JP5789014B2 - Encoding method, encoder, decoder - Google Patents

Description

  The present invention relates to an encoding method, an encoder, and a decoder for a low-density parity-check convolutional code (LDPC-CC).

  In recent years, attention has been focused on a low-density parity check (LDPC) code as an error correction code that exhibits high error correction capability with a feasible circuit scale. Since the LDPC code has a high error correction capability and is easy to implement, the LDPC code is adopted in an error correction coding system such as an IEEE802.11n high-speed wireless LAN system or a digital broadcasting system.

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

  However, many of the current communication systems are characterized in that transmission information is collectively transmitted for each variable-length packet or frame, as in Ethernet (registered trademark). When an LDPC code, which is a block code, is applied to such a system, for example, there is a problem of how a block of a fixed-length LDPC code corresponds to a variable-length Ethernet (registered trademark) frame. In IEEE802.11n, the length of the transmission information sequence and the block length of the LDPC code are adjusted by performing padding processing and puncture processing on the transmission information sequence. However, the coding rate changes depending on the padding and puncture. It is difficult to avoid transmitting redundant sequences.

  An LDPC code of such a block code (hereinafter referred to as LDPC-BC: Low-Density Parity-Check Block Code) can be encoded / decoded for an information sequence of an arbitrary length. Possible LDPC-CC (Low-Density Parity-Check Convolutional Code) has been studied (for example, see 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, an LDPC-CC parity check matrix H ^T [0, n] with a coding rate R = 1/2 (= b / c). Is shown in FIG. Here, the element h ₁ ^(m) (t) of H ^T [0, n] takes 0 or 1. All elements other than h ₁ ^(m) (t) are 0. M represents the memory length in LDPC-CC, and n represents the length of the LDPC-CC codeword. As shown in FIG. 47, in the LDPC-CC parity check matrix, 1 is set only in the diagonal term of the matrix and its neighboring elements, the lower left and upper right elements of the matrix are zero, and a parallelogram type. There is a feature that it is a matrix.

Here, when h ₁ ⁽⁰⁾ (t) = 1, h ₂ ⁽⁰⁾ (t) = 1, the LDPC-CC encoder defined by the parity check matrix H ^T [0, n] T is It is represented in FIG. As shown in FIG. 48, the LDPC-CC encoder is composed of M + 1 shift registers with a bit length c and a mod2 adder. For this reason, the LDPC-CC encoder is realized by a very simple circuit compared to a circuit that performs multiplication of a generator matrix and an LDPC-BC encoder that performs an operation based on the backward (forward) substitution method. There is a feature that can be. Further, since FIG. 48 shows a convolutional code encoder, it is not necessary to encode an information sequence by dividing it into fixed-length blocks, and an information sequence of an arbitrary 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. Y. Kou, S. Lin, and MPC Fossorier, “Low-density parity-check codes based on finite geometries: A rediscovery and new results,” IEEE Trans. Inform. Theory, vol.47, no.7, pp2711-2736 , Nov. 2001. A. J. Felstorom, and K. Sh. Zigangirov, “Time-Varying Periodic Convolutional Codes With Low-Density Parity-Check Matrix,” IEEE Transactions on Information Theory, Vol. 45, No. 6, pp2181-2191, September 1999 . RM Tanner, D. Sridhara, A. Sridharan, TE Fuja, and DJ Costello Jr., “LDPC block and convolutional codes based on circulant matrices,” IEEE Trans. Inform. Theory, vol.50, no.12, pp.2966 -2984, Dec. 2004. G. Richter, M. Kaupper, and K. Sh. Zigangirov, “Irregular low-density parity-Check convolutional codes based on protographs,” Proceeding of IEEE ISIT 2006, pp1633-1637. R. D. Gallager, “Low-Density Parity-Check Codes,” Cambridge, MA: MIT Press, 1963. 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. Yuichi Ogawa, “sum-product decoding of turbo codes,” Master's thesis, Nagaoka University of Technology, 2007. 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,” Trikes. A. Pusane, R. Smarandache, P. Vontobel, and D. J. Costello Jr., “On deriving good LDPC convolutional codes from QC LDPC block codes,” Proc. Of IEEE ISIT 2007, pp.1221-1225, June 2007. A. Sridharan, D. Truhachev, M. Lentmaier, DJ Costello, Jr., K. Sh. Zigangirov, “Distance Bounds for an Ensemble of LDPC Convolutional Codes,” IEEE Transactions on Information Theory, vol.53, no.12, Dec. 2007.

  Here, in the case of a block code, if the number of bits of transmission data is not an integral multiple of the block length of the code, it is necessary to transmit extra bits. Therefore, when LDPC-BC having a large block size or LDPC-CC having a large protograph size is used, the number of extra bits to be transmitted increases. In particular, in packet communication, when a packet having a small number of bits of transmission data is transmitted, there is a problem that the data transmission efficiency is remarkably reduced by transmitting extra bits. However, with the LDPC codes shown in Non-Patent Document 1 to Non-Patent Document 7, it is difficult to solve this problem. In order to solve this problem, it is required to design an LDPC-CC that can be configured with a protograph smaller in size than Non-Patent Document 1 to Non-Patent Document 7.

  In this regard, if the LDPC-CC is created from the convolutional code, the size of the protograph can be made smaller than those in Non-Patent Document 1 to Non-Patent Document 7.

  Then, when an LDPC-CC is created from a convolutional code and error correction coding using LDPC-CC is performed on the information sequence and transmitted, a device for improving reception quality is required.

  The present invention has been made in consideration of such points. Good reception is achieved when an LDPC-CC is generated from a convolutional code and error correction coding using LDPC-CC is performed on an information sequence and transmitted. An encoding method, an encoder, and a decoder for LDPC-CC capable of obtaining quality are provided.

  One aspect of the transmission apparatus of the present invention is an LDPC-CC (Low-Density Parity-Check Convolutional Code) having a time-varying period m using input data, a parity sequence generated in the past, and a parity check matrix of a convolutional code. And an encoder that generates an information sequence and a parity sequence as codewords, and a modulation unit that generates a transmission symbol obtained by modulating the codeword of the LDPC-CC, and the parity check matrix is expressed by Equation (120). Of the m different parity check polynomials represented by the following equation, km + q rows are defined based on the q-th parity check polynomial, and k is an integer of 0 or more and q is an integer of 1 to m.

  One aspect of the receiving apparatus of the present invention includes: a receiving unit that receives a modulated signal encoded by LDPC-CC (Low-Density Parity-Check Convolutional Code); and a parity check matrix for the received signal. And a decoder for performing BP (Belief Propagation) decoding, wherein the decoder performs a row processing operation unit that performs a row processing operation using the parity check matrix, and a column processing operation using the parity check matrix. A column processing calculation unit to perform, and a determination unit that estimates a codeword using calculation results in the row processing calculation unit and the column processing calculation unit, and the parity check matrix is expressed by Expression (120). Of the m different parity check matrices, km + q rows are defined based on the q-th parity check polynomial, and k is an integer of 0 or more and q is an integer of 1 to m.

  According to the present invention, attention is paid to a convolutional code as a small-sized protograph, and the parity check polynomial of the convolutional code is used as a protograph, whereby the reception quality is good and transmission is performed in the LDPC-CC design method. The number of extra bits can be reduced. Further, when creating an LDPC-CC from a convolutional code, “1” is added to a predetermined position of the approximate lower triangular matrix or upper trapezoidal matrix of the check matrix H, and the degree of the parity check polynomial of the convolutional code at this time is added. By increasing the size, if the receiving apparatus performs BP decoding or approximated BP decoding using the created LDPC-CC parity check matrix, good reception quality can be obtained.

The figure which shows the encoder of a (7,5) convolutional code. The figure which shows the check matrix of a (7,5) convolutional code. The figure which shows the check matrix of a (7,5) convolutional code. The figure which shows an example at the time of adding "1" to the approximate lower triangular matrix of the check matrix of FIG. The figure which shows an example of a structure of the check matrix of LDPC-CC in Embodiment 1. FIG. The figure which shows the check matrix of a (7,5) convolutional code. The figure which shows an example of a structure of the check matrix of LDPC-CC in Embodiment 1. FIG. The figure which shows the check matrix of a (7,5) convolutional code. The figure which shows an example at the time of adding "1" to the upper trapezoid matrix of the check matrix of FIG. The figure which shows an example of a structure of the check matrix of LDPC-CC in Embodiment 2. FIG. The figure which shows an example of a structure of the check matrix at the time of termination | terminus in Embodiment 3 The figure which shows an example of a structure of the check matrix at the time of termination | terminus in Embodiment 3 The figure which shows an example of a structure of the check matrix at the time of termination | terminus in Embodiment 3 The figure explaining the method of producing LDPC-CC from a convolutional code FIG. 15 is a diagram illustrating an example of a configuration of an LDPC-CC parity check matrix according to Embodiment 7 The figure which shows an example of a structure of the check matrix of LDPC-CC of the time-varying period 1 in Embodiment 7. FIG. The figure which shows an example of a structure of the check matrix of LDPC-CC of the time-varying period m in Embodiment 7. FIG. Illustration for explaining the number of puncture patterns The figure which shows the relationship between an encoding sequence and a puncture pattern Diagram showing the number of parity check polynomials that must be checked to select a puncture pattern The figure which shows an example of a structure of the check matrix of LDPC-CC of time-varying period 2 The figure which shows an example of a structure of the check matrix of LDPC-CC of time-varying period 4 The figure explaining the method of producing LDPC-CC from the convolutional code of coding rate 1 / n The figure explaining the method of producing LDPC-CC from the convolutional code of coding rate 1 / n The figure which shows an example of a structure of an encoder. The figure which shows an example of a structure of an encoder. Diagram showing decoder configuration using sum-product decoding algorithm The figure which shows an example of a structure of a transmitter Diagram showing an example of transmission format The figure which shows an example of a structure of a receiver The figure which shows an example of a structure of an encoding part. The figure which shows an example of a structure of the LDPC-CC encoding part using the check matrix which added "1" to the upper trapezoid matrix of the check matrix. The figure which shows an example of a structure of the check matrix of LDPC-CC of time-varying period 2 The figure which shows an example of a structure of the check matrix of LDPC-CC of time-varying period 7 The figure which shows the structure of the LDPC-CC check matrix in other Embodiment 7. FIG. Diagram for explaining a general puncture method The figure which shows a response | compatibility with the transmission codeword sequence v by the general puncture method, and the LDPC-CC check matrix H The figure for demonstrating the puncturing method in Embodiment 7 The figure which shows the response | compatibility with the transmission codeword sequence v by the puncture method in Embodiment 7, and the LDPC-CC check matrix H FIG. 10 is a block diagram showing another main configuration of the transmitting apparatus according to Embodiment 7. The figure which shows an example of the puncture pattern in Embodiment 7 The figure which shows another puncture pattern in Embodiment 7. FIG. The figure which shows another puncture pattern in Embodiment 7. FIG. The figure which shows another puncture pattern in Embodiment 7. FIG. The figure which shows another puncture pattern in Embodiment 7. FIG. Diagram for explaining the decoding processing timing Diagram showing FEC Encoder Diagram showing Structure of LDPC Convolusional Encoder a structure of LDPC-CC encoder The figure which shows the check matrix of LDPC-CC The figure which shows the structure of a LDPC-CC encoder.

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

(Embodiment 1)
In Embodiment 1, a method for designing a new LDPC-CC from the (7, 5) convolutional code will be described in detail.

  FIG. 1 is a diagram illustrating a configuration of an encoder for a (7, 5) convolutional code. The encoder shown in FIG. 1 includes shift registers 101 and 102 and exclusive OR circuits 103, 104, and 105. The encoder shown in FIG. 1 outputs an output x and a parity p for an input x. This code is a systematic code.

  In the present invention, it is important to use a convolutional code that is a systematic code. This point will be described in detail in the second embodiment.

Consider a convolutional code of coding rate 1/2 and generator polynomial G = [1 G ₁ (D) / G ₀ (D)] as an example. In this case, _{G 1} is feed-forward polynomial, _{G 0} represents a feedback polynomial. When the polynomial expression of the information sequence (data) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed as the following equation (1).

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

Here, the data at the time point i is represented as X _i , the parity is represented as P _i, and the transmission sequence W _i = (X _i , P _i ). The transmission vector w = (X ₁ , P ₁ , X ₂ , P ₂ ,..., X _i , P _i ...). Then, from equation (2), the check matrix H can be expressed as shown in FIG. At this time, the following relational expression (3) is established.

  Therefore, the receiving apparatus uses the check matrix H, BP (Belief Propagation) decoding as shown in Non-Patent Document 8 to Non-Patent Document 10, min-sum decoding approximating BP decoding, offset BP decoding, and Normalized. Decoding can be performed by using BP decoding, shuffled BP decoding, or the like.

  Here, in the parity check matrix of FIG. 2, the lower left portion (the lower left portion of 201 in FIG. 2) from row number = column number “1” is defined as an approximate lower triangular matrix. The upper right part of row number = column number “1” is defined as an upper trapezoid matrix.

  Next, the LDPC-CC design method in the present invention will be described in detail.

  In order to realize the encoder with a simple configuration, in the present embodiment, “1” is added to the approximate lower triangular matrix of the parity check matrix H for the (7, 5) convolutional code shown in FIG. Take the technique.

<Encoding method>
Here, as an example, it is assumed that “1” added to the parity check matrix in FIG. 2 is one for each of data and parity. When “1” is added to the approximate lower triangular matrix of the parity check matrix H in FIG. 2 for each of data and parity, the parity check polynomial is expressed as in the following equation (4). However, in formula (4), α ≧ 3 and β ≧ 3.

Therefore, the parity P (D) is expressed as the following equation (5).

When “1” is added to the approximate lower triangular matrix of the parity check matrix, D ^β P (D), D ² P (D), and DP (D) are past data and are known values. Parity P (D) can be obtained.

<Location to add “1”>
Next, the position of “1” to be added will be described in detail with reference to FIG. In FIG. 3, reference numeral 301 is “1” related to the decoding of the data X _{i at} the time point i, and reference numeral 302 is “1” related to the parity P _i at the time point i. A dotted line 303 is a protograph related to the propagation of external information with respect to the data X _i and the parity P _i at the time point i when one BP decoding is performed. That is, the reliability from time point i-2 to time point i + 2 is involved in propagation.

A boundary line 305 is drawn on the vertical axis for “1” (304) on the rightmost side of the protograph 303. Then, a boundary line 307 is drawn with respect to the leftmost “1” (306) adjacent to the boundary line 305. Then, “1” is added to the area 308 so that the reliability after the boundary line 305 is propagated to the data X _i and the parity P _i at the time point i. Accordingly, it is possible to propagate a probability that was not obtained before adding “1”, that is, a reliability other than the time point i−2 to the time point i + 2. In order to propagate a new probability, it is necessary to add to the area 308 in FIG.

  Here, in each row of the parity check matrix H in FIG. 3, the width of the rightmost “1” and the leftmost “1” is L. So far, the position where “1” is added has been described in the column direction. Considering this in the row direction, in the parity check matrix of FIG. 2, “1” is added to the left position of L−2 or more from the leftmost “1”. Further, in the case of explanation using a check polynomial, in equation (4), α may be set to 5 or more and β may be set to 5 or more.

This is expressed by a general formula. A general expression of the parity check polynomial of the convolutional code is expressed as the following expression (6).

When “1” is added to the approximate lower triangular matrix of the parity check matrix H, one for each of the data and parity, the parity check polynomial is expressed as the following equation (7).

  In this case, α may be set to 2K + 1 or more, and β may be set to 2K + 1 or more. K ≧ 2.

FIG. 4 is a diagram illustrating an example when “1” is added to the approximate lower triangular matrix of the parity check matrix in FIG. 3. When “1” is added to the data and parity at all times, the check matrix is represented as shown in FIG. FIG. 5 is a diagram illustrating an example of a configuration of an LDPC-CC parity check matrix according to the present embodiment. In FIG. 5, “1” in the areas 501 and 502 is the added “1”, and the code having the check matrix H is the LDPC-CC in the present embodiment. At this time, the check polynomial is expressed by the following equation (8).

  As described above, the transmission apparatus adds “1” to the approximate lower triangular matrix of the parity check matrix H and creates an LDPC-CC from the convolutional code, so that the reception apparatus uses the created LDPC-CC parity check matrix. By using BP decoding or approximated BP decoding, good reception quality can be obtained.

In this embodiment, the case where one “1” is added to each of data and parity has been described. However, the present invention is not limited to this, and for example, “1” is set to either data or parity. The method of adding may be used. For example, “1” may be added to data and “1” may not be added to parity. As an example, let us consider a case where there is no ^Dβ in the above equation (7). At this time, if α is set to 2K + 1 or more, the receiving apparatus can obtain good reception quality. Conversely, consider the case where there is no ^Dα in equation (7). At this time, if β is set to 2K + 1 or more, the receiving apparatus can obtain good reception quality.

Also, the reception quality is greatly improved by a code in which a plurality of “1” s are added to both data and parity. For example, as an example of inserting a plurality, a parity check polynomial of a certain convolutional code is expressed by equation (9). In Equation (9), K ≧ 2.

When a plurality of “1” s are added to the approximate lower triangular matrix of the parity check matrix H for data and parity, the parity check polynomial is represented by the following equation (10).

In this case, when α ₁ ,..., Α _{n is set} to 2K + 1 or more and β ₁ ,..., Β _m are set to 2K + 1 or more, good reception quality can be obtained in the receiving apparatus. This point is important in the present embodiment.

However, even if one or more of α ₁ ,..., Α _n satisfy 2K + 1 or more, good reception quality can be obtained in the receiving apparatus. Further, even when one or more of β ₁ ,..., Β _m satisfy 2K + 1 or more, good reception quality can be obtained in the receiving apparatus.

In addition, when the LDPC-CC parity check polynomial is expressed as in the following equation (11), when α ₁ ,..., Α _n are set to 2K + 1 or more, good reception quality can be obtained in the receiver. Can do. This point is important in the present embodiment.

However, even when one or more of α ₁ ,..., Α _n satisfy 2K + 1 or more, good reception quality can be obtained in the receiving apparatus.

Similarly, when the LDPC-CC parity check polynomial is expressed by the following equation (12), if β ₁ ,..., Β _m are set to 2K + 1 or more, good reception quality is obtained in the receiving apparatus. be able to. This point is important in the present embodiment.

However, even when one or more of β ₁ ,..., Β _m satisfy 2K + 1 or more, good reception quality can be obtained in the receiving apparatus.

  Next, a method for designing an LDPC-CC from a parity check polynomial different from Equation (2) of the (7, 5) convolutional code will be described in detail. Here, as an example, a case where two “1” s are added to data and two “1” s are added to parity will be described as an example.

Non-Patent Document 11 shows a parity check polynomial different from Equation (2) of the (7, 5) convolutional code. An example of this is expressed by the following equation (13).

  In this case, the check matrix H can be represented as shown in FIG.

<Encoding method>
Here, a case will be described in which two “1” s are added to each of data and parity in the parity check matrix of FIG. 6. When two “1” s are added to each of the data and parity in the approximate lower triangular matrix of the parity check matrix H in FIG. 6, the parity check polynomial is expressed as the following equation (14).

Therefore, the parity P (D) can be expressed as the following equation (15).

Thus, when “1” is added to the approximate lower triangular matrix of the parity check matrix, D ^β1 P (D), D ^β2 P (D), D ⁹ P (D), D ⁸ P (D), D ³ Since P (D) and DP (D) are past data and are known values, the parity P (D) can be easily obtained.

<Location to add “1”>
In order to obtain the same effect as described above, when α ₁ and α ₂ are set to 19 or more and β ₁ and β ₂ are set to 19 or more, good reception quality can be obtained in the receiving apparatus. As an example, in the parity check matrix of FIG. 7, α ₁ = 26, α ₂ = 19, β ₁ = 30, and β ₂ = 24. Thereby, for the same reason as described above, the reception apparatus can obtain good reception quality.

  From the above example, a method for creating an LDPC-CC from a convolutional code is as follows. The following procedure is an example when the convolutional code is an encoding rate of 1/2.

  <1> Select a convolutional code that gives good characteristics.

  <2> A check polynomial for the selected convolutional code is generated (for example, Equation (6)). However, it is important to use the selected convolutional code as a systematic code. Further, the check polynomial is not limited to one as described above. It is necessary to select a check polynomial that gives good reception quality. At this time, it is better to use an equivalent check polynomial having a higher degree than the check polynomial generated from the generator polynomial (see Non-Patent Document 11).

  <3> A check matrix H of the selected convolutional code is created.

  <4> Probability propagation is considered for data or (and) parity, and “1” is added to the parity check matrix. The position where “1” is added is as described above.

  In the present embodiment, the method of creating the LDPC-CC from the (7, 5) convolutional code has been described. However, the present invention is not limited to the (7, 5) convolutional code, and other convolutional codes are used. Can be similarly implemented. At this time, the generating polynomial G of the convolutional code that gives good reception quality is described in detail in Non-Patent Document 12.

As described above, the transmitting apparatus according to this embodiment, in Formula _{(10), α 1, ···} , the alpha _n 2K + 1 or more, beta _1, · · ·, a beta _m is set to 2K + 1 or more By creating an LDPC-CC from a convolutional code, the receiving apparatus can obtain good reception quality by performing BP decoding or approximated BP decoding using the created LDPC-CC parity check matrix. Further, when the LDPC-CC is created from the convolutional code, the size of the protograph, that is, the check polynomial, is much smaller than the protographs shown in Non-Patent Document 6 and Non-Patent Document 7, so that the transmission data Therefore, it is possible to reduce the number of extra bits generated when a packet having a small number of bits is transmitted, and to suppress the problem that the data transmission efficiency is lowered.

(Embodiment 2)
In the second embodiment, a method for designing a new LDPC-CC from a (7, 5) convolutional code, in particular, a method for adding “1” to the upper trapezoid matrix of the parity check matrix will be described in detail.

  The structure of the (7, 5) convolutional code parity check polynomial and parity check matrix H is as described in the first embodiment.

  The LDPC-CC design method in the present invention will be described in detail.

  In order to realize the encoder with a simple configuration, in the invention in this embodiment, “1” is added to the upper trapezoid matrix of the check matrix H for the (7, 5) convolutional code shown in FIG. Take a technique.

<Encoding method>
Here, as an example, it is assumed that “1” to be added to the parity check matrix in FIG. 8 is added to each of data and parity. In this case, the check polynomial is expressed by the following equation (16). In the equation _{(16), α 1, ···} , α n ≦ -1, β 1, ···, a beta _m ≦ -1.

Therefore, the parity P (D) can be expressed as the following equation (17).

Here, in the equation (17), D ^α1 X (D),..., D ^αn X (D) is known because it is input data, but D ^β1 P (D) ^{,. βm} P (D) is an unknown value. Therefore, although it is possible to insert “1” for the upper trapezoid matrix of the parity check matrix H, the parity can be inserted even if “1” is inserted for the parity related one. It is difficult to find a bit. Therefore, “1” is inserted into the upper trapezoid matrix of the check matrix H related to the data. That is, when the parity check polynomial is expressed by equation (18), the parity P (D) can be expressed by the following equation (19), and the parity P (D) can be obtained.

  Here, in the case of a non-systematic code, since only parity bits exist in the check polynomial, it is difficult to obtain parity bits when “1” is added to the upper trapezoid matrix of the check matrix H as described above. It is. Thus, in the present invention, it can be seen that it is important to use a systematic code convolutional code.

<Location to add “1”>
Next, the position of “1” to be added will be described in detail with reference to FIG. In FIG. 8, reference numeral 801 is “1” related to the decoding of the data X _{i at} the time point i, and reference numeral 802 is “1” related to the parity p _i at the time point i. A dotted line 803 is a protograph related to the propagation of external information for the data X _i and the parity P _i at the time point i when BP decoding is performed once. That is, the reliability from time point i-2 to time point i + 2 is involved in propagation.

Then, the boundary lines 804 and 805 are drawn as in the first embodiment. Then, “1” is added to one of the regions 806 so that the reliability before the boundary line 804 is propagated to the data X _i at the time point i. As a result, it is possible to propagate a probability that was not obtained before adding “1”, that is, a probability other than the time point i + 2 to the time point i + 2. In order to propagate a new probability, it is necessary to add to the area 806 in FIG.

Here, in each row of the parity check matrix H in FIG. 8, the width of the rightmost “1” and the leftmost “1” is L. So far, the position where “1” is added has been described in the column direction. Considering this in the row direction, in the parity check matrix of FIG. 2, “1” is added to a position to the right of L−2 or more from the rightmost “1”. Further, in the case of explanation using a check polynomial, in the equation (18), α ₁ ,..., Α _n may be set to −2 or less.

  This is expressed by a general formula. A general expression of the parity check polynomial of the convolutional code is expressed as Expression (6).

When “1” is added to the upper trapezoidal matrix of the parity check matrix H, the parity check polynomial is represented by the following equation (20).

In this case, better reception quality can be obtained by setting α ₁ ,..., Α _n to −K−1 or less. However, even if one or more of α ₁ ,..., Α _n satisfy the condition of −K−1 or less, good reception quality can be obtained.

FIG. 9 is a diagram illustrating an example when “1” is added to the upper trapezoidal matrix of the parity check matrix in FIG. 3. FIG. 9 shows an example in which “1” is added to the area 806. Then, when “1” is added to the data at all points in the upper trapezoid matrix of the parity check matrix H, the parity check matrix is represented as shown in FIG. FIG. 10 is a diagram illustrating an example of a configuration of an LDPC-CC parity check matrix according to the present embodiment. In FIG. 10, “1” in the area 1001 is the added “1”, and the code having the matrix H shown in FIG. 10 as the check matrix is the LDPC-CC in the present embodiment. At this time, the check polynomial is expressed by the following equation (21).

As described above, according to the present embodiment, in the transmission apparatus, α ₁ ,..., Α _n are set to −K−1 or less in Equation (20), and an LDPC-CC is created from the convolutional code. Thus, the reception apparatus can obtain good reception quality by performing BP decoding or approximated BP decoding using the created LDPC-CC parity check matrix. In the present embodiment, an example has been described in which “1” is added to the upper trapezoid matrix of the parity check matrix for the data. However, the present invention is not limited to this, and the parity check matrix is combined with the first embodiment. In addition to adding “1” to the upper trapezoidal matrix, “1” may be added to the approximate lower triangular matrix of the parity check matrix. At this time, if the conditions described in Embodiment 1 are satisfied, better reception quality can be ensured.

  When “1” is added to the upper trapezoidal matrix of the check matrix, there is also an advantage that the convergence speed at the end of the third embodiment to be described later is improved. This point will be described in detail in Embodiment 3.

  Further, according to the present embodiment, LDPC-CC can be designed from a parity check polynomial different from equation (2) of the (7, 5) convolutional code, as in the first embodiment.

  In the present embodiment, the method of creating the LDPC-CC from the (7, 5) convolutional code has been described. However, the present invention is not limited to the (7, 5) convolutional code, and other convolutional codes can be used similarly. Can be implemented. At this time, the generating polynomial G of the convolutional code that gives good reception quality is described in detail in Non-Patent Document 12.

  Further, when the LDPC-CC is created from the convolutional code, the size of the protograph, that is, the check polynomial, is much smaller than the protographs shown in Non-Patent Document 6 and Non-Patent Document 7, so that the transmission data It is possible to reduce the number of extra bits to be transmitted that occur when a packet having a small number of bits is transmitted, and to suppress the problem that the data transmission efficiency is reduced.

(Embodiment 3)
In the third embodiment, as described in the first embodiment, when generating an LDPC-CC from a convolutional code, the problem of termination when “1” is added to the approximate lower triangular matrix of the parity check matrix A method for solving the problem will be described.

  FIG. 11 is a diagram illustrating an example of a parity check matrix at the time of termination. In FIG. 11, reference numeral 1100 denotes a boundary between information bits and termination bits. The “information bit” is a bit related to information that the transmitting apparatus wants to transmit to the receiving apparatus. On the other hand, the “termination bit” is an extra bit for accurately transmitting the information bit, and the termination bit itself does not belong to the information required by the receiving apparatus, and is necessary for accurately receiving the information bit. Is a bit.

Here, in the information bits, the last bit of the data bit is X _f , the last bit of the parity bit is P _f , and the time point is f. 11, 1101 corresponds to “1” regarding the data at the time point f, and 1102 corresponds to “1” regarding the parity at the time point f.

A check polynomial corresponding to the protograph of FIG. 11 is expressed as the following equation (22).

  In FIG. 11, reference numeral 1104 denotes a check matrix for the termination bit. The data bit to be transmitted with the termination bit is set to “0”. However, it is only an example that the data bit to be transmitted with the termination bit is set to “0”. If the transmitter / receiver is known information, the data bit to be transmitted with the termination bit is terminated regardless of the sequence. Can be a bit.

In FIG. 11, the time point f + 1, that is, the first check polynomial of the end bit is expressed as the following Expression (23).

Further, the check polynomial at the terminal bit at the time point f + 2 is expressed as the following Expression (24).

  As described above, in the present embodiment, as shown in FIG. 11, with the termination bit, the position of the added “1” is shifted with time, and the order of the check polynomial is reduced with time. It is characterized by. In FIG. 11, reference numeral 1105 indicates an example of the configuration of “1” related to the addition of the termination bit. In FIG. 11, the added “1” exists in the parity.

  Since the terminal bit sequence transmitted from the transmitter is known, the receiver can set the likelihood of the terminal bit to be known when performing BP decoding.

  As described above, according to the present embodiment, the speed at which the trellis diagram is stabilized (converges) is improved by decreasing the order of the check polynomial with time in the termination bit. Therefore, the number of bits transmitted for termination can be reduced, and the data transmission efficiency can be improved.

  FIG. 12 is a diagram illustrating an example of a check matrix configuration related to “information bits” and “termination bits” different from those in FIG. In FIG. 12, reference numeral 1200 indicates a boundary between information bits and termination bits.

Here, in the information bits, the last bit of the data bit is X _f , the last bit of the parity bit is P _f , and the time point is f. The code 1201 in the area 1203 in FIG. 12 corresponds to “1” regarding the data at the time point f, and the code 1202 corresponds to “1” regarding the parity at the time point f.

The check polynomial corresponding to the protograph of FIG. 12 is expressed as the following equation (25).

  In FIG. 12, reference numeral 1204 denotes a parity check matrix for terminal bits. The data bit to be transmitted with the termination bit is set to “0”. Note that the data bit to be transmitted by the termination bit is an example, and the transmission / reception apparatus may have any sequence of data bits to be transmitted by the termination bit as long as it is known information. .

In FIG. 12, the time point f + 1, that is, the first check polynomial of the terminal bit is expressed as the following Expression (26).

Further, the check polynomial at the terminal bit at the time point f + 2 is expressed as the following equation (27).

  Thus, as shown in FIG. 12, the termination bit is characterized in that the position of the added “1” is shifted with time, and the order of the check polynomial is reduced with time. In FIG. 12, reference numeral 1205 is an example of the configuration of “1” related to the addition of the termination bit. In FIG. 12, the added “1” exists in the data.

Further, in order to prevent the degradation of the reception quality of information bits, as described in Embodiment 1, the order of the check polynomial is reduced so as to satisfy the condition “2K + 1 or more”. Therefore, the final check bit polynomial of the end bit is expressed as the following Expression (28), for example.

  Since the terminal bit sequence transmitted from the transmitter is known, the receiver can set the likelihood of the terminal bit to be known when performing BP decoding.

  As described above, according to the present embodiment, the speed at which the trellis diagram stabilizes (converges) can be improved by reducing the order of the parity check polynomial with time in the terminal bit. Therefore, the number of bits transmitted for termination can be reduced, and the data transmission efficiency can be improved.

  Next, an example of a termination method using the method of adding “1” to the upper trapezoid matrix of the parity check matrix described in the second embodiment will be described. FIG. 13 is a diagram illustrating an example of a configuration of a check matrix related to “information bits” and “termination bits” different from those in FIGS. 11 and 12. In FIG. 13, reference numeral 1300 indicates a boundary between information bits and termination bits.

Here, in the information bits, the last bit of the data bit is X _f , the last bit of the parity bit is P _f , and the time point is f. In the area 1303 in FIG. 13, the code 1301 corresponds to “1” regarding the data at the time point f, and the code 1302 corresponds to “1” regarding the parity at the time point f.

The parity check polynomial corresponding to the protograph of FIG. 13 is assumed to be expressed by the following equation (29).

  In FIG. 13, reference numeral 1304 denotes a parity check matrix for terminal bits. The data bit to be transmitted with the termination bit is set to “0”. Note that the data bit to be transmitted by the termination bit is an example, and the transmission / reception apparatus may have any sequence of data bits to be transmitted by the termination bit as long as it is known information. .

In FIG. 13, the time point f + 1, that is, the first check polynomial of the end bit is expressed as the following equation (30).

Further, the check polynomial for the terminal bit at the time point f + 2 is expressed by the following equation (31).

  Thus, as shown in FIG. 13, in the termination bit, the position of the added “1” is shifted with time, and the order of the check polynomial is decreased with time (reference numeral 1305 in FIG. 13). Equivalent). In FIG. 13, reference numeral 1304 is an example of the configuration of a protograph of terminal bits. In FIG. 13, the added “1” exists in data and parity.

  Further, in order to prevent the degradation of the reception quality of information bits, as described in Embodiment 1, the order of the check polynomial is reduced so as to satisfy the condition “2K + 1 or more”.

  Another feature of the last bit in FIG. 13 is that the number of “1” additionally inserted in the parity check matrix is changed from 2 to 1 as shown in FIG. 13 from 1305 to 1306. is there. As a result, the speed at which the trellis diagram is stabilized (converged) is improved.

  In this embodiment, the number of “1” added to the check matrix is described as being reduced to 2 when transmitting information bits and then 1 when transmitting end bits. For example, the same effect can be obtained even if the number of “1” added to the check matrix is reduced to M when transmitting information bits and then to N (M> N) when transmitting termination bits. .

In FIG. 13, an advantage when “1” is added to the upper trapezoidal matrix of the check matrix (“1” of reference numeral 1307 in FIG. 13) will be described. For example, the data X _f-2 (1308) and the parity P _f-2 (1309) at the time point f-2 in FIG. 13 are affected by the termination bit 1310. As a result, the reception device improves the reception quality of the data X _f-2 (1308) at the time point f-2. Similarly, the same effect can be obtained for data after time point f-2. Thus, when “1” is added to the upper trapezoidal matrix of the check matrix, the speed at which the trellis diagram is stabilized (converges) can be improved due to the above-described effects.

  In the present embodiment, the order of the check polynomial is regularly decreased (the order is decreased every time the number of rows is increased by one), but the present invention has the same effect even if it is not regular. For example, the same effect can be obtained even if the order is reduced every few rows.

(Embodiment 4)
In the first and second embodiments, the method of designing the LDPC-CC from the (7, 5) convolutional code, that is, the feedback type convolutional code has been described. In this embodiment, a case will be described in which the LDPC-CC design method described in Embodiments 1 and 2 is applied to a feedforward type convolutional code. The advantage of using a feedforward type convolutional code is that if the constraint length is the same, the parity check matrix of the feedforward type convolutional code has lower row weights and column weights than the parity check matrix of the feedback type convolutional code. In addition, there is a feature that the number of loops of length 4 when a Tanner graph is drawn is small. A loop is a circuit (path that circulates) that starts at a certain node and ends at that node. If the number of loops having a length of 4 is large, the reception quality deteriorates (see Non-Patent Document 13). Therefore, when a feedforward type convolutional code is used, it is highly possible that reception quality is improved when BP decoding is performed. Therefore, the LDPC-CC designed from the feedforward type convolutional code has a feature that the performance is better than the LDPC-CC designed from the feedback type convolutional code.

Non-Patent Document 12 describes a feedforward type convolutional code that is a systematic code. Below, the case where the convolutional code of (1,1547) is used is demonstrated as an example. The check polynomial of the (1,1547) convolutional code is expressed as follows.

そして、ＬＤＰＣ−ＣＣ用の検査多項式として、以下式より与えられるＰ（Ｄ）を考える。

Then, the following equation is used as an example of a parity check polynomial different from equation (32) of the convolutional code (1,1547).

Then, P (D) given by the following equation is considered as a parity check polynomial for LDPC-CC.

In this case, α _1, ···, α _e is 15 or more integer, β _1, ···, β _f is 15 or more integer, γ _1, ···, γ _g is set to -1 or less integer . At this time, as described in the first embodiment and the second embodiment, at least one of α ₁ ,..., Α _e is set to an integer of 29 or more, and β _{1 ,.} At least one of them is set to an integer of 29 or more, and at least one of γ ₁ ,..., Γ _g is set to an integer of −15 or less. In addition, α _1, ···, α _e all the settings to 29 or more of integer, β _1, ···, β all _f is set to 29 or more of integer, γ _1, ···, γ _g all It is more effective to set the value to -15 or less. With this setting, the reception quality (decoding performance) can be greatly improved.

For example, in equation (40), γ ₁ = −25, γ ₂ = −55, and γ ₃ = −95, or in equation (40), γ ₁ = −25 and γ ₂ = −65. Or, in equation (39), when β ₁ = 35, γ ₁ = −40, and γ ₂ = −90, the reception quality (decoding performance) is greatly improved.

However, in Formula (36), Formula (37), and Formula (39), at least one of α ₁ ,..., Α _e is set to an integer of 29 or more, or β ₁ ,. , β _f is set to an integer greater than or equal to 29, or at least one of γ ₁ ,..., γ _g is set to −15 or less, the reception quality (decoding performance) Can greatly improve.

(Embodiment 5)
In the present embodiment, a method of creating an LDPC-CC with a coding rate of 1/3 from an LDPC-CC with a coding rate of 1/2 will be described in detail. Below, it demonstrates using the convolutional code | cord | chord which is a feedforward type | system | group code | symbol shown by the nonpatent literature 12, and a systematic code | cord | chord, and the (1,1547) convolutional code | symbol. The check polynomial of the (1,1547) convolutional code is expressed as follows.

Then, the following equation is used as an example of a parity check polynomial different from the equation (41) of the convolutional code of (1,1547).

Here, as a new parity sequence polynomial, consider Pn (D) given by the following equation.

The data at the time point i is X _i , the parity for P (D) of the equation (42) at the time point i is P _i , the equation (43) at the time point i, the equation (44), or the Pn of the equation (45) Assuming that the parity Pn _{i for} D), the transmission sequence W _i = (X _i , P _i , Pn _i ) can be expressed.

Then, the following equation is considered as a check polynomial for X (D) and P (D) for LDPC-CC, as in the fourth embodiment.

In this case, α _1, ···, α _e is 15 or more integer, β _1, ···, β _f is 15 or more integer, γ _1, ···, γ _g is set to -1 or less integer . At this time, as described in the first embodiment and the second embodiment, at least one of α ₁ ,..., Α _e is set to an integer of 29 or more, and β _{1 ,.} At least one of them is set to an integer of 29 or more, and at least one of γ ₁ ,..., Γ _g is set to −15 or less. However, α _1, ···, α _e all the settings to 29 or more of integer, β _1, ···, β all _f is set to 29 or more of integer, γ _1, ···, γ _g all It is more effective to set the value to -15 or less. With this setting, the reception quality (decoding performance) is greatly improved.

Then, the parity check polynomial for the new parity sequence Pn (D) for LDPC-CC is any one of Equations (43) to (45). At this time, at least one of a ₁ ,..., A _v is an integer of 29 or more, or at least one of a ₁ ,..., A _v is set to an integer of −15 or less. . Then, at least one of b _w ,..., B _w is set to an integer of 29 or more. However, if all of a ₁ ,..., A _v are set to an integer of 29 or more or an integer of −15 or less, reception quality (decoding performance) is greatly improved. Further, even if all of b ₁ ,..., B _w are set to integers of 29 or more, the reception quality (decoding performance) is greatly improved. Here, c _1, · · ·, but do not give a constraint for c _y, c _1, · · ·, at least one of c _y is effective when 29 or more integer, and generally thereof include, c _1, · · ·, in the c _y is made "0" is present one.

  Hereinafter, a method for generating an LDPC-CC of a convolutional code with a coding rate of 1/3 from a convolutional code with a coding rate of 1/2 will be summarized.

A parity check polynomial of a convolutional code with a coding rate of 1/2 is expressed by the following equation: + K _x (maximum order of terms of data X (D)), K ₁ (maximum order of terms of parity P (D)) _Is the maximum value of K _max .

Then, as in Embodiments 1 to 4 and other Embodiments 1, X (D) and P (D) LDPC-CC parity check polynomials are created. Thereafter, Pn (D) obtained from the equations (54) to (56) is considered as a new parity sequence polynomial.

At this time, at least one of a ₁ ,..., A _v is an integer greater than or equal to 2K _max +1, or at least one of a ₁ ,..., A _v is −K _max −1 or less. Set to an integer. Then, at least one of b ₁ ,..., B _w is set to an integer equal to or greater than 2K _max +1. If all of a ₁ ,..., A _v are set to integers of 2K _max +1 or more, or integers of −K _max −1 or less, reception quality (decoding performance) is greatly improved. Also, even if all b ₁ ,..., B _w are set to integers of 2K _max +1 or more, the reception quality (decoding performance) is greatly improved. Here, c _1, · · ·, but do not give a constraint for _{c y,} c _1, · · ·, at least one of _{c y} is effective when a _{2K max} +1 or greater, also generally, c _1, · · ·, in the c _y is made "0" is present one.

As described above, according to the present embodiment, the coding rate 1 is obtained by using the polynomial Pn (D) obtained from the equations (54) to (56) as the new parity sequence for the coding rate 1/3. An LDPC-CC with a coding rate of 1/3 is generated from a / 2 convolutional code. In this _{case, a 1, ···, a v} , b 1, ···, to b _w, by setting a limit as described above, check polynomial for encoding rate 1/2 P (D) It is possible to expand the range in which the reliability is propagated without adding any change to the reception quality (decoding performance).
Heretofore, the method for generating the LDPC-CC with the coding rate 1/3 from the convolutional code with the coding rate 1/2 has been described. Note that even when an LDPC-CC with a coding rate of 1/4 or less is generated, if a parity check polynomial for a new parity is generated under the same conditions as when an LDPC-CC with a coding rate of 1/3 is generated, An LDPC-CC with a coding rate of ¼ or less can be generated.

(Embodiment 6)
A modification of the method for generating LDPC-CC from the convolutional code described in Embodiment 4 will be described in detail.

Any of the following polynomials is considered as the parity check polynomial for LDPC-CC described in the fourth embodiment.

In this case, α _1, ···, α _e is 15 or more integer, β _1, ···, β _f is 15 or more integer, γ _1, ···, γ _g is set to -1 or less integer . At this time, as described in the first embodiment and the second embodiment, at least one of α ₁ ,..., Α _e is set to an integer of 29 or more, and β _{1 ,.} At least one of them is set to an integer of 29 or more, and at least one of γ ₁ ,..., Γ _g is set to an integer of −15 or less. In addition, α _1, ···, α _e all the settings to 29 or more of integer, β _1, ···, β all _f is set to 29 or more of integer, γ _1, ···, γ _g all It is more effective to set the value to -15 or less.

Then, the terms excluding the original convolutional code “1” and the maximum degree “D ¹⁴ ”, that is, the terms 1401 (D ¹⁰ ) and 1402 (D ⁵ , D ⁴ , D ³ , D ¹ ) in FIG. Select some terms from For example, as shown in FIG. 14, the term 1401 (D ¹⁰ ) is selected. Then, the selected terms are removed, and check polynomials such as the polynomial 1403 and the polynomial 1404 in FIG. 14 are considered. In polynomial 1403 in FIG. ^{14, D 10} is deleted, section ^{D z} is added relates X (D). In polynomial 1404 in FIG. ^{14, D 10} is deleted, section ^{D z} is added relates P (D). At this time, similarly to the description of the fourth embodiment, the reception quality is improved by setting z to an integer equal to or greater than 2K _max +1 with respect to the maximum order K _max (= 14). In the case of the polynomial 1403 in FIG. 14, the reception quality is improved even if z is an integer equal to or smaller than −K _max −1.

In FIG. 14, the case where the term 1401 (D ¹⁰ ) is selected and the term of D ^z is added has been described. However, the present invention is not limited to this, and a plurality of terms 1401 and 1402 are selected and the terms are removed. In addition, a plurality of D ^z terms may be added to create an LDPC-CC parity check polynomial.

Thus, in the present embodiment, at least one term is deleted except for the maximum degree D ^K of the original convolutional code, and at least one term of D ^z satisfying z ≧ 2K _max +1, Added for (D) or P (D). The LDPC-CC is configured using the parity check polynomial having the above configuration. Note that the term ^Dz may be added to X (D) and P (D).

  Moreover, although Formula (57) was demonstrated to the example, it is not restricted to this, In any case of Formula (58)-Formula (63), it can implement similarly. By performing such an operation, it is possible to delete a loop having a length of 4 in the Tanner graph described in Non-Patent Document 13 or a loop having a small length, for example, a loop having a length of 6, so This leads to a significant improvement.

(Embodiment 7)
In this embodiment, a configuration of a time-varying LDPC-CC that can easily perform puncturing and that has a simple encoder configuration will be described. In particular, in this embodiment, an LDPC-CC capable of periodically puncturing data will be described. In the LDPC code, a puncturing method for periodically puncturing data has not been sufficiently studied so far, and a method for performing puncturing in particular has not been sufficiently discussed. In LDPC-CC in the present embodiment, if data can be punctured periodically and regularly instead of being randomly punctured, degradation of reception quality can be suppressed. In the following, a configuration method of time-varying LDPC-CC capable of realizing the coding rate R = 1/2 will be described.

When the coding rate is 1/2 and the polynomial expression of the information sequence (data) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed as follows.

In the formula (64), a1, a2,..., An are integers of 1 or more (where a1 ≠ a2 ≠ ... ≠ an). Further, b1, b2,... Bm are integers of 1 or more (where b1 ≠ b2 ≠ ... ≠ bm). Here, in order to enable easy encoding, it is assumed that the terms D ⁰ X (D) and D ⁰ P (D) (D ⁰ = 1) exist. Therefore, P (D) is expressed as follows.

As can be seen from the equation (65), since D ⁰ = 1 exists and past parity terms, that is, b1, b2,..., Bm are integers of 1 or more, the parity P is sequentially changed. Can be sought.

Next, a parity check polynomial with a coding rate of 1/2 different from the equation (64) is expressed as follows.

In formula (66), A1, A2,..., AN are integers of 1 or more (provided that A1 ≠ A2 ≠... AN). Further, B1, B2,..., BM are integers of 1 or more (where B1 ≠ B2 ≠ ... ≠ BM). Here, it is assumed that the terms D ⁰ X (D) and D ⁰ P (D) (D ⁰ = 1) exist in order to enable easy encoding. At this time, P (D) is expressed as shown in Expression (67).

Hereinafter, data X and parity P at time 2i are represented by X _2i and P _2i , respectively, and data X and parity P at time 2i + 1 are represented by X _{2i + 1} and P _{2i + 1} , respectively (i: integer).

In the present embodiment, an LDPC-CC with a time-varying period of 2 calculated using the equation (65) for the parity P _2i at the time point 2i and calculated using the equation (67) for the parity P _{2i + 1} at the time point 2i + 1 is proposed. To do. Similar to the above-described embodiment, there is an advantage that the parity can be easily obtained sequentially.

Below, it demonstrates using Formula (68) and Formula (69) as an example of Formula (64) and Formula (66).

  At this time, the parity check matrix can be expressed as shown in FIG. In FIG. 15, (Ha, 11) is a portion corresponding to the equation (68), and (Hc, 11) is a portion corresponding to the equation (69). When the BP decoding is performed using the parity check matrix of FIG. 15, that is, the time-varying periodicity 2 parity check matrix, the data reception quality is greatly improved as compared with the LDPC-CC described in the first to sixth embodiments. Confirmed to do.

  Although the case where the time varying period is 2 has been described above, the time varying period is not limited to 2. However, if the time-varying period is too large, it is difficult to puncture periodically, and for example, it is necessary to puncture at random, so that reception quality may be deteriorated. Hereinafter, the advantage that the reception quality is improved by reducing the time-varying period will be described.

ここで、送信系列ベクトルｖ＝（ｖ１、ｖ２、ｖ３、ｖ４、ｖ５、ｖ６、・・・、ｖ2i、ｖ2i+1、・・・）である。 FIG. 16 shows an example of a puncturing method in the case of time varying period 1. In the figure, H is an LDPC-CC parity check matrix, and when a transmission sequence vector is represented by v, a relational expression of Expression (70) is established.

Here, the transmission sequence vector v = (v1, v2, v3, v4, v5, v6,..., V2i, v2i + 1,...).

  FIG. 16 shows an example in which a transmission sequence with a coding rate R = 1/2 is punctured to obtain a coding rate R = 3/4. When puncturing is performed periodically, first, a block cycle for selecting puncture bits is set. FIG. 16 shows an example in which the block period is set to 6 and the block is set as indicated by a dotted line (1602). Of the 6 bits constituting one block, 2 bits are selected as puncture bits, and the selected 2 bits are set as bits that are not transmitted. In FIG. 16, a bit 1601 surrounded by a circle is a bit that is not transmitted. In this way, a coding rate of 3/4 can be realized. Therefore, the transmission data series are v1, v3, v4, v5, v7, v9, v11, v13, v15, v16, v17, v19, v21, v22, v23, v25,.

  In FIG. 16, “1” surrounded by a square frame is set to 0 because the initial log likelihood ratio does not exist at the time of reception due to puncturing.

  In BP decoding, row operations and column operations are repeated. Therefore, if two or more bits (erasure bits) for which no initial log likelihood ratio exists (log likelihood ratio is 0) are included in the same row, the initial log likelihood ratio is calculated by column operation in that row. The log-likelihood ratio is not updated by the row operation alone until the log-likelihood ratio of bits for which there is no (the log-likelihood ratio is 0) is updated. That is, the reliability is not propagated by the row operation alone, and in order to propagate the reliability, it is necessary to repeat the row operation and the column operation. Therefore, when there are a large number of such rows, there is a limit on the number of iteration processes in BP decoding, or the reliability is not propagated even if the iteration process is performed many times, which causes deterioration in reception quality. It becomes. In the example shown in FIG. 16, the bit corresponding to 1 surrounded by a square frame indicates the erasure bit, and the row 1603 is a row in which reliability is not propagated by the row operation alone, that is, it causes deterioration in reception quality. Line.

  Therefore, as a method for determining puncture bits (bits not to be transmitted), that is, a method for determining a puncture pattern, it is necessary to search for a method that minimizes the number of rows whose reliability is not propagated by puncture alone. Hereinafter, a search for a puncture bit selection method will be described.

When 2 bits out of 6 bits constituting one block are set as puncture bits, there are _{3 × 2} C ₂ selection methods for 2 bits. Among these, the selection method that is cyclically shifted within 6 bits of the block period can be regarded as the same. Hereinafter, supplementary explanation will be given with reference to FIG. 18A. As an example, FIG. 18A shows six puncture patterns in the case of continuously puncturing 2 bits out of 6 bits. As shown in FIG. 18A, the puncture patterns # 1 to # 3 become the same puncture pattern by changing the block delimiter. Similarly, puncture patterns # 4 to # 6 become the same puncture pattern by changing the block delimiter. As described above, the selection methods that are cyclically shifted in the 6 bits of the block period can be regarded as the same. Therefore, there are _{3 × 2} C ₂ × 2 / (3 × 2) = 5 ways to select puncture bits.

When one block is composed of L × k bits and k bits of L × k bits are punctured, there are the number of puncture patterns obtained by Expression (71).

FIG. 18B shows the relationship between the encoded sequence and the puncture pattern when attention is paid to one puncture pattern. Although not shown, puncture bits are also used for Xi + 3 and Pi + 3. For this reason, as can be seen from FIG. 18B, when 2 bits out of 6 bits constituting one block are punctured, the existing check expression pattern is (3 × 2) × 1/2 for one puncture pattern. It becomes. Similarly, when one block is composed of L × k bits and k bits of L × k bits are punctured, there are the number of check equations obtained by Equation (72) for one puncture pattern.

Therefore, in the puncture pattern selection method, it is necessary to check whether or not the reliability is propagated independently for the number of check expressions (rows) obtained from Expression (73).

From the above relationship, when the coding rate is 1/2 and the coding rate is 3/4, when the k bits are punctured from the L × k bit block, the number of check equations obtained from Equation (74) ( It is necessary to check whether or not the reliability is propagated by itself.

  If no good puncture pattern is found, L and k need to be increased.

  Next, consider the case where the time-varying period is m. Also in this case, as in the case where the time-varying period is 1, m different inspection formulas represented by the formula (64) are prepared. Hereinafter, m inspection formulas are named “inspection formula # 1, inspection formula # 2,..., Inspection formula #m”.

なお、式（７５）において、ＬＣＭ｛α，β｝は、自然数αと自然数βとの最小公倍数をあらわす。 Then, the parity P _{mi + 1} at the time point mi + 1 is obtained using the “check equation # 1”, the parity P _{mi + 2} at the time point mi + 2 is obtained using the “check equation # 2”, and the parity P _{mi + m} at the time point mi + m is obtained as “ Consider the LDPC-CC obtained using the “check formula #m”. At this time, when considered in the same manner as in FIG. 15, the parity check matrix is represented as shown in FIG. 17. Then, in the case where the coding rate is 1/2 to the coding rate 3/4, for example, when puncturing 2 bits from a 6-bit block, when considered similarly to Equation (73), Equation (75) It is necessary to check whether or not the number of check formulas (rows) obtained from (1) alone is a row whose reliability is not propagated.

In Expression (75), LCM {α, β} represents the least common multiple of the natural number α and the natural number β.

  As can be seen from equation (75), as m increases, the number of check equations that must be checked increases. Therefore, a puncturing method that periodically punctures is not suitable, and for example, a method of puncturing at random is used, so that reception quality may be deteriorated.

  It should be noted that in FIG. 18C, when puncturing is performed to generate a code sequence of coding rate R = 2/3, 3/4, and 5/6 by puncturing from L × k bits to k bits, this must be checked. Indicates the number of parity check polynomials that should not be.

  In reality, the time-varying period during which the best puncture pattern can be searched is about 2 to 10. In particular, the time-varying cycle 2 is suitable in consideration of the time-varying cycle in which the best puncture pattern can be searched and the improvement in reception quality. Further, when the time-varying cycle is 2, and the check equations such as the equations (64) and (66) are periodically repeated, there is an advantage that the encoder / decoder can be configured very easily.

  In the case of time-varying periods 3, 4, 5,..., The configuration of the code / decoder is slightly larger than when the time-varying period is 2. Similarly to the above, when a plurality of parity check expressions based on the expressions (64) and (66) are periodically repeated, a simple configuration can be adopted.

  Note that when the time-varying period is semi-infinite or when an LDPC-CC is created based on the LDPC-BC, the time-varying period is generally very long, and therefore puncture bits are selected periodically. It is difficult to adopt the method and search for the best puncture pattern. For example, it is conceivable to adopt a method of selecting puncture bits at random, but there is a possibility that the reception quality at the time of puncture is greatly deteriorated.

Incidentally, formula (64), (66), (68), it is also possible to express check polynomial by multiplying the ^{D n} in, on both sides (69). In the present embodiment, there are D ⁰ X (D) and D ⁰ P (D) terms (D ⁰ = 1) in formulas (64), (66), (68), and (69). It was.

In this way, since the parity can be calculated sequentially, the configuration of the encoder is simplified, and in the case of the systematic code, considering the reliability propagation to the data at the time point i, the data If the term of D ⁰ exists in both the parity and the parity, since the reliability propagation to the data can be easily understood, the code design can be easily performed. If the ease of code design is not taken into consideration, D ⁰ X (D) does not need to exist in the equations (64), (66), (68), and (69).

  FIG. 19A shows an example of an LDPC-CC parity check matrix with a time varying period of 2. As shown in FIG. 19A, in the case of time-varying period 2, two parity check expressions, a parity check expression 1901 and a parity check expression 1902, are used alternately.

  FIG. 19B shows an example of an LDPC-CC parity check matrix with a time varying period of 4. As shown in FIG. 19B, in the case of time-varying period 4, four parity check expressions, that is, a parity check expression 1901, a parity check expression 1902, a parity check expression 1903, and a parity check expression 1904 are repeatedly used.

  As described above, according to the present embodiment, a parity sequence is obtained by using a parity check matrix (64) and a parity check polynomial (66) different from equation (64), which is a time-varying period 2 parity check matrix. I did it. Note that the time-varying period is not limited to 2, and for example, a parity sequence may be obtained using a parity check matrix having a time-varying period 4 as shown in FIG. 19B. However, if the time-varying period m is too large, it is difficult to puncture periodically, and, for example, punctures at random, so that reception quality deteriorates. Realistically, the time-varying period during which an optimum puncture pattern can be searched is about 2 to 10. In this case, reception quality can be improved and puncturing can be performed periodically, so that an LDPC-CC encoder can be configured easily.

  It has been confirmed that good reception quality can be obtained when the row weight in the parity check matrix H, that is, the number of elements with 1 standing among the row elements constituting the parity check matrix is 7 to 12. As described in Non-Patent Document 12, when a code having an excellent minimum distance in a convolutional code is considered, the row weight increases as the constraint length increases. For example, in a feedback convolutional code with a constraint length of 11, Considering that the weight is 14, the point where the row weight is 7 to 12 can be considered as a value peculiar to the LDPC-CC of the present proposal. Further, when considering the merit of code design, the design is facilitated by making the row weights of the rows of the LDPC-CC parity check matrix equal.

  In the above description, the case of coding rate 1/2 has been described. However, the present invention is not limited to this, and a parity sequence is obtained using a check matrix having a time-varying period m even in cases other than coding rate 1/2. The same effect can be obtained when the time varying period is 2 to about 10 time varying periods.

  In particular, when the coding rate R = 5/6, 7/8 or more, in the LDPC-CC having the time varying period 2 or the time varying period m described in the present embodiment, only by a row including two or more erasure bits. Select a puncture pattern that is not configured. In other words, selecting a puncture pattern in which there are 0 or one erasure bit is a good reception when the coding rate is high, such as coding rate R = 5/6, 7/8 or higher. It is important in obtaining quality.

(Embodiment 8)
In this embodiment, a time-varying LDPC- that uses a check equation in which “1” exists in the upper trapezoid matrix of the check matrix described in Embodiment 2 and that can easily configure an encoder. CC will be described. In the following, a configuration method of time-varying LDPC-CC capable of realizing the coding rate R = 1/2 will be described.

When the coding rate is 1/2 and the polynomial expression of the information sequence (data) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed as follows.

In the formula (76), a1, a2,..., An are integers of 1 or more (where a1 ≠ a2 ≠ ... ≠ an). In addition, b1, b2,..., Bm are integers of 1 or more (however, b1 ≠ b2 ≠ ... ≠ bm. Also, c1, c2,..., Cq are −1 or less. As an integer, c1 ≠ c2 ≠... ≠ cq, where P (D) is expressed as follows.

  Similar to the second embodiment, the parity P can be obtained sequentially.

Next, Equation (78) and Equation (79) are considered as parity check polynomials with a coding rate of 1/2 different from Equation (76).

In the expressions (78) and (79), A1, A2,..., AN are integers of 1 or more (provided that A1 ≠ A2 ≠ ... ≠ AN). Further, B1, B2,..., BM are integers of 1 or more (where B1 ≠ B2 ≠ ... ≠ BM). C1, C2,..., CQ are integers equal to or less than −1 (where C1 ≠ C2 ≠ ... ≠ CQ). At this time, P (D) is expressed as follows.

Hereinafter, data X and parity P at time 2i are represented by X _2i and P _2i , respectively, and data X and parity P at time 2i + 1 are represented by X _{2i + 1} and P _{2i + 1} , respectively (i: integer).

At this time, the parity P _2i at the time point 2i is obtained by using the equation (77), and the parity P _{2i + 1} at the time point 2i + 1 is obtained by using the equation (80). P _2i is found using equation (77), parity _{P 2i + 1} of point in time 2i + 1 is considered the varying period of 2 LDPC-CC when determined using equation (81).

Such LDPC-CC codes are:
The encoder can be easily configured and the parity can be obtained sequentially.
• Puncture bits can be set periodically.
-It has the advantage that it is possible to reduce the number of termination bits and improve the reception quality at the time of puncturing at the termination.

Next, consider LDPC-CC with a time-varying period of m. As in the case of the time-varying cycle 2, “check expression # 1” represented by the expression (78) is prepared, and from “check expression # 2” represented by either the expression (78) or the expression (79), “ “Inspection formula #m” is 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, the data X and the parity P at the time point mi + 2 are respectively represented as X _{mi + 2} , P _{mi + 2 ,.} , P _{mi + m} (i: integer).

At this time, the parity P _{mi + 1} at the time point mi + 1 is obtained using the “check equation # 1”, the parity P _{mi + 2} at the time point mi + 2 is obtained using the “check equation # 2,” and the parity P _{mi + m} at the time point mi + m is obtained. Consider an LDPC-CC obtained using “checking formula #m”. Such LDPC-CC codes are:
The encoder can be easily configured and the parity can be obtained sequentially.
-It has the advantage that it is possible to reduce the number of termination bits and improve the reception quality at the time of puncturing at the termination.

  As described above, according to the present embodiment, a parity sequence is obtained from a parity check matrix (76) and a parity check polynomial (78) different from equation (76), and a parity check matrix having a time-varying period of 2. I did it.

  Thus, when using a check equation in which “1” exists in the upper trapezoidal matrix of the check matrix, a time-varying LDPC-CC encoder can be easily configured. The time varying period is not limited to 2. However, in the same manner as in the seventh embodiment, when the method of periodically puncturing is employed, the time-varying period during which the best puncture pattern can be searched is about 2 to 10.

  In the case of time-varying periods 3, 4, 5,..., The configuration of the code / decoder is slightly larger than when the time-varying period is 2. Similarly to the above, when the inspection formulas of the formulas (78) and (79) are periodically repeated, a simple configuration can be adopted.

Incidentally, formula (76), (78), it is also possible to express check polynomial by multiplying the ^{D n} in, on both sides (79). In this embodiment, it is assumed that the terms (D ⁰ = 1) of D ⁰ X (D) and D ⁰ P (D) exist in formulas (76), (78), and (79). .

In this way, since the parity can be calculated sequentially, the configuration of the encoder is simplified, and in the case of the systematic code, considering the reliability propagation to the data at the time point i, the data In addition, if there is a term of D ⁰ in both the parity and the parity, code design can be easily performed. If the ease of code design is not taken into consideration, D ⁰ X (D) does not need to exist in the equations (76), (78), and (79).

  In addition, it has been confirmed that good reception quality can be obtained when the row weight in the parity check matrix H, that is, the number of elements with 1 standing among the row elements constituting the parity check matrix is 7-12. As described in Non-Patent Document 12, when a code having an excellent minimum distance in a convolutional code is considered, the row weight increases as the constraint length increases. For example, in a feedback convolutional code with a constraint length of 11, Considering that the weight is 14, the point where the row weight is 7 to 12 can be considered as a value peculiar to the LDPC-CC of the present proposal. Further, when considering the merit of code design, the design is facilitated by making the row weights of the rows of the LDPC-CC parity check matrix equal.

(Embodiment 9)
In this embodiment, a method for creating an LDPC-CC with a coding rate of 1/3 from an LDPC-CC with a coding rate of 1/2 (time-varying period m) described in Embodiments 7 and 8. explain in detail. As an example, an LDPC-CC with a time varying period of 2 will be described as an example.

Data X and parity P at time _2i are represented as X _2i and P _2i , respectively, and data X and parity P at time 2i + 1 are represented as X _{2i + 1} and P _{2i + 1} (i: integer), respectively. At this time, parity _{P 2i} of point in time 2i is found using Equation (64), parity _{P 2i + 1} of point in time 2i + 1 is the varying period when determined using Equation (66) Consider the second LDPC-CC.

Here, a new parity sequence polynomial is Pn (D), and any one of the equations (82) to (84) is considered.

  It should be noted that a1, a2,..., Ay are integers of 1 or more (where a1 ≠ a2 ≠ ... ≠ ay). In addition, b1, b2,..., Bw are integers of 1 or more (where b1 ≠ b2 ≠ ... ≠ bw). In addition, c1, c2,..., Cy (where c1.noteq.c2.noteq.cy) are integers of 0 or more.

  Then, different check polynomials “check formula # 1” and “check formula # 2” configured by any one of formulas (82) to (84) are prepared.

The data at the time point 2i is determined as X _2i and the parity P2i at the time point 2i using the equation (64), and the parity Pn _{, 2i} (the parity for the coding rate 1/3) at the time point 2i is expressed as “check equation # 1 ". At this time, the transmission sequence can be expressed as W _2i = (X _2i , P _2i , Pn _2i ).

Similarly, _{X 2i + 1} data at the time 2i + 1, and the parity _{P 2i + 1} at time 2i + 1, calculated using equation (66), the parity _{Pn 2i + 1} at point in time 2i + 1 of the (parity for a coding rate of 1/3) It calculates | requires using "inspection type | formula # 2." At this time, the transmission sequence can be expressed as W _{2i + 1} = (X _{2i + 1} , P _{2i + 1} , Pn _{2i + 1} ). In general, there is one of c1,..., Cy that is “0”.

  Consider terms corresponding to X (D), P (D), and Pn (D) in equations (82), (83), and (84), respectively. The check expression for the coding rate 1/2 is composed of Expressions (64) and (66). At this time, X (D) and P (D) each have a plurality of terms (a plurality of “1” s in the check matrix). When the coding rate is 1/3, a check expression configured by any one of the expressions (82), (83), and (84) is added.

Consider the column weight at this time. According to the check equation when the coding rate is 1/2, the data X and the parity P have a certain column weight, for example, a weight of about 5. In this state, if a check expression configured by any one of the expressions (82), (83), and (84) is added to make the coding rate 1/3, the column weight of the data X and the parity P increases. However, if the BP decoding is performed unless the column weight is suppressed to some extent, the reception quality cannot be improved. Therefore, when the coding rate is set to 1/3, the number of increases in the column weights of the data X and the parity P when the check equation configured by any one of the equations (82), (83), and (84) is added. Must be limited to 1 or 2. Therefore, Formula (82) becomes either of Formula (85)-Formula (88).

Moreover, Formula (83) becomes either Formula (89) or (90).

Moreover, Formula (84) becomes either Formula (91) or (92).

  As described above, in this embodiment, the parity check polynomial (82) is added to the parity check matrix (64) and the parity check polynomial (66) different from the equation (64) with the time-varying period 2 check matrix. A check matrix having a time-varying period 2 composed of (84) is added, and a parity sequence is obtained using the added check matrix.

  By doing in this way, LDPC-CC of the coding rate 1/3 of the time-varying period 2 can be produced | generated from the convolutional code of the coding rate 1/2 of the time-varying period 2. Also, when generating an LDPC-CC with a coding rate of ¼ or less, it can be generated in the same way as when generating an LDPC-CC with a coding rate of ３.

  Note that the time-varying cycle is not limited to 2, and the same can be applied to the case of the time-varying cycle m described in the seventh and eighth embodiments. Of course, the same can be applied to the case of the time varying period 2 of the eighth embodiment. Also, in the above description, in order to set the coding rate to 1/3, a parity check equation of time-varying period 2 configured by any one of Equations (82) to (84) is newly used as a parity check equation. Although the case where it is used has been described, it can be similarly implemented even if a parity check polynomial having a time-varying period n is used. In the formula (82) to the formula (84), as in the eighth embodiment, a1, a2,.

(Other embodiment 1)
In the above description, the convolutional code when the coding rate is 1/2 has been described as an example. In the present embodiment, a configuration method of LDPC-CC when the coding rate is 1 / n will be described.

When the coding rate is 1 / n, the polynomial representation of the information sequence (data) is X (D), the polynomial representation of the parity 1 sequence is P ₁ (D), and the polynomial representation of the parity 2 sequence is P ₂ (D). ,..., P _n−1 (D) is a polynomial expression of the parity n−1 sequence, the parity check polynomial can be expressed as the following equation (93).

At this _{time, Kx, K 1, K 2} , ···, K n-1 is set to an integer of 0 or _{more, Kx, K 1, K 2} , ···, maximum value _{K max} of _{K n-1} And

Here, data at time point i is represented as X _i , parity 1 is represented as P _{1, i} , parity 2 is represented as P _{2, i} ,..., And parity n−1 is represented as P _{n−1, i} . The transmission vector _{w = (X 1, P 1,1} , P 2,1, ···, P n-1,1, X 2, P 1,2, P 2,2, ···, P n _1,2, representing _{···, X i, P 1,} i, P 2, i, ···, P n-1, i, ···) and. In this case, when the check matrix is H, the above equation (3) is established.

Here, as in the first embodiment, “1” is added to the parity check matrix in consideration of probability propagation for data or (and) parity. At this time, one or more of the terms 2001_0, 2001_1, 2001_2,..., 2001_n−1 in FIG. 20 are selected and changed to the terms 2002_0, 2002_1, 2002_2,. For example, when 2001_0 in FIG. 20 is selected, 2001_0 is changed to 2002_0, and the others are not changed. When 2001_0 and 2001_n-1 in FIG. 20 are selected, 2001_0 is changed to 2002_0, and 2001_n-1 is changed to 2002_n-1, and the others are not changed. Naturally, all of the terms 2001_0, 2001_1, 2001_2,..., 2001_n−1 in FIG. That is, the check polynomial is expressed by the following equation (94).

At this time, s _x , s ₁ , s ₂ ,..., S _n−1 in FIG. 20 and Expression (94) are 1 or more, and h1, h2,..., Hs _k ≧ 2K _max +1 are set. (K = x, 1, 2,..., N−1). Thereby, good reception quality can be obtained. Further, h1, h2, ···, one or more of hs _k can obtain good reception quality even if it meets the above _{2K max} +1.

  Next, a method of adding “1” to the upper trapezoid matrix of the parity check matrix with the coding rate of 1 / n will be described in detail.

When the coding rate is 1 / n, the polynomial representation of the information sequence (data) is X (D), the polynomial representation of the parity 1 sequence is P ₁ (D), and the polynomial representation of the parity 2 sequence is P ₂ (D). ,..., P _n−1 (D) is a polynomial expression of the parity n−1 sequence, the parity check polynomial is expressed by Equation (32).

Here, data at time point i is represented as X _i , parity 1 is represented as P _{1, i} , parity 2 is represented as P _{2, i} ,..., And parity n−1 is represented as P _{n−1, i} . The transmission vector _{w = (X 1, P 1,1} , P 2,1, ···, P n-1,1, X 2, P 1,2, P 2,2, ···, P n _1,2, representing _{···, X i, P 1,} i, P 2, i, ···, P n-1, i, ···) and. In this case, when the check matrix is H, the above equation (3) is established.

Here, as in the second embodiment, “1” is added to the parity check matrix in consideration of probability propagation for data or (and) parity. At this time, the term 15_0 in FIG. 21 is changed to the term 15_1, 0. That is, the check polynomial is expressed by the following equation (95).

At this time, s _x in FIG. 21 is 1 or more, and is set to h1, h2,... Hs _x ≦ −K _max −1. Thereby, good reception quality can be obtained. Also, good reception quality can be obtained even when one or more of h1, h2,..., Hs _x satisfy −K _max −1 or less.

  As described above, the method described in Embodiments 1 and 2 may be extended to a method for generating an LDPC-CC from a convolutional code having a coding rate of 1 / n as in the present embodiment. it can. Also, when creating an LDPC-CC from a convolutional code with a coding rate other than those described above, the LDPC-CC can be created in the same manner by extending the method described so far.

  In the present invention, even when data is transmitted by performing puncturing as described in Non-Patent Document 12, data can be obtained by performing BP decoding in the receiving device. At this time, since the LDPC-CC described in the embodiment is represented by a simple parity check matrix, data can be easily punctured as compared with the LDPC-BC.

In the present embodiment, an example in which “1” is added to the upper trapezoid matrix of the parity check matrix as shown in FIG. 21 has been described. However, the present invention is not limited to this, and the case of FIG. In addition to adding “1” to the upper trapezoidal matrix of the combination and parity check matrix, “1” may be added to the approximate lower triangular matrix of the parity check matrix. As a result, further improvement in reception quality can be expected. The check polynomial in this case is represented by the following equation (96).

  Also, the termination method at the coding rate 1/2 described in the third embodiment can be similarly performed at the coding rate 1 / n as in the present embodiment.

(Other embodiment 2)
Here, the configuration of the encoder of the present invention will be described. FIG. 22 is a diagram illustrating an example of the configuration of the encoder of Expression (15).

22, the parity calculation unit 2202 includes data x (2201) (that is, X (D) of (Expression 15)), stored data 2205 (that is, D ^α1 X (D) and D of ( ^Expression 15)). ^α2 X (D), D ⁹ X (D), D ⁶ X (D), D ⁵ X (D)), stored parity 2207 (ie, D ^β1 P (D), D ^{β2 of} ( ^Equation 15)) P (D), D ⁹ P (D), D ⁸ P (D), D ³ P (D), DP (D)) are input, the calculation of Expression (15) is performed, and parity 2203 (ie, Expression (P (D)) of (15) is output.

  The data storage unit 2204 receives the data x (2201) and stores the value. Similarly, the parity storage unit 2206 receives the parity 2203 and stores the value.

FIG. 23 is a diagram illustrating an example of the configuration of the encoder of Expression (19). 23 that operate in the same manner as in FIG. 22 are given the same reference numerals. The storage unit 2302 stores the data 2301 and outputs the stored data 2303 (D ^α1 X (D)... D ^αn X (D) in Expression (19)).

The data storage unit 2204 outputs the stored data 2205 (that is, D ² X (D) in Expression (19)).

The parity storage unit 2206 outputs the stored parity 2207 (that is, D ² P (D), DP (D) in Expression (19)).

  The parity calculation unit 2202 receives each signal as input, calculates the parity of Equation (19), and outputs it.

  As described above, basically, an encoder can be configured by a shift register and exclusive OR.

  Next, sum-product decoding will be described as an example of a decoder algorithm. The algorithm for sum-product decoding is as follows.

sum-product decoding A binary M × N matrix H = {H _mn } is set as a parity check matrix of an LDPC code to be decoded. Subsets A (m) and B (n) of the set [1, N] = {1, 2,..., N} are defined as the following equations (97) and (98).

  A (m) means a set of column indexes that are “1” in the m-th row of the parity check matrix H, and B (n) is a row index that is “1” in the n-th row of the parity check matrix H. It is a set.

Step A ・ 1 (Initialization)
The log likelihood ratio β ⁽⁰⁾ _mn = λ _n is set for all pairs (m, n) satisfying H _mn = 1. The loop variable (number of iterations) is set to l _sum = 1, and the maximum number of loops is set to l _{sum and mux} .

Step A ・ 2 (line processing)
Logarithm using the following update formulas (99), (100), and (101) for all pairs (m, n) satisfying H _mn = 1 in the order of m = 1, 2,... The likelihood ratio α ⁽ⁱ⁾ _mn is updated. Here, i represents the number of iterations, and f is a Gallager function.

Step A ・ 3 (column processing)
For all pairs (m, n) that satisfy H _mn = 1 in the order of n = 1, 2,..., N, the log likelihood ratio β ⁽ⁱ⁾ _mn using the following update equation (102): Update.

Step A ・ 4 (Calculation of log-likelihood ratio)
The log likelihood ratio L ⁽ⁱ⁾ _{n is obtained} by the following equation (103) for n∈ [1, N].

Step A ・ 5 (Counting the number of iterations)
If l _sum <l _{sum, mux} , increment l _sum and return to step A · 2. On the other hand, if l _sum = l _{sum, mux} , codeword w is estimated as shown in equation (104), and sum-product decoding is terminated.

By the way, as shown in FIG. 3, the transmission sequence (data after encoding) is n ₁ , n ₂ , n ₃ , n ₄ ,..., And u = (n ₁ , n ₂ , n ₃ , n ₄ , ..) And the generator matrix is G, the following relational expression (105) is established.

If the information sequence vector i = (i ₁ , i ₂ ,...), The following relational expression (106) is established.

  By using the relational expressions of the expressions (105) and (106), a transmission sequence is obtained.

  FIG. 24 is a diagram illustrating an example of a configuration when sum-product decoding is used as a decoder. 24 includes a log likelihood ratio storage unit 2403, a row processing calculation unit 2405, a post-row processing data storage unit 2407, a column processing calculation unit 2409, a post-column processing data storage unit 2411, a control unit 2413, a log likelihood. A degree ratio calculation unit 2415 and a determination unit 2417 are provided.

  The log likelihood ratio storage unit 2403 receives the log likelihood ratio signal 2401 and the timing signal 2402 and stores the log likelihood ratio of the data section based on the timing signal 2402. Then, the log likelihood ratio storage unit 2403 outputs the stored log likelihood ratio as a signal 2404 to the row processing calculation unit 2405.

  The row processing calculation unit 2405 receives the log likelihood ratio signal 2404 and the column-processed signal 2412 as input, and performs the above Step A · 2 (row processing) calculation at a position where “1” exists in the check matrix H. Do. Since the decoder performs iterative decoding, the row processing operation unit 2405 performs row processing using the log likelihood ratio signal 2404 at the time of the first decoding (corresponding to the processing of Step A · 1 described above). In the second decoding, row processing is performed using the signal 2412 after column processing. Then, the row processing operation unit 2405 outputs the signal 2406 after the row processing to the post-row processing data storage unit 2407.

  The post-row processing data storage unit 2407 receives the post-row processing signal 2406 and stores all post-row processing values (signals). Then, the post-row processing data storage unit 2407 outputs the post-row processing signal 2408 to the column processing calculation unit 2409 and the log likelihood ratio calculation unit 2415.

  The column processing operation unit 2409 receives the signal 2408 and the control signal 2414 after row processing as input, confirms from the control signal 2414 that it is not the last iterative operation, and at the position where “1” exists in the check matrix H, Perform Step A • 3 (column processing). Then, the column processing calculation unit 2409 outputs the signal 2410 after column processing to the column processing data storage unit 2411.

  The post-column processing data storage unit 2411 receives the post-column processing signal 2410 and stores all post-column processing values (signals). Then, the post-column processing data storage unit 2411 outputs the post-column processing signal 2412 to the row processing calculation unit 2405.

  The control unit 2413 receives the timing signal 2402, counts the number of iterations, and outputs the number of iterations as a control signal 2414 to the column processing computation unit 2409 and the log likelihood ratio computation unit 2415.

  The log likelihood ratio calculation unit 2415 receives the row-processed signal 2408 and the control signal 2414 as input, and determines that the last iterative calculation is based on the control signal 2414, the check matrix H has “1”. Step A · 4 (logarithmic likelihood ratio calculation) is performed on the position to obtain a log likelihood ratio signal 2416. Then, the log likelihood ratio calculation unit 2415 outputs the log likelihood ratio signal 2416 to the determination unit 2417.

  The determination unit 2417 receives the log likelihood ratio signal 2416, estimates a codeword, and outputs an estimated bit 2418.

  Here, sum-product decoding has been described as BP decoding, but decoding can also be performed by using min-sum decoding approximating BP decoding, offset BP decoding, Normalized BP decoding, shuffled BP decoding, and the like.

(Other embodiment 3)
In the LDPC-CC described in the embodiments so far, when puncturing is performed, there arises a problem of whether data or parity should be punctured preferentially (selected as a bit not to be transmitted).

When a row of the parity check matrix is considered, that is, when a parity check polynomial is considered, the number of 1s in the position corresponding to the data in the row of the parity check matrix is Nx, and the number of 1s in the position corresponding to the parity is Np may be selected, and a bit to be punctured preferentially (selected as a bit not to be transmitted) may be selected as in 1) or 2) below, depending on the comparison result between Np and Nx.
1) When Np <Nx: data is punctured preferentially 2) When Nx <Np: parity is preferentially punctured

  In this way, it is possible to suppress deterioration in reception quality when puncturing is performed.

(Other embodiment 4)
In this embodiment, a transmission device and a reception device that realize the puncturing method described in the above embodiments will be described. The transmission apparatus and the reception apparatus according to the present embodiment can support a plurality of coding rates.

  FIG. 25 is a diagram illustrating a configuration of the transmission apparatus according to the present embodiment. 25 includes an LDPC-CC encoding unit (LDPC-CC encoder) 2510, a puncturing unit 2520, an interleaving unit 2530, and a modulation unit 2540.

  The LDPC-CC encoding unit 2510 performs encoding on the data X using an LDPC-CC parity check matrix having a coding rate specified by the control signal. For example, when the control signal specifies an encoding rate of 1/2 or more, the LDPC-CC encoding unit 2510 encodes the data X using an LDPC-CC parity check matrix with an encoding rate of 1/2. The data X and the parity P are output to the puncture unit 2520. In addition, when the control signal specifies the coding rate 1/3, the LDPC-CC coding unit 2510 performs coding on the data X using the LDPC-CC parity check matrix with the coding rate 1/3. The data X, the parity P, and the parity Pn are output to the puncturing unit 2520.

  Puncturing section 2520 performs puncturing on data X, parity P, or parity Pn output from LDPC-CC encoding section 2510 according to the coding rate specified by the control signal. In the present embodiment, puncturing section 2520 does not puncture at random, but periodically punctures bits periodically. Puncturing section 2520 outputs the punctured transmission sequence to interleaving section 2530.

  Specifically, when the coding rate specified by the control signal exceeds 1/2, the puncturing unit 2520 punctures the parity P periodically to obtain a predetermined coding rate.

  On the other hand, when the coding rate specified by the control signal is 1/2 or 1/3, puncturing section 2520 outputs the transmission sequence to interleaving section 2530 without performing puncturing.

  Interleaving section 2530 rearranges the order of transmission sequences, and outputs the rearranged transmission sequences to modulation section 2340.

  Modulation section 2540 modulates the interleaved transmission sequence using the modulation scheme specified by the control signal.

  FIG. 26 shows an example of the transmission format of the transmission sequence. The transmission sequence is composed of control information symbols and data symbols. The control information symbol is a symbol for notifying the communication partner of the coding rate and modulation method.

  FIG. 27 is a diagram illustrating a configuration of the reception apparatus according to the present embodiment. 27 includes a receiving unit 2710, a log likelihood ratio generating unit 2720, a control information generating unit 2730, a deinterleaving unit 7540, a depuncturing unit 2750, and a BP decoding unit 2760.

  The reception unit 2710 receives a reception signal transmitted from the transmission device 2500, performs radio demodulation processing such as RF (Radio Frequency) filter processing, frequency conversion, A / D (Analog to Digital) conversion, orthogonal demodulation, and the like. The demodulated baseband signal is output to log likelihood ratio generation section 2720. In addition, the reception unit 2710 estimates a channel variation in the wireless transmission path between the transmission device 2500 and the reception device 2700 using a known signal included in the baseband signal, and uses the estimated channel estimation signal as a log likelihood ratio. The data is output to the generation unit 2720.

  Log likelihood ratio generation section 2720 obtains the log likelihood ratio of each transmission sequence using the baseband signal, and outputs the obtained log likelihood ratio to deinterleave section 2740.

  The control information generation unit 2730 extracts control information from control information symbols included in the baseband signal. The control information symbol includes coding rate and modulation scheme information. Control information generation section 2730 outputs the extracted control information as a control signal to log likelihood ratio generation section 2720, deinterleave section 2740, depuncture section 2750, and BP decoding section 2760.

  Deinterleaving section 2740 rearranges the order of log-likelihood ratio sequences in the original order using the reverse processing of the rearrangement processing performed in interleaving section 2530 of transmitting apparatus 2500, and the log likelihood after rearrangement. The ratio is output to the depuncture unit 2750.

  Depuncturing section 2750 performs depuncturing on the log likelihood ratio output from deinterleaving section 2740 using the inverse processing of puncturing performed by puncturing section 2520 of transmitting apparatus 2500. That is, in puncturing section 2520 of transmitting apparatus 2500, when the coding rate exceeds 1/2, parity P is periodically punctured, and in this case, deinterleaving section 2740 has bits punctured by puncturing section 2520. 0 is inserted as the log likelihood ratio of. Puncturing section 2520 does not perform puncturing when the coding rate is ½ or ３, and therefore outputs the log likelihood ratio to BP decoding section 2560 without performing the depuncturing process.

  The BP decoding unit 2760 switches the LDPC-CC parity check matrix according to the coding rate indicated by the control signal, and performs BP decoding. Specifically, BP decoding section 2760 includes an LDPC-CC parity check matrix corresponding to coding rate 1/2 and coding rate 1/3, and when the control signal indicates coding rate 1/3, BP decoding is performed using a parity check matrix with a coding rate of 1/3. On the other hand, when the control signal indicates a coding rate other than coding rate 1/3, BP decoding is performed using a parity check matrix of coding rate 1/2.

  In addition, in FIG. 28, the structural example of the LDPC-CC encoding part 2510 in case coding rate R = 1/2 is shown as an example. As illustrated in FIG. 28, the LDPC-CC encoding unit 2510 includes shift registers 2511-1 to 2511 -M and 2514-1 to 2514 -M, weight multipliers 2512-0 to 2512 -M, and 2513-0 to 2513. -M, a weight control unit 2316, and a mod2 adder 2515.

Shift registers 2511-1 to 2511 -M and 2514-1 to 2514 -M are registers that hold v _{1, ti} , v _{2, ti} (i = 0,..., M), respectively. Is input to the shift register on the right and the value output from the shift register on the left is newly stored. The initial state of the shift register is all zero.

The weight multipliers 2512-0 to 2512-M and 2513-0 to 2513-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 2316. Switch. The weight control unit 2516 calculates the values of h ₁ ^(m) and h ₂ ^{(m) at} the timing based on the check matrix held inside the weight multipliers 2512-0 to 2512-M and 2513-0. Output to 2513-M.

The mod2 adder 2515 performs mod2 addition on the outputs of the weight multipliers 2512-0 to 2512-M and 2513-0 to 2513-M, and calculates v2 _{, t} .

  By adopting such a configuration, LDPC-CC encoder (LDPC-CC encoder) 2510 can perform LDPC-CC encoding according to a parity check matrix.

  Note that, when the rows of the parity check matrix held by the weight control unit 2516 are different from row to row, the LDPC-CC encoding unit 2510 is a time varying convolutional encoder.

In FIG. 29, when D ^−K (X) (K: positive integer) is included in the parity check polynomial, that is, using a check matrix in which “1” is added to the upper trapezoid matrix of the check matrix, encoding is performed. The structural example of the LDPC-CC encoding part (LDPC-CC encoder) in case of rate R = 1/2 is shown. The LDPC-CC encoding unit 2910 in FIG. 29 is different from the LDPC-CC encoding unit (LDPC-CC encoder) 2510 in FIG. 28 in terms of shift registers 2911-1 to 2911 -K and a weight multiplier 2912-. The structure which added 1-292-K is taken.

The shift registers 2911-1 to 2911 -K are registers that hold v _{1, ti} (i = −1,..., −K), and are held at the timing when the next input is input. Is output to the shift register on the right and the value output from the shift register on the left is newly held. The initial state of the shift register is all zero.

Weight multipliers 2912-0 to 2912 ^-K switch the values of h ₁ ^(−k) and h ₂ ^(−k) to 0/1 in accordance with the control signal output from weight control section 2316.

The weight control unit 2516 calculates the values of h ₁ ^(m) and h ₂ ^{(m) at} the timing based on the check matrix held inside the weight multipliers 2512-0 to 2512-M and 2513-0. Output to 2513-M. Also, the weight control unit 2516 sends the values of h ₁ ^(−k) and h ₂ ^{(−k) at} the timing to the weight multipliers 2912-1 to 2912 ^-K based on the check matrix held inside. Output.

The mod2 adder 2515 performs mod2 addition on the outputs of the weight multipliers 2512-0 to 2512-M, 2513-0 to 2513-M, 2912-0 to 2912-K _, and calculates v2 _{, t} .

With the configuration as shown in FIG. 29, the LDPC-CC encoder (LDPC-CC encoder) 2510 includes D ^−K (X) (K: positive integer) in the parity check polynomial. Can also respond.

  In addition, the LDPC-CC encoding part (LDPC-CC encoder) corresponding to coding rate R = less than 1/2 can be comprised by the structure similar to FIG. 28, FIG. For example, when the coding rate R = 1/3, a shift register, a weight multiplier, and a mod 2 adder for generating the parity sequence Pn may be added to FIGS. 28 and 29.

  Further, in the above description, the LDPC-CC encoding unit 2510 generates a coding sequence according to the case where the coding rate R = 1/2 or more and the case where the coding rate R = 1/3. However, regardless of the coding rate, the LDPC-CC coding unit 2510 generates all the transmission sequences (including the parity Pn), and the coding rate R = 1/2. The parity Pn may not be output. In this way, the LDPC-CC encoder (LDPC-CC encoder) can be made to correspond to the coding rate R = 1/2 and the coding rate R = 1/3.

  Further, in the above description, when BP decoding section 2760 switches the decoding method of the encoded sequence according to the case where coding rate R = 1/2 or more and the case where coding rate R = 1/3. However, regardless of the coding rate, the BP decoding unit 2760 performs BP decoding using a parity check matrix with a coding rate of 1/3, and the coding rate indicated by the control signal indicates other than 1/3. Alternatively, the log likelihood ratio for the obtained parity Pn may be replaced with 0. In this way, the BP decoding unit can be shared.

(Other embodiment 5)
In the present embodiment, a modification of the eighth embodiment will be described in detail. Hereinafter, a configuration method of time-varying LDPC-CC with a coding rate R = 1/2 will be described.

When the coding rate is 1/2 and the polynomial expression of the information sequence (data) is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed as follows.

In the formula (107), a1, a2,..., An are integers greater than or equal to 0 (where a1 ≠ a2 ≠ ... ≠ an). In addition, b1, b2,..., Bm are integers of 1 or more (where b1 ≠ b2 ≠ ... ≠ bm). C1, c2,..., Cq are integers of −1 or less (where c1 ≠ c2 ≠ ... ≠ cq). At this time, P (D) is expressed as follows.

  Therefore, the parity P can be obtained sequentially (see Embodiment 2 and Embodiment 8).

Next, equations (109) and (110) are considered as parity check polynomials of coding rate ½ different from equation (107).

  In the expressions (109) and (110), A1, A2,..., AN are integers greater than or equal to 0 (where A1 ≠ A2 ≠ ... ≠ AN). Further, B1, B2,..., BM are integers of 1 or more (where B1 ≠ B2 ≠ ... ≠ BM). Further, C1, C2,..., CQ are integers equal to or less than −1 (where C1 ≠ C2 ≠ ... ≠ CQ). At this time, P (D) is expressed as follows.

Data X and parity P at time _2i are represented by X _2i and P _2i , respectively, and data X and parity P at time 2i + 1 are represented by X _{2i + 1} and P _{2i + 1} , respectively (i: integer).

At this time, the parity P _2i at the time point 2i is obtained by using the equation (108), and the parity P _{2i + 1} at the time point 2i + 1 is obtained by using the equation (111). The LDPC-CC having the time varying period of 2 or the parity at the time point 2i Consider an LDPC-CC with a time-varying period of 2 where P _2i is obtained using equation (108), and parity P _{2i + 1} at time 2i + 1 is obtained using equation (112).

In such LDPC-CC,
The encoder can be easily configured and the parity can be obtained sequentially.
• Puncture bits can be set periodically.
-It has the advantage that it is possible to reduce the number of termination bits and improve the reception quality at the time of puncturing at the termination.

Next, consider LDPC-CC with a time-varying period of m. As in the case of the time-varying period 2, “inspection formula # 1” expressed by either formula (109) or formula (110) and either by formula (109) or formula (110), “ “Inspection Formula # 2”, “Inspection Formula # 3”... “Inspection Formula #m” are prepared. The data X and the parity P at the time point mi + 1 are X _{mi + 1} and P _{mi + 1} , the data X and the parity P at the time point mi + 2 are X _{mi + 2} and P _{mi + 2} , respectively. The data X and the parity P at the time point mi + m are 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 also determined by the “check equation # 1”, the parity P _{mi + 2} at the time point mi + 2 is also determined by the “check equation # 2,” and the parity P _{mi + m} at the time point mi + m is determined by the “check equation # 1”. Consider the LDPC-CC obtained by “m”. Such LDPC-CC codes are:
The encoder can be easily configured and the parity can be obtained sequentially.
-It has the advantage that it is possible to reduce the number of termination bits and improve the reception quality at the time of puncturing at the termination.

  Hereinafter, a configuration example of the parity check matrix in the present embodiment will be shown.

FIG. 30 illustrates a configuration example of an LDPC-CC parity check matrix with a time varying period of 2. In FIG. 30, reference numeral 3001 indicates a portion corresponding to the data X _i and the parity P _i at the time point i. Similarly, reference numeral 3002 indicates a portion corresponding to the data X _{i + 1} and the parity P _{i + 1} at the time point i + 1.

A parity check polynomial (for example, a parity check polynomial at time point i) corresponding to the code 3003 in FIG. 30 can be expressed as follows.

  In the formula (113), a1, a2,..., An are integers other than −1 and 0 (provided that a1 ≠ a2 ≠ ... ≠ an). In addition, b1, b2,..., Bm are integers of 1 or more (where b1 ≠ b2 ≠ ... ≠ bm). In FIG. 30, a1, a2,..., An are positive integers. At this time, P (D) can be obtained sequentially.

Similarly, the parity check polynomial denoted by reference numeral 3004 in FIG. 30 (for example, the parity check polynomial at time point i + 1) can be expressed as follows.

  In formula (114), A1, A2,..., AN are integers other than 1 and 0 (where A1 ≠ A2 ≠ ... ≠ AN). Further, B1, B2,..., BM are integers of 1 or more (where B1 ≠ B2 ≠ ... ≠ BM). At this time, P (D) can be obtained sequentially.

That is, in the case of time 2j, the parity P is obtained based on the equation (113), and in the case of time 2j + 1, the parity P is obtained based on the equation (114) (j is an integer). In the case of a time-varying LDPC-CC with a time-varying period 2 adopting the configuration shown in FIG. 30, the reliability of the parity P _{i at} the time point i propagates to the data X _{i + 1} at the time point i + 1, and as a result, the data X _{i + 1 at the} time point _{i + 1} Is decrypted. Then, the reliability of the parity P _{i + 1 at} the time point i + 1 is propagated to the data X _i at the time point i, and as a result, the data X _i at the time point _i is decoded.

  In the seventh embodiment, data and parity at the same time are related and the data is decoded, whereas in this embodiment, a parity check expression in which data and parity at different time are related is provided. Will exist. Then, considering the positional relationship between the related data and the parity except for the case of the same time point, in the example shown in FIG. 30, the data Xi + 1 and the parity Pi at the time point i and the time point i + 1 are related. Therefore, in the time-varying LDPC-CC with the time-varying period 2, the positional relationship is closest in time. Therefore, there is an advantage that it is less necessary to consider the temporal positional relationship between related data and parity during decoding. As described above, the LDPC-CC having the time varying period of 2 is configured so that the data Xi + 1 and the parity Pi at the time point i and the time point i + 1 are related to each other, and are related within the time varying period 2. .

  Similar characteristics can be provided to time-varying LDPC-CCs other than the time-varying period 2. That is, the LDPC-CC can be configured so that the data and the parity are related within the time varying period m. Hereinafter, the case of the time varying period 7 will be described with reference to FIG.

FIG. 31 shows a configuration example of an LDPC-CC parity check matrix with a time varying period of 7. In FIG. 31, reference numeral 3101 denotes a portion corresponding to data Xi and parity P _i at time point i. Reference numeral 3102 denotes a portion corresponding to the data X _{i + 1} and the parity P _{i + 1} at the time point i + 1. Reference numeral 3103 denotes a portion corresponding to the data X _{i + 2} and the parity P _{i + 2} at the time point i + 2. Reference numeral 3104 denotes a portion corresponding to the data X _{i + 3} and the parity P _{i + 3} at the time point i + 3. Reference numeral 3105 denotes a portion corresponding to the data X _{i + 4} and the parity P _{i + 4} at the time point i + 4. Reference numeral 3106 denotes a portion corresponding to the data X _{i + 5} and the parity P _{i + 5} at the time point i + 5. Reference numeral 3107 denotes a portion corresponding to the data X _{i + 6} and the parity P _{i + 6} at the time point i + 6.

For varying LDPC-CC when varying period 7 when employing a configuration shown in FIG. 31, the reliability of the parity _{P i} at point in time i is (are arranged "1"), propagated to data _{X i + 6} at point in time i + 6 (“1” is arranged in the same row as the parity P _i ) As a result, the data X _{i + 6} at the time point _{i + 6} is decoded.

The reliability of the parity P _{i + 1 at} the time point i + 1 is propagated to the data X _{i + 1} at the time point i + 1. As a result, the data X _{i + 1} at the time point _{i + 1} is decoded.

The reliability of the parity P _{i + 2 at} the time point i + 2 propagates to the data X _{i + 5} at the time point i + 5, and as a result, the data X _{i + 5} at the time point _{i + 5} is decoded.

The reliability of the parity P _{i + 3 at} the time point i + 3 is propagated to the data X _{i + 4} at the time point i + 4, so that the data X _{i + 4} at the time point _{i + 4} is decoded.

The reliability of the parity P _{i + 4 at} the time point i + 4 is propagated to the data X _{i + 3} at the time point i + 3, so that the data X _{i + 3} at the time point _{i + 3} is decoded.

The reliability of the parity P _{i + 5 at} the time point i + 5 is propagated to the data X _{i + 2} at the time point i + 2, and as a result, the data X _{i + 2} at the time point _{i + 2} is decoded.

The reliability of the parity P _{i + 6 at} the time point i + 6 propagates to the data X _i at the time point i, so that the data X _i at the time point _i is decoded.

  As shown in FIG. 31, an LDPC-CC with a time-varying period of 7 is configured so that data and parity from time point i to time point i + 6 are related to each other and are related within time-varying period of time 7. .

  Thus, it is necessary to consider the temporal positional relationship between data and parity in decoding by configuring the LDPC-CC so that the parity and data are related within a time-varying period. Has the advantage of low.

(Other embodiment 6)
In the present embodiment, the method for creating a time-varying LDPC-CC with a coding rate of 1/2 explained in Embodiment 7 is expanded, and a method for creating a time-varying LDPC-CC with a coding rate of 1/3. explain.

Data X time 2i, parity P, and parity Pn respectively _{X 2i,} P 2i, expressed in _{Pn 2i,} represents time 2i + 1 of data X, parity P, and parity Pn each _{X 2i + 1, P 2i +} 1, Pn 2i + 1 (i: integer). Here, the polynomial of data X is X (D), the polynomial of parity P is P (D), the polynomial of parity Pn is Pn (D), and the following parity check polynomial is considered.

  In the formula (115), a1, a2,..., An are integers other than 0 (where a1 ≠ a2 ≠ ... ≠ an). In addition, b1, b2,..., Bm are integers of 1 or more (where b1 ≠ b2 ≠ ... ≠ bm). In addition, c1, c2,..., Cq are integers of 1 or more (where c1 ≠ c2 ≠ ... ≠ cq). Then, P (D) at time point 2i is obtained using the relational expression of Expression (115). At this time, P (D) can be obtained sequentially.

Next, Equation (116) is considered as a parity check polynomial.

  In the formula (116), A1, A2,..., AN are integers other than 0 (however, A1 ≠ A2 ≠ ... ≠ AN). Further, B1, B2,..., BM are integers of 1 or more (where B1 ≠ B2 ≠ ... ≠ BM). Further, C1, C2,..., CQ are integers of 1 or more (where C1 ≠ C2 ≠ ... ≠ Cq). Then, using the relational expression of Expression (116), Pn (D) at time 2i is obtained. At this time, Pn (D) can be obtained sequentially.

Next, Equation (117) is considered as a parity check polynomial.

  In equation (117), α1, α2,..., Αω are integers other than 0 (where α1 ≠ α2 ≠ ... ≠ αω). In addition, β1, β2,..., Βξ are integers of 1 or more (where β1 ≠ β2 ≠ ... ≠ βξ). .Gamma.1, .gamma.2,..., .Gamma..lambda. Then, P (D) at time point 2i + 1 is obtained using the relational expression of Expression (117). At this time, P (D) can be obtained sequentially.

Next, Equation (118) is considered as a parity check polynomial.

  In the equation (118), E1, E2,..., EΩ are integers other than 0 (however, E1 ≠ E2 ≠... EΩ). F1, F2,..., FZ are integers of 1 or more (where F1 ≠ F2 ≠ ... ≠ FZ). In addition, G1, G2,..., GΛ are integers of 1 or more (where G1 ≠ G2 ≠ ... ≠ GΛ). Then, Pn (D) at time point 2i + 1 is obtained using the relational expression of Expression (118). At this time, Pn (D) can be obtained sequentially.

  As described above, by creating an LDPC-CC code having a time-varying period of 2, an optimum puncture pattern can be easily obtained when a method of periodically selecting puncture bits is employed, as in the seventh embodiment. There is an advantage that can be selected.

  If the time variation period is within 10, it is easy to search for the best puncture pattern by adopting a periodic puncturing method.

  Next, consider LDPC-CC with a time-varying period of m.

  In the case of the time-varying period m, m different inspection formulas expressed by the equation (115) are prepared, and the m inspection formulas are expressed as “inspection formula A # 1, inspection formula A # 2,. A # m ”. Also, m different check expressions represented by Expression (116) are prepared, and the m check polynomials are referred to as “check expression B # 1, check expression B # 2,..., Check expression B # m”. Name it.

Then, data X, parity P, and parity Pn at time mi + 1 are X _{mi + 1} , P _{mi + 1} , Pn _{mi + 1} , and data X, parity P, and parity Pn at time mi + 2 are X _{mi + 2} , P _{mi + 2} , Pn _{mi + 2} ,. Data X, parity P, and parity Pn of _{mi + m} are represented by X _{mi + m} , P _{mi + m} , and Pn _{mi + m} , respectively (i: integer).

At this time, the parity P _{mi + 1} at the time point mi + 1 is obtained using the “check equation A # 1”, the parity Pn _{mi + 1} is obtained using the “check equation B # 1,” and the parity P _{mi + 2} at the time point _{mi + 2} is obtained from the “check equation A #”. 2 ”, the parity Pn _{mi + 2} is obtained using“ check equation B # 2 ”,..., The parity P _{mi + m} of the time point _{mi + m} is obtained using“ check equation A # m ”, and the parity Pn _{mi + m} Consider an LDPC-CC with a time-varying period m determined using "check equation B # m". Such an LDPC-CC code is a code with good reception quality and has the advantage that the parity can be obtained sequentially.

  Note that the coding rate is not limited to 1/3, and an LDPC-CC code having a coding rate of 1/3 or less can be similarly created.

(Other embodiment 7)
In the present embodiment, an example of a transmission apparatus and a puncture method for performing puncturing suitable for a transmission codeword sequence obtained by LDPC-CC coding will be described.

FIG. 32 is a diagram illustrating a configuration of a time-invariant LDPC-CC parity check matrix used in the present embodiment. Figure 32 is different from FIG. 47, instead of ^{H T,} shows the configuration of parity check matrix H. If the transmission codeword vector is represented by v, the relational expression of Hv = 0 holds.

  In the description of the puncturing method in the present embodiment, first, a problem when a general puncturing method is applied to the transmission codeword sequence v will be described. A general puncturing method is described in Non-Patent Document 12, for example. In the following description, an example in which the LDPC-CC is configured using a convolutional code having a coding rate R = 1/2 and (177, 131) will be described.

FIG. 33 is a diagram for explaining a general puncturing method. In the figure, v _{1, t} , v _{2, t} (t = 1, 2,...) Indicate a transmission codeword sequence v. In a general puncturing method, the transmission codeword sequence v is divided into a plurality of blocks, and the same puncture pattern is used for each block, and transmission codeword bits are thinned out.

FIG. 33 shows that the transmission codeword sequence v is divided into blocks every 6 bits, and the same puncture pattern is used for all blocks, and transmission codeword bits are thinned out at a constant rate. ing. In the figure, bits surrounded by circles indicate bits that are punctured (bits that are not transmitted), and v is set so that the coding rate after puncturing is 3/4 for all the blocks 1 to 5. _{2,1, v 2,3, v 2,4,} v 2,6, v 2,7, v 2,9, v select _{2,10, v 2,12, v 2,13,} v 2,15 Then, puncture is performed (the bit is not transmitted).

  Next, the influence of the reception side (decoding side) when a general puncture as shown in FIG. 33 is applied to a transmission codeword sequence obtained by encoding using LDPC-CC will be considered. In the following, the case where BP decoding is used on the reception side (decoding side) will be considered. In BP decoding, decoding processing is performed based on an LDPC-CC parity check matrix. FIG. 34 shows the correspondence between transmission codeword sequence v and LDPC-CC parity check matrix H. In FIG. 34, bits surrounded by circles are transmission codeword bits that are thinned out by puncturing. As a result, in check matrix H, the bit corresponding to 1 surrounded by a square frame is not included in the transmission codeword sequence. As a result, when performing BP decoding, the log likelihood ratio is set to 0 because there is no initial log likelihood ratio for the bit corresponding to 1 surrounded by a square frame.

  In BP decoding, row operations and column operations are repeated. Therefore, if two or more bits (bits corresponding to 1 surrounded by a square frame in FIG. 34) for which there is no initial log likelihood ratio (the log likelihood ratio is 0) are included in the same row, In a row, the log-likelihood ratio is updated in the row operation alone in the row until the log-likelihood ratio of the bit where the initial log-likelihood ratio does not exist (log-likelihood ratio is 0) is updated by the column operation. Will not be. That is, the reliability is not propagated by the row operation alone, and in order to propagate the reliability, it is necessary to repeat the row operation and the column operation. Therefore, if there are a large number of such rows, the reliability is not propagated when the number of iteration processes is limited in BP decoding, which causes deterioration in reception quality. In the example illustrated in FIG. 34, the row 3410 is a row in which reliability is not propagated by a row operation alone, that is, a row that causes deterioration in reception quality.

  On the other hand, when the puncturing method according to the present embodiment is used, the number of rows in which reliability is not propagated by row operations alone can be reduced. In the present embodiment, for each processing unit of transmission codeword bits on the reception side (decoding side), a first puncture pattern and a second puncture pattern that thins out more bits than the first puncture pattern Is used to puncture the transmitted codeword bits. This will be described below with reference to FIGS. 35 and 36.

FIG. 35 is a diagram for explaining a puncturing method according to the present embodiment. Similarly to FIG. 33, v _{1, t} , v _{2, t} (t = 1, 2,...) Indicate a transmission codeword sequence v. In the following, as in FIG. 33, a case where one block is composed of 6 bits will be described. Further, it is assumed that the processing units of transmission codeword bits on the reception side (decoding side) are block 1 to block 5. In the example shown in FIG. 35, the first puncture pattern that is not punctured is used for the first block 1, and the second puncture pattern that is punctured is used for blocks 2 to 5. As a _{result, v 2,1, v 2,3, v} 2,4, v 2,6, v 2,7, v 2,9, v 2,10, v 2,12, v 2,13, v _It shows how _2,15 is punctured. Thus, in the present embodiment, puncture patterns with different coding rates are used to provide a range in which the number of bits to be thinned out is small within the processing unit of transmission codeword bits.

  FIG. 36 shows the correspondence between transmission codeword sequence v and LDPC-CC parity check matrix H in this case. In FIG. 36, although three lines including two or more 1 surrounded by a square frame are generated in the same line, it can be seen that the number of lines is reduced compared to the case of FIG. This is because block 1 is not punctured.

  In this way, by providing blocks that are not punctured, it is possible to reduce the number of rows that cause deterioration in reception quality during BP decoding. As a result, in the lines up to line 3610, log likelihood exists in the initial stage, the reliability is reliably updated in BP decoding, and the updated reliability is propagated to line 3610. Deterioration can be suppressed. Thus, the reliability of the row obtained by the row operation alone is propagated sequentially by performing iterative decoding a plurality of times from the characteristics of the structure of the parity check matrix of the convolutional code (LDPC-CC), and the reception quality by puncture is transmitted. Can be prevented. In addition, since the number of rows where the reliability is not propagated is reduced by the row operation alone, the number of iterations necessary to propagate the reliability can be reduced.

  By the way, in the example shown in FIG. 35, by providing a block that is not punctured, transmission codeword bits to be transmitted increase and the transmission rate decreases. However, if a relationship of N << M is established between the number N of bits in which the first puncture pattern is used and the number of bits M in which the second puncture pattern is used, a decrease in transmission rate is suppressed. However, the reception quality can be improved. FIG. 35 shows an example in which N = 6 and M = 24, and the number of additional transmission codeword bits is as small as 2 bits. Can be reduced to lines.

  Hereinafter, the configuration of the transmission apparatus according to the present embodiment will be described. FIG. 37 is a block diagram showing a main configuration of the transmission apparatus according to the present embodiment. In the description of the present embodiment, the same components as those in FIG. The transmission apparatus 3700 in FIG. 37 includes a puncture unit 3710 in place of the puncture unit 2520 with respect to the transmission apparatus 2500 in FIG. The puncture unit 3710 includes a first puncture unit 3711, a second puncture unit 3712, and a switching unit 3713.

  Puncturing section 3710 performs puncturing on a transmission codeword sequence including a transmission information sequence and a termination sequence, and outputs the punctured transmission codeword sequence to interleaving section 2530.

  Specifically, puncturing section 3710 punctures a transmission codeword sequence using a first puncture pattern and a second puncture pattern that thins out more bits than the first puncture pattern. The first puncture pattern and the second puncture pattern are different in the ratio of bits to be punctured. Puncturing section 3710 punctures the transmission codeword sequence using, for example, a puncture pattern as shown in FIG. In FIG. 38, (N + M) bits are a processing unit on the receiving side (decoding side).

  First puncturing section 3711 performs puncturing on a transmission codeword sequence using the first puncture pattern. Second puncturing section 3712 performs puncturing on the transmission codeword sequence using the second puncture pattern.

  When the puncture pattern of FIG. 38 is used, the first puncturing unit 3711 does not perform puncturing on the N-bit transmission codeword sequence from the beginning of the processing unit on the receiving side (decoding side), and the first puncturing unit 3711 The input transmission codeword sequence is output to switching section 3713. Second puncturing section 3712 performs puncturing on a transmission codeword sequence of (N + 1) to (N + M) bits, and outputs the punctured transmission codeword sequence to switching section 3713.

  Note that the first puncturing unit 3711 and the second puncturing unit 3712 may determine whether to puncture the transmission codeword sequence based on the control information from the control information generating unit 1050. The switching unit 3713 transmits a transmission codeword sequence output from the first puncture unit 3711 or a transmission codeword output from the second puncture unit 3712 in accordance with control information from a control information generation unit (not shown). One of the sequences is output to the interleave unit 2530.

  Hereinafter, the operation of transmitting apparatus 3700 configured as described above will be described mainly with respect to the puncturing process of puncturing section 3710. Hereinafter, a case will be described as an example where LDPC-CC encoding section 2510 performs LDPC-CC encoding using a convolutional code with encoding rate R = 1/2 and (177, 131).

In LDPC-CC encoding unit 2510, transmission information sequence u _t (t = 1,..., N) is subjected to LDPC-CC encoding processing, and v = (v _{1, t} , v _{2, t} ) is obtained. To be acquired. In the case of an organized code, v _{1, t} is a transmission information sequence u _t , and v _{2, t} indicates parity. The parity v _{2, t} is obtained based on the transmission information sequence v _{1, t} and the check expression of each row in FIG.

Puncturing section 3710 performs puncturing processing on transmission codeword sequence v with coding rate R = 1/2. For example, when the puncture shown in FIG. 35 is used by the puncture unit 3710, the block 1 is not punctured, and the blocks 2 to 5 are regularly spaced at predetermined intervals. Be drawn. That is, for block 2, the bits v _2,4 and v _2,6 are thinned out, and for block 3, the bits v _2,7 and v _2,9 are thinned out, and block 4 V ₂ , ₁₀ and v _2,12 are thinned out, and v ₂ , ₁₃ and v _2,15 are thinned out for block 5. In this way, a transmission codeword sequence having a coding rate R = 3/4 is acquired for blocks 2 to 5.

The punctured transmission codeword sequence is transmitted to the reception side (decoding side) via interleave section 2530 and modulation section 2540. At this time, when the puncture pattern shown in FIG. 35 _{used, v 2,4, v 2,6, v} 2,7, v 2,9, v 2,10, v 2,12, v 2,13 , V _2,15 will not be transmitted.

In this way, when the puncture pattern shown in FIG. 35 is used, blocks that are not punctured are generated every predetermined period. As shown in FIG. 35, by preventing the block 1 from being punctured, v ₂ , ₁ , v _2,3 that were not transmitted when the general puncturing method of FIG. 33 was used. Will be sent. In this way, when the BP decoding is used, the rows whose reliability is not propagated by the row operation alone are the three rows shown in the row 3610 in FIG. As can be seen from the comparison between FIG. 33 and FIG. 35, by adding 2 transmission bits, the number of rows in which the reliability is not propagated by the row operation alone is reduced from 6 rows to 3 rows. As a result, the number of rows in which the log likelihood is initially present increases, the initial reliability is reliably updated by BP decoding, and this reliability is further propagated to the row 3610 in FIG. It becomes like this.

  Thereafter, due to the structure of the parity check matrix of the convolutional code (LDPC-CC), the reliability existing at the head of the parity check matrix is propagated sequentially by performing iterative decoding multiple times, and reception by puncture is performed. Quality degradation can be suppressed.

  In the example of FIG. 35, since the increased number of bits to be transmitted is as small as 2 bits, the decrease in transmission speed is small and the deterioration in reception quality can be suppressed. Such an effect can be obtained because the LDPC-CC adopts a type in which the locations where 1 exists are concentrated in the range of the parallelogram as shown in FIG. Therefore, even if it is applied to the case of LDPC-BC, it is unlikely that the same effect can be obtained.

  Thus, by providing blocks that are not punctured, it is possible to reduce the number of rows that adversely affect BP decoding. At this time, in consideration of transmission efficiency, it is important that a relationship of N << M is established between the bit M constituting the block that is not punctured and the bit N constituting the block to be punctured. By setting N << M, it is possible to suppress deterioration in reception quality while suppressing deterioration in transmission efficiency.

  It should be noted that the puncturing unit 3710 may puncture the blocks 2 to 5 to which the second puncture pattern is applied, according to a predetermined rule, instead of puncturing at random. Compared with puncturing at random, when puncturing is performed according to a predetermined rule, puncture calculation processing is simplified.

(Other puncture patterns)
The puncture pattern used by the puncture unit 3710 is not limited to FIG. For example, as shown in FIG. 39, the puncture unit 3710 uses a puncture pattern with a coding rate R1 = 2/3 as the first puncture pattern, and uses a coding rate R2 = as the second puncture pattern. A 5/6 puncture pattern may be used.

  Also, as shown in FIGS. 40A and 40B, puncturing may be performed with n frames as processing units on the receiving side (decoding side). As shown in FIG. 40A, the first puncture pattern that does not perform puncturing is used for N bits from the beginning of n frames (n is an integer of 1 or more), and (N + 1) to (N + M) bits are used. Thus, a second puncture pattern for performing puncturing may be used.

  Also, as shown in FIG. 40B, the first puncture pattern with coding rate R1 = 2/3 is used for N bits from the beginning of n frames, and for (N + 1) to (N + M) bits. The second puncture pattern with the coding rate R2 = 5/6 may be used. As a result, the number of bits to be punctured can be reduced in N bits from the beginning of the n frame.

  Also, as shown in FIGS. 41A and 41B, a pattern may be used in which the number of bits punctured by puncturing is reduced toward the rear of the processing unit on the receiving side (decoding side). By reducing the number of bits thinned out by puncturing toward the rear of the processing unit on the reception side (decoding side), reception quality can be improved in BP decoding.

  In consideration of the decoding processing timing, for example, if puncturing is performed to reduce the number of bits punctured by puncturing at the rear part of a received data sequence consisting of n frames, This is because the row where the reliability is propagated is included in both the rear and the rear, so that the reliability can be efficiently propagated.

  As in the case of FIG. 38, the relationship of N << M is established between the number N of bits in which the first puncture pattern is used and the number of bits M in which the second puncture pattern is used. For example, it is possible to improve reception quality while suppressing a decrease in transmission speed.

  Further, as shown in FIG. 42A, the first puncture is not performed on the N1 bits from the top of n frames (n is an integer of 1 or more) as a processing unit on the reception side (decoding side). A second puncture pattern that performs puncturing is used for (N1 + 1) to (N1 + M) bits using a puncture pattern, and a first puncture that is not punctured for (N1 + M + 1) to (N1 + M + N2) bits A pattern may be used.

  Also, as shown in FIG. 42B, the coding rate R1 = 2/3 for the N1 bits from the beginning of n frames (n is an integer equal to or greater than 1) as a processing unit on the receiving side (decoding side). For the (N1 + 1) to (N1 + M) bits, the second puncture pattern with the coding rate R2 = 5/6 is used, and for the (N1 + M + 1) to (N1 + M + N2) bits. May use the first puncture pattern with the coding rate R1 = 2/3.

  Compared to the case where the first puncture pattern in which the number of bits thinned out by puncturing is small is used in one processing unit on the receiving side (decoding side) (see FIGS. 40 and 41), 42), the number of test rows with high reliability increases, so that the convergence speed at the time of BP decoding is high, and a decoding result can be obtained with a small number of iterations.

  Note that the number of places where the first puncture pattern with a small number of bits thinned out by puncturing is used in the processing unit is not limited to two, and may be three or more.

  In addition, when the number of bits where the first puncture pattern with a small number of bits punctured by the puncture is used is two or more, the total number N of bits where the first puncture pattern is used and the second If the relationship of N << M is established with the total number M of bits in which the puncture pattern is used, reception quality can be improved while suppressing a decrease in transmission rate.

  40, 41, and 42, the case where the first puncture pattern and the second puncture pattern are used for n frames has been described. However, n may be an integer of 1 or more. It can also be applied to the case of one frame.

  In the following, a puncture pattern suitable for a transmission codeword sequence obtained by LDPC-CC coding will be considered in consideration of the relationship with the decoding processing timing.

  FIG. 43 is a diagram for explaining the decoding processing timing. In FIG. 43, each received data sequence is composed of n frames (for example, n OFDM (Orthogonal Frequency Division Multiplexing) symbols: OFDM symbols), and the OFDM scheme is composed of 32 subcarriers. In the case where the modulation signal is configured, the symbol is composed of all carriers (32 subcarriers). This received data sequence length is a processing unit on the receiving side (decoding side), and the n frames (or n OFDM symbols) are delivered to the upper layer as one unit. In general, there is a time lag until the upper layer takes in the next n frames of data, so the timing of t3, t6, t9 in FIG. 43, that is, the timing of receiving the last part of the n frames is BP decoded. It is realistic to end the period.

  Since LDPC-CC has the nature of a convolutional code, in order to make the data estimated by BP decoding effective from the timing of t2 (data that is highly likely to be correct), the BP before the timing of t2 Decoding needs to be started. For example, in the example shown in FIG. 43, in order to make the estimated data obtained by BP decoding between t2 and t5 valid data, it is necessary to perform BP decoding between t1 and t6. Similarly, in order to make the estimated data obtained between t5 and t8 valid data, it is necessary to perform BP decoding between t4 and t9.

  In consideration of such decoding processing timing, for example, when puncturing is performed so that the number of bits punctured by puncturing is reduced at the rear part of a received data sequence composed of n frames, in the BP decoding processing period, Since both the front side and the rear side include the row where the reliability is propagated, the reliability can be efficiently propagated.

  As described above, according to the present embodiment, puncturing section 3710 has a second puncture pattern that thins out more bits than the first puncture pattern and the first puncture pattern for each processing unit of transmission codeword bits. The transmission codeword bits are punctured using the puncture pattern.

  By using the first and second puncture patterns having different coding rates after puncturing instead of puncturing the transmission codeword sequence at a certain rate, it is possible to suppress degradation of decoding characteristics due to BP decoding. It becomes like this.

  As long as puncturing is performed, a line that causes degradation in reception quality occurs, but a method for suppressing degradation in reception quality while suppressing a decrease in transmission speed as in the puncturing method in the present embodiment is This is very important for building a system with good performance.

  Each of the first and second puncture patterns may be composed of the same plurality of sub-patterns. That is, as shown in FIG. 35, transmission codeword bits may be regularly thinned out by using the same subpuncture pattern for each of blocks 2 to 5. Thereby, puncture calculation processing can be simplified.

  Also, the first puncture pattern with a low coding rate is not necessarily arranged at the last part of the n frame, and as shown in FIG. 43, is provided between t1 to t3, t4 to t6, and t7 to t9. You can do it. In addition, since the periods t1 to t3, t4 to t6, and t7 to t9 are specified by the relationship between the BP decoding process period and the period during which valid data is obtained, the first period is changed when the BP decoding process period changes. The position suitable for arranging the puncture pattern varies.

  In the above description, as an example, the puncturing method in the case where BP decoding is performed on the convolutional code has been described. 7 and Non-Patent Document 14 as described above can be similarly applied to time-invariant LDPC-CC and time-variant LDPC-CC.

  Further, the puncturing method in the present embodiment can be used for the time-invariant LDPC-CC and the time-varying LDPC-CC described in each of the embodiments of the present invention and other embodiments, and the reception quality deteriorates. The effect of suppressing is obtained.

(Time-invariant and time-variant LDPC-CC based on convolutional code)
The outline of the time-invariant / time-variant LDPC-CC based on the convolutional code will be described below.

Consider a systematic convolutional code with coding rate R = 1/2 and generator matrix G = [1 G1 (D) / G0 (D)]. At this time, G1 represents a feedforward polynomial, and G0 represents a feedback polynomial. When the polynomial expression of the information sequence is X (D) and the polynomial expression of the parity sequence is P (D), the parity check polynomial is expressed as follows.

Here, the parity check polynomial of equation (120) that satisfies equation (119) is considered.

  In the formula (120), ai (i = 1, 2,..., R) is an integer other than 0, and bj (j = 1, 2,..., S) is an integer of 1 or more. A code defined by a parity check matrix based on the parity check polynomial of equation (120) is referred to herein as time invariant LDPC-CC.

M different parity check polynomials based on Expression (120) are prepared (m is an integer of 2 or more). The parity check polynomial is expressed as follows.

At this time, i = 0, 1,..., M−1. The data and parity at the time point j are represented by X _j and P _j , and u _j = (X _j , P _j ). At this time, the parity P _j at the time point j is obtained from the equation (122).

  A code defined by a parity check matrix based on the parity check polynomial of Equation (122) is referred to herein as time-varying LDPC-CC. At this time, the time-invariant LDPC-CC defined by the parity check polynomial of Equation (121) and the time-varying LDPC-CC defined by the parity check polynomial of Equation (122) sequentially register the parity and exclusive OR. It has the feature that it can be obtained easily.

In the decoding unit, a time-invariant LDPC-CC creates a check matrix H from the equation (121), and a time-variant LDPC-CC from the equation (122), and the vector u = (u ₀ , u ₁ ,..., U _i , )), The following relational expression is established.

  Then, BP decoding is performed from the relational expression of Expression (123) to obtain a data series.

(Appendix)
Here, a description example when a specification or proposal is created is shown.

1.
It is proposed to use LDPC-CC (Low-Density Parity-Check Convolutional Code), which is an error correction code that can handle multiple coding rates, as FEC (Forward Error Correction) Scheme. LDPC-CC is a convolutional code defined by a low-density parity check matrix and, like CTC (Convolutional Turbo Code) and LDPC-BC (Block Code), is a code class that has a correction capability approaching the Shannon Limit ( Non-patent document 12 and Non-patent document 15).

LDPC-CC has the following advantages over CTC.
(1) No interleaver is required for the encoder.-The encoder can be configured with only a shift register and an adder.-Since the length of the information sequence is not limited to the interleaver length, an information sequence of any length can be encoded. (2 ) Sum-Product decoding that can be processed in parallel can be used for the decoding algorithm, so processing delay can be reduced compared to CTC decoding that requires serial processing. Also, compared to LDPC-BC standardized by IEEE802.11n Has the following advantages.
(3) Since the length of the information sequence is not limited by the block length of the parity check matrix, it is possible to encode an information sequence of an arbitrary length. (4) Encoding is performed with an operation scale proportional to the memory length (constraint length). Compared to LDPC-BC, which requires a computation scale proportional to the information sequence length, the encoder configuration is simple (memory length <information sequence length)
(5) Decoding processing delay can be reduced by applying a decoding algorithm that uses the parity check matrix structure unique to LDPC-CC

2.
2-1. FEC Encoding
FIG. 44 shows a block diagram of an error correction code scheme (FEC Scheme).
The error correction code system is composed of an LDPC-CC Encoder and a puncture unit (Puncture). The payload data length to be encoded is k bits, and the code word data length obtained after encoding is n bits.

2-2. LDPC-CC Encoding
Payload data is encoded by the LDPC-CCEncoder.
FIG. 45 shows the configuration of the LDPC-CC Encoder. The LDPC-CC Encoder outputs k-bit systematic bits and k-bit parity bits for k-bit payload data. The coding rate R of the LDPC-CC Encoder is 1/2.

The LDPC Convolutional Encoding process is shown below.
(1) The input of k-bit information bits is branched into two, one is output as k-bit systematic bits, and the other is input to a constituent encoder.
(2) The Constituent Encoder performs an encoding process on k information bits and outputs k bit parity bits.
The LDPC-CC Encoder outputs Code Bits bit by bit in the order {d1, p1}, {d2, p2}, {d3, p3}, ..., {dk, pk}.

検査行列Hは、k×2kの行列である。検査行列Hの各列は、d1,p1,d2,p2,…dt, pt, …,dk,pkという並びでSystematic Bits（d1、…、dk）とParity Bits（p1、…、pk）に対応する。また、Mは、LDPC-CCのメモリ長を表す。 LDPC-CC is defined by the parity check matrix given by Equation (124).

The check matrix H is a k × 2k matrix. Each column of the check matrix H corresponds to Systematic Bits (d1, ..., dk) and Parity Bits (p1, ..., pk) in the order of d1, p1, d2, p2, ... dt, pt, ..., dk, pk To do. M represents the memory length of the LDPC-CC.

Each row of the check matrix H represents a parity check polynomial.
h _d ⁽ⁱ⁾ (t) (i = 0,..., M) represents the weight (1 or 0) of the Systematic Bit in the t-th parity check polynomial, and h _p ⁽ⁱ⁾ (t) (i = 0 ,..., M) represent parity bit weights (1 or 0) in the t-th parity check polynomial.
In the check matrix H, all elements other than h _d ⁽ⁱ⁾ (t) and h _p ⁽ⁱ⁾ (t) are 0. As shown in Expression (1), the LDPC-CC parity check matrix H is a matrix in which 1 stands only in the diagonal term of the matrix and its vicinity.

ただしn=0,1,2,…である。 The inspection formula used in FEC Scheme is shown in Formula (125) and Formula (126).

However, n = 0, 1, 2,.

ここで、X(D)は、Systematic Bits（d1,…,dk），P(D)はParity Bits（p1,…,pk）を表す。 Moreover, the polynomial expression of Formula (125) and Formula (126) is as follows.

Here, X (D) represents Systematic Bits (d1,..., Dk), and P (D) represents Parity Bits (p1,..., Pk).

  The proposed LDPC-CC Encoder is a time-varying LDPC-CC Encoder with a period of 2 and a memory length of 421, which uses two polynomials, the polynomial of Equation (125) and the polynomial of Equation (126), switched at each time point.

The LDPC-CC Encoder takes an arbitrary configuration for performing the calculation of Expression (129).

である。 The initial state of the LDPC-CC Encoder is all zero. That is,

It is.

  LDPC-CC supports encoding of Information Bits of arbitrary length k with the same encoder configuration. LDPC-CC also supports multiple memory lengths.

3. Encoding Termination
Termination is necessary to make the LDPC-CC Encoder state unique at the end of encoding. Termination is performed by Zero-tailing.

  Zero-tailing is realized by LDPC-CC Encoding a tail-bit consisting of M with a memory length of M bits. In addition, when termination is performed, the tail-bit is a known bit string on the receiving side, so it is not included in systematic bits and transmitted, but only the M-bit parity bits obtained when encoding the tail-bit are transmitted. To do.

4). Puncturing
Puncture is a process of discarding several systematic bits and / or parity bits from the output of LDPC-CC Encoder in order to obtain a code with a coding rate higher than 1/2 with a single encoder configuration. . Table 1 shows the coding rates supported by Puncturing. The coding rates to be supported are 1/2, 2/3, and 3/4, and 4/5 and 5/6 are optional.

  Table 2 shows puncture patterns used at each coding rate. P and p of the puncture pattern represent Systematic Bit and Parity Bit, respectively, and when the value in the pattern is 0, the bit is punctured. LPunc represents the length of the puncture pattern.

Use regular rotated puncturing for puncturing. Each systematic bit and parity bit is divided for each LPunc bit, and puncturing is performed regularly according to the puncture pattern shown in Table 1. In the case of coding rates of 3/4, 4/5, and 5/6, Systematic Bits is also punctured, and the resulting code is a non-systematic code.

5.
As mentioned above, it was proposed to use LDPC-CC as the FEC Scheme.
LDPC-CC Encoder configuration, polynomial and puncture pattern are shown, and it can be used as FEC Scheme.

6).
6-1. An Example of LDPC-CC Encoder
The LDPC-CC encoding can be realized by an arbitrary encoder that realizes the equation (129).
A configuration shown in FIG. 46 as an example of the LDPC-CC Encoder is shown in Non-Patent Document 12.

As shown in FIG. 46, the LDPC-CC Encoder includes M1 shift registers that hold ut, M2 shift registers that hold pt, and h _d ⁽ⁱ⁾ (t), h of each column of the check matrix H. _p ⁽ⁱ⁾ A weight controller that outputs weights according to the sequence of (t) and a mod2 adder.

  By adopting such a configuration, the LDPC-CC Encoder performs LDPC-CC encoding processing according to the equation (125). As shown in FIG. 46, an LDPC-CC encoder can be configured with only a shift register, an adder, and a weight multiplier.

  The present invention is not limited to all the above embodiments, and can be implemented with various modifications. For example, in the above-described embodiment, the case of performing as a wireless communication device has been described.

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

  Further, a program for executing the communication method is stored in a computer-readable storage medium, the program stored in the storage medium is recorded in a RAM (Random Access Memory) of the computer, and the computer is operated according to the program. You may do it.

  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 present invention can be widely applied to communication systems using LDPC-CC.

101, 102, 2511-1 to 2511 -M, 2514-1 to 2514 -M, 2911-1 to 2911 -K Shift register 103, 104, 105 Exclusive OR circuit 304, 402, 501, 502, 1001 Check matrix "1" to add to
1105, 1205, 1305, 1306 “1” added to the check matrix at the end
2202 Parity calculation unit 2204 Data storage unit 2206 Parity storage unit 2302 Storage unit 2403 Log likelihood ratio storage unit 2405 Row processing operation unit 2407 Row processing data storage unit 2409 Column processing operation unit 2411 Column processing data storage unit 2413 Control unit 2415 Log Likelihood Ratio Operation Unit 2417 Determination Unit 2500, 3700 Transmitting Device 2510, 2910 LDPC-CC Encoding Unit (LDPC-CC Encoder)
2512-0 to 2512-M, 2513-0 to 2513-M, 2912-1 to 2912-K Weight multiplier 2316 Weight control unit 2515 mod2 adder 2520, 3710 Puncture unit 2530 Interleaving unit 2540 Modulating unit 2700 Receiver 2710 Reception Unit 2720 log likelihood ratio generating unit 2730 control information generating unit 7540 deinterleaving unit 2750 depuncturing unit 2760 BP decoding unit 3711 first puncturing unit 3712 second puncturing unit 3713 switching unit

Claims (9)

Define m + 1 rows based on the first parity check polynomial using m different first parity check polynomials, second parity check polynomials,... M parity check polynomials expressed by Equation (1), providing a parity check matrix defining km + 2 rows based on the second parity check polynomial, ... km + m rows defined based on the mth parity check polynomial;
Obtaining an LDPC-CC (Low-Density Parity-Check Convolutional Code) codeword having a time-varying period m from a convolutional code by linear operation of the check matrix, input data, and termination sequence added to the input data;
An encoding method comprising :
The termination sequence further comprises a step of reducing the order of the check polynomial over time.
Encoding method .
(D ^a1 + D ^a2 + ... + D ^ar +1) X (D) + (D ^b1 + D ^b2 + ... + D ^bs +1) P (D) = 0 (1)
Where X (D) is a polynomial representation of an information sequence, P (D) is a polynomial representation of a parity sequence, a1, a2,..., Ar is an integer greater than or equal to 1 (where a1, a2,... Ar Are integers different from each other), b1, b2,..., Bs is an integer of 1 or more (however, b1, b2,..., Bs are all integers different from each other).   The encoding method according to claim 1, wherein row weights in the parity check matrix are equal.   The encoding method according to claim 1, wherein the time varying period m is 2 to 10. Puncturing the LDPC-CC codeword periodically and regularly;
The encoding method according to claim 1. In the formula (1), ai (i = 1, 2,..., R) is an integer of 1 or more.
The encoding method according to claim 1. An encoder that creates an LDPC-CC (Low-Density Parity-Check Convolutional Code) from a convolutional code,
Encoder comprising a parity calculation section for obtaining a parity sequence by a coding method as claimed in any one of claims 5. The parity calculation unit has a memory length M;
The termination sequence has a sequence length of M bits.
The encoder according to claim 6 . The LDPC-CC codeword includes the input data and the parity sequence obtained by linearly calculating the input data and the termination sequence.
The encoder according to claim 6 or 7 . A decoder for decoding LDPC-CC (Low-Density Parity-Check Convolutional Code) by BP (Belief Propagation),
A row processing computation section that performs row processing computation using a parity check matrix corresponding to a parity check polynomial used in the claims 6 to 8 encoder according,
A column processing operation unit that performs a column processing operation using the check matrix;
A determination unit that estimates codewords using calculation results in the row processing calculation unit and the column processing calculation unit;
A decoder comprising:

Images