D) to _{AXq-1, k} (D) satisfy the <condition # 1> to <condition # 6> described in the above-mentioned "LDPC-CC having good characteristics". When set to be .. However, as described in the second embodiment, the method for producing LDPC-CC is not limited to the above-mentioned “LDPC-CC having good characteristics”.

Then, the decoder 300 of FIG. 15 has a log-likelihood ratio setting unit for configuring the decoder according to the maximum coding rate among the coding rates that enable the sharing of the decoder circuit. By adding 310, decoding can be performed corresponding to a plurality of coding rates. The log-likelihood ratio setting unit 310 corresponds to (q-2) pieces of information _{from the information X r, i} at the time point i to the information X _{q-1, i according to the coding rate.} Set the ratio to the default value.

In the above description, the case where the maximum code rate supported by the encoder 200 is 3/4 has been described, but the maximum code rate supported is not limited to this, and the code rate (q-1) is not limited to this. ) / Q (q is an integer of 5 or more) is also applicable (naturally, the maximum code rate may be 2/3). In this case, the encoder 200 is configured to include the first to first (q-1) information calculation units, and the addition unit 240 is the calculation result and parity of the first to first (q-1) information calculation units. the exclusive oR operation result of the arithmetic unit 230 may be so obtained as parity P _i at time i.

Further, when all the coding rates supported by the transmitter / receiver (encoder / decoder) are codes based on the method described in the above-described second embodiment, the most supported coding rates By having a coder / decoder having a high coding rate, it is possible to support coding and decoding of a plurality of coding rates, and at this time, the effect of reducing the calculation scale is very large.

Further, in the above description, sum-product decoding has been described as an example of the decoding method, but the decoding method is not limited to this, and is shown in Non-Patent Documents 5 to 7, for example, min. The same can be performed by using a decoding method (BP decoding) using a message-passing algorithm such as -sum decoding, Normalized BP (Belief Propagation) decoding, Shuffled BP decoding, and Offset BP decoding.

Next, a mode in which the present invention is applied to a communication device that adaptively switches the coding rate according to the communication status will be described. In the following, the case where the present invention is applied to a wireless communication device will be described as an example, but the present invention is not limited to this, and the present invention is applied to a power line communication (PLC) device, a visible light communication device, or an optical communication device. Is also applicable.

FIG. 18 shows the configuration of the communication device 400 that adaptively switches the coding rate. The coding rate determination unit 410 of the communication device 400 of FIG. 18 receives a reception signal (for example, feedback information transmitted by the communication partner) transmitted from the communication device of the communication partner as an input, and performs reception processing or the like on the reception signal. Then, the coding rate determination unit 410 provides information on the communication status with the communication device of the communication partner, for example, information such as a bit error rate, a packet error rate, a frame error rate, and a received electric field strength (for example, feedback information). The coding rate and the modulation method are determined from the information on the communication status with the communication device of the communication partner. Then, the coding rate determination unit 410 outputs the determined coding rate and the modulation method to the encoder 200 and the modulation unit 420 as control signals.

The coding rate determining unit 410 uses, for example, a transmission format as shown in FIG. 19 to include information on the coding rate in the control information symbol, so that the coding rate used by the encoder 200 is communicated with the communication partner. Notify the device. However, although not shown in FIG. 19, it is assumed that the communication partner includes, for example, known signals (preamble, pilot symbol, reference symbol, etc.) necessary for demodulation and channel estimation.

In this way, the coding rate determining unit 410 receives the modulated signal transmitted by the communication device 500 of the communication partner, and determines the coding rate of the modulated signal to be transmitted based on the communication status. Adaptively switch the conversion rate. The encoder 200 performs LDPC-CC coding according to the above procedure based on the coding rate specified by the control signal. The modulation unit 420 modulates the coded sequence using the modulation method specified by the control signal.

FIG. 20 shows a configuration example of a communication device of a communication partner that communicates with the communication device 400. The control information generation unit 530 of the communication device 500 of FIG. 20 extracts control information from the control information symbols included in the baseband signal. The control information symbol contains code rate information. The control information generation unit 530 outputs the extracted code rate information as a control signal to the log-likelihood ratio generation unit 520 and the decoder 300.

The receiving unit 510 obtains a baseband signal by performing processing such as frequency conversion and orthogonal demodulation on the received signal corresponding to the modulated signal transmitted from the communication device 400, and transmits the baseband signal to the logarithmic likelihood ratio generation unit 520. Output toward. Further, the receiving unit 510 estimates the channel variation in the (for example, wireless) transmission line between the communication device 400 and the communication device 500 by using the known signal included in the baseband signal, and estimates the estimated channel estimation signal. It is output to the logarithmic likelihood ratio generation unit 520.

Further, the receiving unit 510 estimates the channel variation in the (for example, wireless) transmission line between the communication device 400 and the communication device 500 by using the known signal included in the baseband signal, and determines the state of the propagation path. (Channel fluctuation itself, for example, Channel State Information is an example) is generated and output. This feedback information is transmitted to the communication partner (communication device 400) as a part of the control information through a transmission device (not shown). The log-likelihood ratio generation unit 520 obtains the log-likelihood ratio of each transmission series using the baseband signal, and outputs the obtained log-likelihood ratio to the decoder 300.

_{As described above, the decoder 300 corresponds to the information from the information X s, i} at the time point i to the information X _{s-1, i} according to the coding rate (s-1) / s indicated by the control signal. BP decoding is performed using the LDPC-CC check matrix according to the maximum coding rate among the coding rates shared by the decoder by setting the logarithmic likelihood ratio to the default value. ..

In this way, the coding rates of the communication device 400 to which the present invention is applied and the communication device 500 of the communication partner can be adaptively changed depending on the communication situation.

The method of changing the coding rate is not limited to this, and the communication device 500, which is a communication partner, may include a coding rate determining unit 410 and specify a desired coding rate. Further, the communication device 400 may estimate the fluctuation of the transmission line from the modulation signal transmitted by the communication device 500 and determine the coding rate. In this case, the feedback information described above becomes unnecessary.

(Embodiment 4)
In the first embodiment, the LDPC-CC having a high error correction capability has been described. In the present embodiment, the LDPC-CC having a time-varying period 3 having a high error correction capability will be supplementarily described. In the case of LDPC-CC having a time-varying period 3, if a regular LDPC code is generated, a code having high error correction capability can be created.

The parity check polynomial of LDPC-CC with time-varying period 3 is reprinted.

When the coding rate is 1/2:

For coding rate (n-1) / n:

Here, it is assumed that the following conditions are satisfied so that the parity check matrix becomes full rank and the parity bits can be easily obtained sequentially.

b3 = 0, that is, D ^b3 = 1
B3 = 0, that is, ^DB3 = 1
β3 = 0, that is, D ^β3 = 1

In addition, in order to make the relationship between information and parity easy to understand, the following conditions should be met.
ai, 3 = 0, that is, ^{Dai, 3} = 1 (i = 1, 2, ..., N-1)
Ai, 3 = 0, that is, ^{DAi, 3} = 1 (i = 1, 2, ..., N-1)
αi, 3 = 0, that is, D ^{αi, 3} = 1 (i = 1, 2, ..., N-1)
However, ai, 3% 3 = 0, Ai, 3% 3 = 0, αi, 3% 3 = 0 may be used.

At this time, the following conditions must be satisfied in order to generate a regular LDPC code having high error correction capability by reducing the number of loops 6 in the Tanner graph.

That is, when focusing on the coefficient of the information Xk (k = 1, 2, ..., N-1), any one of # Xk1 to # Xk14 must be satisfied.
# Xk1: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk2: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk3: (ak, 1% 3, ak, 2% 3) = [0,1], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [1,1]
# Xk4: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk5: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk6: (ak, 1% 3, ak, 2% 3) = [0,2], (Ak, 1% 3, Ak, 2% 3) = [2,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk7: (ak, 1% 3, ak, 2% 3) = [1,1], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk8: (ak, 1% 3, ak, 2% 3) = [1,1], (Ak, 1% 3, Ak, 2% 3) = [1,1], (αk, 1% 3, αk, 2% 3) = [1,1]
# Xk9: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [0,1], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk10: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [0,2], (αk, 1% 3, αk, 2% 3) = [2,2]
# Xk11: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [1,1], (αk, 1% 3, αk, 2% 3) = [0,1]
# Xk12: (ak, 1% 3, ak, 2% 3) = [1,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [1,2]
# Xk13: (ak, 1% 3, ak, 2% 3) = [2,2], (Ak, 1% 3, Ak, 2% 3) = [1,2], (αk, 1% 3, αk, 2% 3) = [0,2]
# Xk14: (ak, 1% 3, ak, 2% 3) = [2,2], (Ak, 1% 3, Ak, 2% 3) = [2,2], (αk, 1% 3, αk, 2% 3) = [2,2]

In the above, when a = b, (x, y) = [a, b] represents x = y = a (= b), and when a ≠ b, (x, y) = [a. , B] represents x = a, y = b, or x = b, y = a (the same applies hereinafter).

Similarly, when focusing on the coefficient of parity, any of # P1 to # P14 must be satisfied.
# P1: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [0,1]
# P2: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [1,2]
# P3: (b1% 3, b2% 3) = [0,1], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [1,1]
# P4: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [0,1]
# P5: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [0,2]
# P6: (b1% 3, b2% 3) = [0,2], (B1% 3, B2% 3) = [2,2], (β1% 3, β2% 3) = [1,2]
# P7: (b1% 3, b2% 3) = [1,1], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [1,2]
# P8: (b1% 3, b2% 3) = [1,1], (B1% 3, B2% 3) = [1,1], (β1% 3, β2% 3) = [1,1]
# P9: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [0,1], (β1% 3, β2% 3) = [0,2]
# P10: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [0,2], (β1% 3, β2% 3) = [2,2]
# P11: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [1,1], (β1% 3, β2% 3) = [0,1]
# P12: (b1% 3, b2% 3) = [1,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [1,2]
# P13: (b1% 3, b2% 3) = [2,2], (B1% 3, B2% 3) = [1,2], (β1% 3, β2% 3) = [0,2]
# P14: (b1% 3, b2% 3) = [2,2], (B1% 3, B2% 3) = [2,2], (β1% 3, β2% 3) = [2,2]

The LDPC-CC having good characteristics described in the first embodiment is an LDPC-CC that satisfies the conditions of # Xk12 and # P12 among the above conditions. Further, when used in combination with the second embodiment, the circuit scale of the encoder and the decoder can be reduced and a high error correction capability can be obtained when dealing with a plurality of coding rates.

An example of the parity check polynomial of LDPC-CC having a time variation period 3 satisfying any one of # Xk1 to # Xk14 and any of # P1 to # P14 is shown below.

Code rate R = 1/2:

Code rate R = 2/3:

Code rate R = 3/4:

Code rate R = 4/5:

Since the parity check polynomial of the LDPC-CC satisfies the condition described in the second embodiment, the circuit of the encoder and the decoder can be shared.

By the way, when the parity check polynomial of LDPC-CC shown in the equations (44-i), (45-i), (46-i), and (47-i) is used (i = 1, 2, 3). ), It was confirmed that the required number of terminations differs depending on the number of bits of the data (information) X (hereinafter, referred to as “information size”), as shown in FIG. Here, the number of terminations is the number of parity bits generated by the virtual known information bit “0” after performing the above-mentioned Information-zero-termination, and is the number of redundant bits actually transmitted. In FIG. 21, Real R (effective coding rate) indicates the coding rate when the termination series composed of redundant bits is taken into consideration.

Another example of the parity check polynomial of the LDPC-CC having the time variation period 3 satisfying any one of # Xk1 to # Xk14 and any of # P1 to # P14 is shown below.

Code rate R = 1/2:

Code rate R = 2/3:

Code rate R = 3/4:

Code rate R = 4/5:

FIG. 22 shows (i = 1, when the parity check polynomial of LDPC-CC shown in the equations (48-i), (49-i), (50-i), and (51-i) is used. 2 and 3), an example of the required number of terminations is shown.

なお、ｋ＝Ｉ_ｓ％（ｎ−１）である。 FIG. 23 shows information at each coding rate represented by the formulas (48-i), formula (49-i), formula (50-i), and formula (51-i) (i = 1, 2, 3). shows the relationship between the size I _s and the termination number m _t. Incidentally, during when the number of virtual known information bits ( "0") to be inserted to create a termination sequence and m _z, if the code rate (n-1) / n, and m _t and m _z The following relationship holds.

In addition, k = _Is % (n-1).

(Embodiment 5)
In the present embodiment, when the LDPC-CC having the good characteristics described in the fourth embodiment is used, the communication device can avoid deterioration of the error correction capability and the deterioration of the information transmission efficiency. And the communication method will be described.

From FIGS. 21 and 22, it was confirmed that the number of terminations required for information-zero-termination differs depending on the information size. Therefore, in order to fix the number of terminations uniformly regardless of the information size and not to deteriorate the error correction capability, it is necessary to set the number of terminations to a large number, and Real R (effective coding rate) decreases. , Information transmission efficiency may decrease.

Therefore, in the present embodiment, a communication device and a communication method for changing the number of terminations transmitted as redundant bits according to the information size will be described. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

FIG. 24 is a block diagram showing a configuration of a main part of the communication device 600 according to the present embodiment.

The coding rate setting unit 610 inputs a control information signal including information on the coding rate set by the own device or a feedback signal transmitted from the communication device of the communication partner. When the control information signal is input, the code rate setting unit 610 sets the code rate from the code rate information included in the control information signal.

When the feedback signal is input, the coding rate setting unit 610 provides information on the communication status with the communication device of the communication partner included in the feedback signal, for example, a bit error rate, a packet error rate, and a frame. Information that can estimate the communication quality such as the error rate and the received electric field strength is acquired, and the coding rate is set from the information of the communication status with the communication device of the communication partner. The code rate setting unit 610 includes the set code rate information in the set code rate signal, and directs the set code rate signal toward the termination sequence length determination unit 631 and the parity calculation unit 632 in the encoder 630. Output. Further, the coding rate setting unit 610 outputs the information of the set coding rate to the transmission information generation and information length detection unit 620.

The transmission information generation and information length detection unit 620 generates or acquires transmission data (information), and outputs an information sequence composed of transmission data (information) to the parity calculation unit 632. Further, the transmission information generation and information length detection unit 620 detects the series length of the transmission data (information) (hereinafter referred to as "information length"), that is, the information size, and includes the information of the detected information size in the information length signal. , The information length signal is output to the termination sequence length determination unit 631. Further, the transmission information generation and information length detection unit 620 is composed of known information bits (for example, “0”) necessary for generating redundant bits corresponding to the termination sequence length notified from the termination sequence length determination unit 631. The known information series is added to the end of the information series.

The termination sequence length determination unit 631 determines the termination sequence length (number of terminations) according to the information size indicated by the information length signal and the coding rate indicated by the set coding rate signal. The specific method for determining the termination series length will be described later. The termination sequence length determination unit 631 includes the determined termination sequence length in the termination sequence length signal, and outputs the termination sequence length signal to the transmission information generation and information length detection unit 620 and the parity calculation unit 632.

The parity calculation unit 632 calculates the parity for the information sequence and the known information sequence, and outputs the obtained parity to the modulation unit 640.

The modulation unit 640 performs modulation processing on the information sequence and the parity (including the termination sequence).

Although it is described as "Information Length signal" in FIG. 24, it is not limited to this, and any signal can be used as long as it is information that can be used as an index for controlling the termination sequence length. You may. For example, the frame length of the transmission signal can be obtained from the sum information (Length information) of the number of information excluding termination and the number of parity, and the information of the number of information and the modulation method, and the frame length can be used instead of the information length signal. good.

Next, a method of determining the termination sequence length in the termination sequence length determination unit 631 will be described with reference to FIG. 25. FIG. 25 shows an example in which the termination sequence length is switched to two stages based on the information size and each coding rate. Note that FIG. 25 assumes that the minimum information size of the communication device 600 is set to 512 bits. However, the minimum size does not necessarily have to be defined.

In FIG. 25, α is the information length of the transmission data (information) that must be transmitted. For example, when the coding rate is 1/2, in 512 ≦ α ≦ 1023, the termination series length determination unit 631 sets the termination series length to 380 bits, and in 1024 ≦ α, the termination series length determination unit 631 determines. Set the termination sequence length to 340 bits. In this way, the termination sequence length determination unit 631 sets the termination sequence length based on the information length α of the transmission data (information), so that the termination sequence length does not deteriorate the error correction capability and the error correction capability is not deteriorated. The series length will be set so that the decrease in information transmission efficiency can be prevented.

In the above, the case where the termination sequence length is switched to two stages at each coding rate has been described as an example, but the present invention is not limited to this, and for example, as shown in FIG. 26, there are three stages or more stages. You may switch the termination series length with. In this way, by switching the termination series length (number of terminations) to a plurality of stages based on the information length (information size), the termination series length does not deteriorate the error correction capability and the information transmission efficiency is lowered. It becomes possible to set a suitable series length that can prevent.

The communication device 600 uses, for example, a transmission format as shown in FIG. 27 to include information on the code rate in a symbol relating to the code rate, so that the code rate used by the encoder 630 is set to the communication device of the communication partner. Notify to. Further, the communication device 600 notifies the communication device of the communication partner of the information of the information length (information size) by including the information of the information length (information size) in the symbol related to the information size. Further, the communication device 600 includes the modulation method, the transmission method, or the information for identifying the communication partner in the control information symbol and notifies the communication device of the communication partner. Further, the communication device 600 includes the information sequence and the parity in the data symbol and notifies the communication device of the communication partner.

FIG. 28 shows a configuration example of a communication device 700 of a communication partner that communicates with the communication device 600. In the communication device 700 of FIG. 28, components common to those of FIG. 20 are designated by the same reference numerals as those of FIG. 20, and the description thereof will be omitted. The communication device 700 of FIG. 28 includes a control information generation unit 710 and a decoder 720 in place of the control information generation unit 530 and the decoder 300 with respect to the communication device 500 of FIG.

The control information generation unit 710 extracts code rate information from the code rate symbols obtained by demodulating (and decoding) the baseband signal. Further, the control information generation unit 710 extracts information on the information length (information size) from the symbols related to the information size obtained by demodulating (and decoding) the baseband signal. Further, the control information generation unit 710 extracts information for identifying the modulation method, the transmission method, or the communication partner from the control information symbol. The control information generation unit 710 outputs a control signal including the extracted coding rate information and information length (information size) information to the log-likelihood ratio generation unit 520 and the decoder 720.

The decoder 720 holds a table of the relationship between the information size and the termination sequence length at each code rate as shown in FIG. 25 or 26, and this table, the code rate information, and the code rate information, and From the information of the information length (information size), the termination series length included in the data symbol is determined. The decoder 720 performs BP decoding based on the coding rate and the determined termination sequence length. As a result, the communication device 700 can perform decoding with high error correction capability.

29 and 30 are diagrams showing an example of the flow of information between the communication device 600 and the communication device 700. FIG. 29 and FIG. 30 differ in whether the coding rate is set by the communication device 600 or the communication device 700. Specifically, FIG. 29 shows the flow of information when the communication device 600 determines the coding rate, and FIG. 30 shows the flow of information when the communication device 700 determines the coding rate. ..

As described above, in the present embodiment, the termination sequence length determination unit 631 determines the sequence length of the termination sequence to be added to the tail of the information sequence and transmitted according to the information length (information size) and the coding rate. After determining, the parity calculation unit 632 applies LDPC-CC coding to the information sequence and the known information sequence necessary for generating the termination sequence for the determined termination sequence length, and calculates the parity sequence. I made it. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

(Embodiment 6)
In the fifth embodiment, a case where the termination series length to be added to the tail of the information series is determined (changed) according to the information length (information size) and the coding rate has been described. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

In the present embodiment, as in the fifth embodiment, when the termination sequence length is changed according to the information length (information size), a case where a limit is provided on the coding rate that can be used will be described. As a result, deterioration of the error correction capability can be avoided.

FIG. 31 shows the case where the parity check polynomials of LDPC-CC shown in the equations (44-i), (45-i), (46-i), and (47-i) are used as in FIG. The relationship between the number of terminations required for (i = 1, 2, 3) and the coding rate is shown. As can be seen from FIG. 31, when the information sizes are 512 bits, 1024 bits, and 2048 bits, the effective coding rate (Real R) having a coding rate of 3/4 and the effective coding rate having a coding rate of 4/5 are calculated. By comparison, there is no big difference between the two. For example, when the information size is 1024 bits, the effective coding rate is 0.5735 at the coding rate 3/4, whereas the effective coding rate is 0.5626 at the coding rate 4/5, and the difference is small. It is about 0.01. Further, the effective coding rate of the coding rate 3/4 is larger than the effective coding rate of the coding rate 4/5, and the magnitude of the effective coding rate is reversed. Therefore, depending on the information size, even if the coding rate 3/4 is used, there are cases where a high error correction capability is obtained and it is not suitable for improving the transmission efficiency.

In FIGS. 32A, 32B, 32C and 32D, the bit error rate when the termination sequence of the sequence length shown in FIG. 31 is added to the information sequence having the information sizes of 512 bits, 1024 bits, 2048 bits and 4096 bits. (Bit Error Rate: BER) / Block Error Rate (BLER) characteristics are shown. In FIGS. 32A, 32B, 32C and 32D, the horizontal axis indicates SNR (Signal-to-Noise power ratio) [dB], the vertical axis indicates BER / BLER characteristics, the solid line indicates bit error rate characteristics, and the broken line. Shows the block error rate characteristic. Further, in FIGS. 32A, 32B, 32C and 32D, TMN indicates a terminaltion number.

As can be seen from FIGS. 32A, 32B, 32C and 32D, when the termination sequence is taken into consideration, the BER / BLER characteristic with a coding rate R = 3/4 has a coding rate R regardless of the information size. It can be seen that it is superior to the BER / BLER characteristic of = 4/5.

From these two points, in order to achieve both improvement in error correction capability and improvement in information transmission efficiency, for example, if the information size is less than 4096 bits, the coding rate R = 4/5 is not supported, that is, , When the information size is less than 4096 bits, only the coding rate R = 1/2, 2/3, 3/4 is supported, and when the information size is 4096 bits or more, the coding rate R = 1/2, 2/3. By supporting, 3/4, 4/5, when the information size is less than 4096 bits, the code rate R = 4/5, which is less efficient than the code rate R = 3/4, is used. Therefore, it is possible to achieve both an improvement in error correction capability and an improvement in information transmission efficiency.

Further, from FIGS. 32A, 32B, 32C and 32D, it can be seen that the BER / BLER characteristic having an information size of 512 bits (see FIG. 32A) is remarkably superior to the BER / BLER characteristic having another information size. .. For example, when the information size is 512 bits, the BER characteristic with a coding rate of 2/3 has almost the same characteristics as the BER / BLER characteristic with a coding rate of 1/2 when the information size is 1024 bits. When the information size is 512 bits, it may not actually be necessary to have the BER / BLER characteristic with a coding rate of 1/2. The lower the coding rate, the lower the propagation efficiency. Therefore, in consideration of these points, for example, when the information size is 512 bits, it is possible to take a method of not supporting the coding rate 1/2. ..

FIG. 33 is a correspondence table between the information size and the support coding rate. As shown in FIG. 33, there are unsupported code rates depending on the information size. As long as the supported coding rate is constant regardless of the information size, the communication device 600 and the communication device 700 can communicate with each other in both cases of FIGS. 29 and 30. However, as shown in FIG. 33, in the present embodiment, there is an unsupported code rate depending on the information size, so it is necessary to adjust the specified code rate. Hereinafter, the communication device according to the present embodiment will be described.

FIG. 34 is a block diagram showing a configuration of a main part of the communication device 600A according to the present embodiment. In the communication device 600A of FIG. 34, the components common to those of FIG. 24 are designated by the same reference numerals as those of FIG. 24, and the description thereof will be omitted. The communication device 600A of FIG. 34 includes a encoder 630A instead of the encoder 630 of FIG. 24. The encoder 630A adopts a configuration in which a coding rate adjusting unit 633 is added to the encoder 630.

The coding rate adjusting unit 633 sets the coding rate input from the coding rate setting unit 610 based on the information length (information size) included in the information length signal input from the transmission information generation and information length detecting unit 620. Adjust the coding rate contained in the rate signal. Specifically, the code rate adjusting unit 633 holds a correspondence table between the information size and the support code rate as shown in FIG. 33, and the code rate set based on the control information signal or the feedback signal. To adjust the coding rate by comparing with the correspondence table. For example, if the information length (information size) is 1024 bits and the set code rate signal shows a code rate of 4/5, the code rate adjustment is performed because the code rate of 4/5 is not supported from the correspondence table. Part 633 sets the code rate of 3/4 having the largest value among the code rates smaller than the code rate of 4/5 as the code rate. As shown in FIG. 31, when the information length (information size) is 1024 bits, the Real R at the coding rate of 4/5 is 0.5626, and the Real R with the coding rate of 3/4 is Real R (0.5735). It is smaller, and as shown in FIG. 32B, the BER / BLER characteristic is also better at a coding rate of 3/4. Therefore, when the information length (information size) is 1024, the error correction capability is not deteriorated and the information is provided by using the coding rate 3/4 instead of the coding rate 4/5. It is possible to prevent the transmission efficiency of the above from decreasing.

In other words, when the first code rate (3/4) <the second code rate (4/5), the first effective coding corresponding to the first code rate (3/4). If the rate (0.5735) is comparable to the second effective code rate (0.5626) corresponding to the second code rate (4/5) and a second code rate is specified, then the code The conversion rate adjusting unit 633 adjusts the coding rate to the first coding rate. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

Further, for example, when the information length (information size) is 512 bits and the set code rate signal shows a code rate of 1/2, the code rate 1/2 is not supported from the correspondence table, so the code is used. The conversion rate adjusting unit 633 sets the coding rate to 2/3, which has the smallest value among the coding rates larger than the coding rate 1/2. As shown in FIG. 32A, the BER / BLER characteristic with a coding rate of 1/2 is extremely good. Therefore, even if the coding rate is set to 2/3, the error correction capability is not deteriorated and information is transmitted. It is possible to prevent the efficiency from decreasing.

In other words, when the first coding rate having extremely good BER / BLER characteristics is specified, the coding rate adjusting unit 633 has a coding rate higher than that of the first coding rate and has a predetermined line quality. The coding rate is adjusted to a second coding rate that can secure the above.

As described above, in the present embodiment, the number of coding rates supported by the communication device 600A is changed based on the information length (information size). For example, in the example shown in FIG. 33, when the information length (information size) is less than 512 bits, the communication device 600A supports only two coding rates, and when the information length (information size) is 512 bits or more and less than 4096 bits. Three coding rates are supported, and four coding rates are supported when the information length (information size) is 4096 or more. By changing the supported coding rate, it is possible to achieve both improvement in error correction capability and improvement in information transmission efficiency.

As described above, according to the present embodiment, the coding rate adjusting unit 633 changes the number of coding rates supported by the communication device 600A according to the information length (information size), and sets the coding rate. , Adjusted to one of the supported code rates. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

Further, the communication device 600A supports a code rate having a small value among code rates having the same effective code rate. Further, the communication device 600A does not include the BER / BLER characteristics in the coding rate supporting the extremely good coding rate, and supports only the coding rate capable of ensuring a predetermined line quality. As a result, it is possible to avoid a decrease in transmission efficiency while ensuring a predetermined line quality.

As described above, by changing the number of supported coding rates according to the information length (information size), it is possible to achieve both improvement of error correction capability and improvement of information transmission efficiency.

When changing the number of supported coding rates according to the information length (information size), the communication device 600A adjusts the coding rate, sets the termination sequence length, and these, as shown in FIG. 29. When the code rate information and the information length (information size) information (or the termination sequence length information) are simultaneously transmitted to the communication device 700 of the communication partner, the communication device 700 can correctly decode the information.

As a matter of course, the present embodiment may be used in combination with the fifth embodiment. That is, the number of terminations may be changed depending on the coding rate and the information size.

On the other hand, as shown in FIG. 30, when the communication device of the communication partner of the communication device 600 sets the coding rate before the communication device 600A determines the information length (information size), or as shown in FIG. 35. As described above, when the communication device 600A sets the coding rate before the communication device 600A determines the information length (information size), the communication device of the communication partner of the communication device 600A is based on the information length (information size). It is necessary to adjust the coding rate. FIG. 36 is a block diagram showing the configuration of the communication device 700A in this case.

In the communication device 700A of FIG. 36, components common to those of FIG. 28 are designated by the same reference numerals as those of FIG. 28, and description thereof will be omitted. The communication device 700A of FIG. 36 has a configuration in which a coding rate adjusting unit 730 is added to the communication device 700 of FIG. 28.

In the following, the communication device 600A supports a coding rate of 1/2, 2/3, 3/4 when the information length (information size) is less than 4096 bits, and a code when the information length (information size) is 4097 bits. A case of supporting the conversion rate of 1/2, 2/3, 3/4, 4/5 will be described.

At this time, before the information length (information size) is determined, the coding rate of the information series to be transmitted is determined to be 4/5, and the communication device 600A and the communication device 700A share the information of this coding rate. It is assumed that When the information length (information size) is 512 bits, the code rate adjusting unit 633 of the communication device 600A adjusts the code rate to 3/4 as described above. If this rule is determined in advance between the communication device 600A and the communication device 700A, the communication device 600A and the communication device 700A can communicate correctly.

Specifically, the coding rate adjusting unit 730 receives a control signal including the coding rate information and the information length (information size) information as an input, like the coding rate adjusting unit 633, and the information length (information). The code rate is adjusted based on the size). For example, when the code rate adjusting unit 730 has an information length (information size) of 512 bits and the code rate is 4/5, the code rate adjusting unit 730 adjusts the code rate to 3/4. .. As a result, it is possible to prevent the error correction capability from being deteriorated and the information transmission efficiency from being lowered.

As another coding rate adjusting method, a method of keeping the number of terminations constant regardless of the coding rate can be considered. In the example of FIG. 21, when the information length (information size) is 6144 or more, the number of terminations is uniformly 340 bits. Therefore, when the information length (information size) is 6144 bits or more, the coding rate adjusting unit 633 and the coding rate adjusting unit 730 may set the number of terminations to be constant regardless of the coding rate. .. When the information length (information size) is less than 6144, the code rate adjustment unit 633 and the code rate adjustment unit 730 use, for example, another parity check polypoly suitable for a termination number of 340 bits. It may correspond to the coding rate. Moreover, you may use a completely different code. For example, a block code may be used.

(Embodiment 7)
In each of the above embodiments, the LDPC-CC capable of sharing circuits corresponding to a plurality of coding rates having a coding rate of 1/2 or more in the encoder / decoder has been described. Specifically, an LDPC-CC capable of sharing a circuit and capable of a coding rate (n-1) / n (n = 2, 3, 4, 5) has been described. In this embodiment, a method of dealing with a coding rate of 1/3 will be described.

FIG. 37 is a block diagram showing an example of the configuration of the encoder according to the present embodiment. In the encoder 800 of FIG. 37, the code rate setting unit 810 outputs the code rate to the control unit 820, the parity calculation unit 830, and the parity calculation unit 840.

The control unit 820 controls the coding rate setting unit 810 so that information is not input to the parity calculation unit 840 when the coding rate 1/2, 2/3, 3/4, 4/5 is specified. Further, the control unit 820 controls so that when the coding rate 1/3 is set, the same information as the information input to the parity calculation unit 830 is input to the parity calculation unit 840.

The parity calculation unit 830 is defined by, for example, the equation (44-i), the equation (45-i), the equation (46-i), the equation (47-i) (i = 1,2,3), and the reference numeral. This is an encoder that obtains parity with a conversion rate of 1/2, 2/3, 3/4, 4/5.

Then, when the coding rate setting unit 810 specifies the coding rates 1/2, 2/3, 3/4, 4/5, the parity calculation unit 830 performs coding based on the corresponding parity check polynomial. , Output parity.

Then, when the coding rate setting unit 810 specifies the coding rate 1/3, the parity calculation unit 830 performs the coding rate 1/2 (formula (44-1), formula (44-2), formula ( Coding is performed based on the parity check polynomial of the LDPC-CC having the time variation period 3 (defined in 44-3)), and the parity P is output.

The parity calculation unit 840 is a encoder that obtains a parity with a coding rate of 1/2. When the coding rate setting unit 810 specifies the coding rates 1/2, 2/3, 3/4, 4/5, the parity calculation unit 840 does not output the parity.

When the coding rate setting unit 810 specifies the coding rate 1/3, the parity calculation unit 840 inputs the same information as the information input to the parity calculation unit 830, and the coding rate is 1/2. Coding is performed based on the parity check polypoly of LDPC-CC having a time-varying period 3, and parity Pa is output.

In this way, the encoder 800 outputs information, parity P, and parity Pa, so that the encoder 800 can support a coding rate of 1/3.

FIG. 38 is a block diagram showing an example of the configuration of the decoder according to the present embodiment. The decoder 900 of FIG. 38 is a decoder corresponding to the encoder 800 of FIG. 37.

The control unit 910 inputs the code rate information indicating the code rate and the log-likelihood ratio, and when the code rate is 1/2, 2/3, 3/4, 4/5, the BP decoding unit 930 is used. Control so that the log-likelihood ratio is not input. Further, when the coding rate is 1/3, the control unit 910 controls so that the log-likelihood ratio, which is the same as the log-likelihood ratio input to the BP decoding unit 920, is input to the BP decoding unit 930.

The BP decoding unit 920 operates at all code rates. Specifically, when the coding rate is 1/3, the BP decoding unit 920 performs BP decoding using the parity check polynomial with a coding rate of 1/2 used in the parity calculation unit 830. When the coding rate is 1/3, the BP decoding unit 920 outputs the log-likelihood ratio corresponding to each bit obtained by performing the BP decoding toward the BP decoding unit 930. On the other hand, when the coding rate is 1/2, 2/3, 3/4, 4/5, the BP decoding unit 920 has the coding rate 1/2, 2/3, 3 used in the parity calculation unit 830. BP decoding is performed using the parity check polynomial of / 4, 4/5. The BP decoding unit 920 outputs the obtained log-likelihood ratio after performing iterative decoding a predetermined number of times.

The BP decoding unit 930 operates only when the coding rate is 1/3. Specifically, the BP decoding unit 930 performs BP decoding using the parity check polynomial with a coding rate of 1/2 used in the parity calculation unit 840, and the bits obtained by performing the BP decoding are used. The corresponding log-likelihood ratio is output to the BP decoding unit 920, repeated decoding is performed a predetermined number of times, and then the obtained log-likelihood ratio is output.

In this way, the decoder 900 repeatedly decodes while exchanging the log-likelihood ratio, performs decoding such as turbo decoding, and decodes at a coding rate of 1/3.

(Embodiment 8)
In the second embodiment, coding for creating an LDPC-CC having a time-varying period g (g is a natural number) capable of corresponding to a plurality of coding rates (r-1) / r (r is an integer of 2 or more and q or less). I explained the vessel. In the present embodiment, another LDPC-CC having a time-varying period g (g is a natural number) capable of corresponding to a plurality of coding rates (r-1) / r (r is an integer of 2 or more and q or less) is created. A configuration example of the encoder is shown.

FIG. 39 is a configuration example of the encoder according to the present embodiment. In the encoder of FIG. 39, components common to those of FIG. 37 are designated by the same reference numerals as those of FIG. 37, and the description thereof will be omitted.

In the encoder 800 of FIG. 37, the parity calculation unit 830 is a encoder that obtains the parity of the coding rate of 1/2, 2/3, 3/4, 4/5, and the parity calculation unit 840 is a code. Whereas the encoder 800A in FIG. 39 is a encoder that obtains parity with a conversion rate of 1/2, when both the parity calculation unit 830A and the parity calculation unit 840A have, for example, a coding rate of 2/3. The LDPC-CC of the variable period 3 is encoded, and the parity calculation unit 830A and the parity calculation unit 840A are codes defined by different parity check polynomies.

The control unit 820A controls the coding rate setting unit 810 so that information is not input to the parity calculation unit 840A when the coding rate 2/3 is specified. Further, when the coding rate 1/2 is set, the control unit 820A controls so that the same information as the information input to the parity calculation unit 830A is input to the parity calculation unit 840A.

The parity calculation unit 830A is, for example, an encoder that obtains the parity of the coding rate 2/3 defined by the equations (45-1), (45-2), and (45-3). Then, when the coding rate setting unit 810 specifies the coding rates 1/2 and 2/3, the parity calculation unit 830A outputs the parity P.

The parity calculation unit 840A is a encoder that obtains a parity with a coding rate of 2/3 defined by a parity check polynomial different from that of the parity calculation unit 830A. The parity calculation unit 840A outputs the parity Pa only when the coding rate setting unit 810 specifies the coding rate 1/2.

As a result, when the coding rate 1/2 is specified, the encoder 800A outputs the parity P and the parity Pa for the information 2 bits, so that the encoder 800A sets the coding rate 1/2. It can be realized.

As a matter of course, in FIG. 39, the coding rates of the parity calculation unit 830A and the parity calculation unit 840A are not limited to 2/3, and the coding rates may be 3/4, 4/5, .... The coding rates of the parity calculation unit 830A and the parity calculation unit 840A may be the same.

The embodiments of the present invention have been described above. The invention relating to LDPC-CC described in the first to fourth embodiments and the invention relating to the relationship between the information size and the termination size described in the fifth and subsequent embodiments are independently established. ..

Further, the present invention is not limited to all the above-described embodiments, and various modifications can be made. For example, in the above-described embodiment, the case where it is realized by a encoder and a decoder is mainly described, but the present invention is not limited to this, and it can be applied even when it is realized by a power line communication device. be.

It is also possible to perform this coding method and decoding method as software. For example, a program for executing the coding method and the communication method may be stored in a ROM (Read Only Memory) in advance, and the program may be operated by a CPU (Central Processor Unit).

Further, a program for executing the above-mentioned encoding method and decoding method is stored in a computer-readable storage medium, and the program stored in the storage medium is recorded in a computer's RAM (Random Access Memory), and the computer is stored in the computer. It may be operated according to the program.

Needless to say, the present invention is useful not only in wireless communication but also in power line communication (PLC), visible light communication, and optical communication.

The receiving device and the receiving method according to the present invention can avoid deterioration of the error correction capability and a decrease in information transmission efficiency even when termination is performed.

100 LDPC-CC encoder 110 Data calculation unit 120, 230, 632, 830, 830A, 840, 840A Parity calculation unit 130, 260 Weight control unit 140 mod2 adder 111-1 to 111-M, 121-1 to 121 -M, 221-1 to 221-M, 231-1 to 231-M Shift register 112-0 to 112-M, 122-0 to 122-M, 222-0 to 222-M, 232 to 232-M M weight multiplier 200, 630, 630A, 800, 800A Encoder 210 Information generator 220-1 First information calculation unit 220-2 Second information calculation unit 220-3 Third information calculation unit 240 Adder unit 250, 610 , 810 Code rate setting unit 300, 720, 900 Decoder 310 Log likelihood ratio setting unit 320 Matrix processing calculation unit 321 Storage unit 322 Row processing calculation unit 323 Column processing calculation unit 400, 500, 600, 600A, 700, 700A Communication device 410 Code rate determination unit 420,640 Modulation unit 510 Reception unit 520 Multiplication likelihood ratio generation unit 530,710 Control information generation unit 620 Transmission information generation and information length detection unit 631 Termination series length determination unit 633,730 Code Conversion rate adjustment unit 820, 820A, 910 Control unit 920, 930 BP decoding unit

Claims (10)

It is a transmission device that generates parity bits by a coding operation using a low density parity check convolutional code (LDPC-CC) for an information sequence composed of a plurality of bits and known information added to the information sequence. hand,
The sequence length of the first parity sequence is determined based on the sequence length and coding rate of the information sequence, and a part of the parity bits is generated based on the determined sequence length of the first parity sequence. A decision unit that determines the series length of known information, and
A coding unit that encodes the information sequence and the composite sequence of the known information into the parity bit by a coding operation using the low density parity check convolutional code (LDPC-CC).
A transmission unit that transmits the information sequence and the parity bit generated by the coding operation.
A transmitter. The determined sequence length of the first parity sequence has a different sequence length for each predetermined range of the sequence length of the information sequence.
The transmitting device according to claim 1. The known information is zero information,
The transmitting device according to claim 1 or 2. The determination unit determines one sequence length for each predetermined range of the sequence length of the information sequence as the sequence length of the first parity sequence.
The transmitter according to any one of claims 1 to 3. The determination unit determines a shorter sequence length as the sequence length of the first parity sequence as the sequence length of the information sequence is longer.
The transmitter according to claim 2 or 4. This is a transmission method in which parity bits are generated by a coding operation using a low density parity check convolutional code (LDPC-CC) for an information sequence composed of a plurality of bits and known information added to the information sequence. hand,
The sequence length of the first parity sequence is determined based on the sequence length and coding rate of the information sequence, and a part of the parity bits is generated based on the determined sequence length of the first parity sequence. The decision step to determine the sequence length of known information and
Based on the determined sequence length of the first parity sequence, the known information is added to the information sequence, and the information is obtained by a coding operation using the low density parity check convolutional code (LDPC-CC). A coding step for encoding the sequence and the composite sequence of the known information into the parity bits, and
A transmission method including a step of transmitting the information sequence and the parity bit generated by the coding operation. The determined sequence length of the first parity sequence has a different sequence length for each predetermined range of the sequence length of the information sequence.
The transmission method according to claim 6. The known information is zero information,
The transmission method according to claim 6 or 7. In the determination step, as the sequence length of the first parity sequence, one sequence length is determined for each predetermined range of the sequence length of the information sequence.
The transmission method according to any one of claims 6 to 8. In the determination step, the longer the sequence length of the information sequence, the shorter the sequence length is determined as the sequence length of the first parity sequence.
The transmission method according to claim 7 or 9.

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