JP4755104B2 - LDPC code generation method, communication apparatus, and code string generation method - Google Patents

Description

  The present invention relates to a communication apparatus that employs an LDPC code as an error correction method, and more particularly to an LDPC code generation method and a communication apparatus that search for an optimal order ensemble of a parity check matrix in an LDPC code.

  Non-Patent Document 1 below proposes a scheme using an LDPC (Low-Density-Parity-Check) code for each level of multilevel coding as a coding scheme for the multilevel modulation scheme. Here, as an LDPC code optimization method for each level, a probability density function that is an initial value is obtained for each bit position mapped to a modulation symbol, and is used by “Density Evolution (density evolution method)”. The optimal degree ensemble of the LDPC code for each bit position (which indicates the structure of the parity check matrix and represents the number of “1” s in the rows or columns of the parity check matrix as the order (weight)) is obtained.

J. Hou, Paul H. Siegel, Laurence B. Milstein, and Henry D. Pfister, “Multilevel Coding with Low-Density Parity-Check Component Codes, 2” Proceedings of IEEE Global Telecommunications Conference, San Antonio, TX, USA, November 25-29, 2001

  However, in the method based on multilevel encoding proposed in Non-Patent Document 1, it is necessary to prepare an encoder and a decoder for each bit position mapped to a modulation symbol, which increases the circuit scale. There was a problem that.

  In the above multi-level coding method, it is necessary to divide and encode the information length for each bit number mapped to the modulation symbol. However, in the LDPC code, the characteristic deteriorates as the code length becomes shorter. It is known to tend to.

  The present invention has been made in view of the above, and obtains an LDPC code generation method capable of generating a code suitable for a multi-level modulation scheme with one LDPC code while avoiding an increase in circuit scale. For the purpose.

  In order to solve the above-described problems and achieve the object, an LDPC code generation method according to the present invention is an LDPC code generation method applicable to a multi-level modulation method, for example, for each bit position of a modulation symbol. After classifying the signal distribution, the order ensemble of the parity check matrix that minimizes the SNR threshold value (the SNR value at which the bit error rate sharply decreases when the code length is sufficiently long) An order ensemble search step for searching a column weight ensemble), and a code generation step for generating a parity check matrix and a generation matrix based on the order ensemble obtained as the search result.

  In the LDPC code generation method according to the present invention, after classifying the distribution of the received signal for each bit position of the modulation symbol, the order ensemble of the parity check matrix that minimizes the SNR threshold is searched. Furthermore, since the parity check matrix and the generation matrix are generated according to the order ensemble, it is possible to construct a communication system that can realize encoding suitable for the multi-level modulation scheme with one LDPC code.

FIG. 1 is a diagram showing a configuration of a communication system including an LDPC encoder / decoder. FIG. 2 is a diagram illustrating an example of “16QAM Gray Mapping”. FIG. 3 is a diagram illustrating an example of an order ensemble of a multi-edge type LDPC code. FIG. 4 is a diagram for explaining the order ensemble search method according to the first embodiment. FIG. 5 is a diagram for explaining the order ensemble search method according to the first embodiment. FIG. 6 is a diagram illustrating a configuration example of an LDPC encoder. FIG. 7 is a diagram illustrating a configuration example of an LDPC encoder. FIG. 8 is a flowchart illustrating the order ensemble search method according to the second embodiment. FIG. 9 is a diagram showing an example of the search result of the order ensemble according to the procedure of FIG. FIG. 10 is a diagram illustrating an example of the search result of the order ensemble according to the procedure of FIG. FIG. 11 is a diagram showing a comparison result between the SNR threshold value obtained from the order ensemble of FIG. 3 and the SNR threshold value obtained by the procedure of FIG. FIG. 12 is a diagram for explaining the LLR probability density function calculation process according to the third embodiment. FIG. 13 is a diagram for explaining the calculation processing of the LLR probability density function according to the third embodiment. FIG. 14 is a diagram for explaining the LLR probability density function calculation processing according to the third embodiment. FIG. 15 is a diagram for explaining processing for calculating the LLR probability density function according to the third embodiment. FIG. 16 is a diagram for explaining the LLR probability density function calculation process according to the third embodiment. FIG. 17 is a diagram for explaining the LLR probability density function calculation process according to the third embodiment. FIG. 18 is a diagram illustrating a configuration of a communication system including an LDPC encoder / decoder according to a fourth embodiment. FIG. 19 is a diagram illustrating a configuration example of an LDPC encoder. FIG. 20 is a diagram illustrating a specific example of the LDPC code generation method according to the fourth embodiment. FIG. 21 is a diagram illustrating an order ensemble search method according to the fifth embodiment. FIG. 22 is a diagram illustrating an example of a state in which encoding is performed using a parity check matrix having an LDGM structure. FIG. 23 is a diagram illustrating parity check matrix generation processing according to the fifth embodiment. FIG. 24 is a diagram illustrating a conversion process from codeword C to codeword C ′ in the sixth embodiment. FIG. 25 is a diagram illustrating a conversion process from codeword C to codeword C ′ according to the seventh embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 LDPC encoder 2 Modulator 3 Communication path 4 Demodulator 5 LDPC decoder 6 Channel quality estimation part 11, 11a encoding part 12 Communication path type estimation part 13 Degree ensemble calculation part 14, 14a LDPC code generation part

  Embodiments of an LDPC code generation method according to the present invention will be described below in detail with reference to the drawings. Note that the present invention is not limited to the embodiments.

Embodiment 1 FIG.
First, the positioning of the encoder capable of realizing the LDPC code generation method of the present embodiment in the communication system will be described. FIG. 1 is a diagram showing a configuration of a communication system including an LDPC encoder / decoder. In FIG. 1, the transmission side communication device includes an LDPC encoder 1 and a modulator 2, and the reception side communication device includes a demodulator 4 and an LDPC decoder 5.

Here, the flow of encoding and decoding when the LDPC code is employed will be briefly described. The LDPC encoder 1 on the transmission side generates a k × n generation matrix G (k: information length, n: codeword length) by the LDPC code generation method of the present embodiment described later. Then, a message (m ₁ , m ₂ ,..., M _k ) having an information length k is received, and a code word C is generated using the message and the generation matrix G as shown in the following equation (1). However, when the parity check matrix for LDPC is H, the generator matrix G is a matrix satisfying GH ^T = 0 (T is a transposed matrix), H (c ₁ , c ₂ ,..., C _n ) ^T = 0. Become.
C = (m ₁ , m ₂ ,..., M _k ) G
= (C ₁ , c ₂ ,..., C _n ) (1)

  Then, the modulator 2 digitally modulates the code word C generated by the LDPC encoder 1 by a modulation method having a multi-value number of 2 or more such as multi-value PSK, multi-value QAM, and the like. And transmitted to the receiving side via the communication path 3.

On the other hand, on the receiving side, the demodulator 4 performs digital demodulation such as multi-level PSK and multi-level QAM on the modulated signal received via the communication path 3, and the LDPC decoder 5 The log likelihood ratio (LLR) is iteratively decoded by the “sum-product algorithm”, and the estimation results (corresponding to the original m ₁ , m ₂ ,..., M _k ) are output. To do.

Next, an error characteristic of a demodulation result obtained from a modulation signal in multilevel modulation will be described. In multilevel modulation, the error probability for each bit position differs depending on the mapping method of “0” and “1” to the modulation point. This will be described using an example of “16QAM Gray Mapping” shown in FIG. First, focusing on the first bit, when the I component is fixed, the values of the Q component are all the same value. Therefore, only the I component is considered when considering the error probability. Therefore, when “0” is transmitted as the transmission signal, the probability that the received signal is “0” (the probability that a correct signal is obtained) and the probability that it is “1” (the probability that an incorrect signal is obtained) are obtained. Respectively, the following equations (2) and (3) are obtained.
p (y | x = -3) + p (y | x = -1) (2)
p (y | x = + 1) + p (y | x = + 3) (3)
However, x represents a transmission signal, y represents a reception signal, and p (y | x) represents a probability that the reception signal received through the communication path 3 is y when the transmission signal is x.

Next, paying attention to the second bit, since the transmission signal is “0” and “1” and the error probabilities are different, it is necessary to consider each. That is, when “0” is transmitted as the transmission signal, the probability that the received signal is “0” (the probability that a correct signal is obtained) and the probability that it is “1” (the probability that an incorrect signal is obtained) are obtained. The following equations (4) and (5) are obtained respectively. On the other hand, when “1” is transmitted as the transmission signal, the probability that the reception signal is “1” (the probability that a correct signal is obtained) and When the probability of “0” (probability of obtaining an incorrect signal) is obtained, the following equations (4) and (5) are obtained, respectively.
p (y | x = -3) + p (y | x = + 3) (4)
p (y | x = -1) + p (y | x = + 1) (5)

  For the third bit and the fourth bit, when the Q component is fixed, the values of the I component are all the same value, so the error probability can be considered in the same way as the first bit and the second bit.

  As described above, since the error probability is different for each bit position of the modulation symbol, there is a possibility that a code with higher performance can be generated by considering it.

  Next, the multi-edge type LDPC code will be described. The multi-edge type LDPC code is an LDPC code proposed by the document “T. Richardson, and R. Urbanke,“ Modern Coding Theory, ”available at http://lthcwww.epfl.ch/papers/ics.ps”. Yes, the received signal distribution can be classified and reflected in the code structure.

FIG. 3 is a diagram illustrating an example of an order ensemble of the multi-edge type LDPC code disclosed in the above document. In the column b of FIG. 3, the first column shows the BEC (Binary Erasure Channel) with an erasure probability of 1, and the second column shows the order of AWGN (Additive White Gaussian Noise) channel. Incidentally, the column of d indicates the order of each edge type between a variable node and a check node, v _{b, d} represents the ratio of variable nodes indicated b, and d, the ratio of the check nodes u _d represented by d Indicates.

  By analyzing the order ensemble as shown in this example by the method of “Density Evolution” described in the above document, the SNR threshold (when the code length is sufficiently long) The average value of the SNR at which the bit error rate falls steeply) is obtained. By searching for an order ensemble that minimizes the SNR threshold and constructing a code based on the order ensemble, a high-performance code can be obtained.

  Next, on the premise of the above description, the LDPC code generation method of the present embodiment, specifically, the order ensemble search method will be described. FIG. 4 and FIG. 5 are diagrams for explaining the order ensemble search method of the present embodiment. In the present embodiment, as a specific example, the example of “16QAM Gray Mapping” in FIG. 2 is used. However, the present invention is not limited to M-value QAM and “Gray Mapping”, and is not limited to M-value QAM. , Mapping methods other than “Gray Mapping” are also applicable. Moreover, although this Embodiment has demonstrated the case where a communication path is AWGN, it is not restricted to this.

First, the LDPC encoder 1 classifies the received signal distribution for each bit position of the modulation symbol, and then searches for the order ensemble of the parity check matrix (FIG. 4, step S1). For example, as shown in FIG. 5, the AWGN in the column b is divided for each bit position of the modulation symbol with respect to the order ensemble of FIG. At this time, the ratio of each bit position is made equal, that is, the sum of v _{b, d} is made equal to the distribution of the divided received signals (constraint condition). In addition to the above-described constraint conditions, for example, a constraint condition such as fixing a part of the order ratio in order to set the diagonally upper right triangular area of the parity check matrix H to “0” may be added. Good. The reason why the 1-bit, 3-bit, 2-bit, and 4-bit are summarized will be described later.

  Next, since the LDPC encoder 1 designates a search range for searching for the SNR threshold value, predetermined initial values (values considered to be a sufficient range as a search range) are set as upper and lower search ranges. ) Is substituted (step S2). Then, the average value of the search upper limit and the search lower limit of SNR is calculated (step S3).

  Next, the LDPC encoder 1 receives the average value (input SNR) calculated above and generates an LLR probability density function for each bit position of the modulation symbol (step S4). In the example of “16QAM Gray Mapping” shown in FIG. 2, the 1-bit LLR is obtained from the above equations (2) and (3) as in equation (6). Then, the probability density function of the received signal with respect to the transmission signal “0” is considered, and the probability density function is obtained for the LLR in the above equation (6).

  As described above, since the error probability differs between the second bit when the transmission signal is “0” and “1”, when the transmission signal is “0”, the probability density function of the LLR is expressed as in the first bit. In the case where the transmission signal is “1”, the LLR is obtained by replacing “0” and “1” in the mapping in FIG. 2, and the probability density function of the LLR is obtained. Then, by averaging the two probability density functions, the probability density function of the second bit LLR is obtained.

  In addition, since the probability density functions for the third bit and the fourth bit are calculated exactly the same as those for the first bit and the second bit, respectively, the classification of the LLR probability density functions is 2 for the first, third bit, and second and fourth bits. Classify.

  Next, the LDPC encoder 1 executes “Density Evolution” with the order ensemble generated in step S1 and the LLR probability density function generated in step S4 as inputs (step S5).

  Next, the LDPC encoder 1 determines whether or not the probability density function of the LLR updated by the iterative process diverges in an infinite direction as a result of executing “Density Evolution” (step S6). For example, when diverging (step S6, Yes), since it can be determined that the SNR threshold exists in a direction smaller than the input SNR (average value), the search upper limit of SNR is updated with the input SNR (step S7). On the other hand, if it does not diverge (step S6, No), it can be determined that the SNR threshold value is present in a direction larger than the input SNR, and therefore the search lower limit of SNR is updated with the input SNR (step S8).

  Next, in the LDPC encoder 1, when the SNR search lower limit is subtracted from the SNR search upper limit and the accuracy becomes equal to or lower than a predetermined accuracy (when a desired accuracy is reached) (step S9, Yes), the SNR The SNR threshold value (SNR limit value) is obtained by calculating the average of the search upper limit and the search lower limit of the SNR through the threshold search processing loop (steps S3 to S9) (step S10). On the other hand, when the set accuracy has not been reached (No at Step S9), the SNR threshold value search processing loop is executed again.

  Next, the LDPC encoder 1 determines whether or not the SNR threshold value obtained above is a sufficiently good SNR threshold value (step S10: is the value equal to or greater than a specific threshold value)? And determining whether the value is the best value for a specific number of searches). For example, if a sufficiently good SNR threshold value is obtained (step S10, Yes), the value is set as the SNR threshold value (the average of the SNRs where the bit error rate drops sharply when the code length is sufficiently long). The order ensemble with the smallest SNR threshold is output. On the other hand, when a sufficiently good SNR threshold value is not obtained (No at Step S10), the process returns to Step S1 and the SNR threshold value search process (Steps S1 to S11) for another order ensemble is executed. Decide whether to end or end. When returning to step S1 and generating another order ensemble, in the above search process, for example, “Differential Evolution (R. Storn, and K. Price, “Differential Evolution-A simple and efficient adaptive scheme for global optimization over continuous spaces,” Technical Report TR-95-012, ICSI), etc. Generate.

  Then, based on the order ensemble obtained as described above, for example, a parity check matrix H is generated by a technique using Euclidean geometric codes described in Japanese Patent Laid-Open No. 2003-198383, and a generation matrix G is generated. . When generating the LDPC code, the parity check matrix is not classified by the conventional method, for example, based on the conventional order ensemble as shown in FIG. 3, in which the distribution of the received signal is not classified for each bit position of the modulation symbol. H may be generated, and the columns of the parity check matrix H may be rearranged based on the order ensemble of FIG. 5 in which the received signal distribution is classified for each bit position of the modulation symbol.

  As described above, in the present embodiment, the distribution of the received signal is classified for each bit position of the modulation symbol, and then the SNR threshold value (SNR of which the bit error rate sharply drops when the code length is sufficiently long). The order ensemble with the smallest (average value) is searched, and the parity check matrix and the generation matrix are generated according to the order ensemble with the smallest SNR threshold. Thereby, it is possible to construct a communication system capable of realizing encoding suitable for the multi-level modulation scheme with one LDPC code.

  In the present embodiment, the LDPC code generated by the above method may be directly provided to the encoding unit 11 in the LDPC encoder 1 as shown in FIG. 6, for example. Further, for example, as shown in FIG. 7, the channel type estimation unit 12 in the LDPC encoder 1 estimates a channel type serving as a model such as an AWGN channel, a Rayleigh fading channel, and the like. With the LDPC code generation method, the order ensemble calculation unit 13 and the LDPC code generation unit 14 may generate the LDPC code in real time. In this case, the generated parity check matrix H and generation matrix G are input to the encoding unit 11a, and the parity check matrix H is transmitted to the receiving side through the encoding unit 11a.

Further, the LDPC code generation method of the present embodiment is not limited to the multi-edge type LDPC code, but can also be applied to the order ensemble of an irregular LDPC code. Equations (7) and (8) below show the order distribution generation functions of the variable node and the check node, respectively. Where λ _i and ρ _i represent the ratio of the variable node of degree i and the edge belonging to the check node (representing “1” of the parity check matrix H as an edge), and d _l is the maximum degree of the variable node. , _Dr is the maximum degree of the check node.

Corresponding to the above equations (7) and (8), for example, based on λ _i ^k and ρ _i ^{k obtained} by classifying λ _i and ρ _i for each bit position k of the modulation symbol, the following (9) Expression functions of variable nodes and check nodes are expressed as in Expression (10), and the probability density function of LLR is divided for each bit position of the modulation symbol. An order ensemble that minimizes the SNR is obtained by the LDPC code generation method, and an LDPC code is generated.

Embodiment 2. FIG.
In the second embodiment, when searching for an order ensemble having a sufficiently small SNR threshold in the LDPC code generation method of the first embodiment, the calculation time required for the search is divided by dividing the process into two stages. To shorten. Note that the configuration of the communication system of the present embodiment is the same as that of FIG. 1 of the first embodiment described above.

  FIG. 8 is a flowchart illustrating the order ensemble search method according to the second embodiment. In the present embodiment, only processing different from that of the first embodiment will be described.

  In the present embodiment, first, LDPC encoder 1 calculates an order ensemble that minimizes the SNR threshold by a conventional method that does not classify the distribution of received signals for each bit position of a modulation symbol ( FIG. 8, Step S21: For example, a conventional order ensemble as shown in FIG. 3 is obtained. Here, not limited to the processing in step S21 described above, for example, a known order ensemble that does not classify the distribution of the received signal for each bit position of the symbol may be fixedly used.

  Next, the LDPC encoder 1 assigns a ratio for each modulation symbol bit position for each order, and generates an order ensemble of the parity check matrix by an optimization method such as “Differential Evolution” using the ratio as a parameter. (Step S22). At this time, as a parameter constraint condition, the sum of the ratios is defined to be 1 for each order, and the ratio of each bit position is determined to be equal. In addition, it is good also as adding constraint conditions other than the above.

  The processing of step S22 will be specifically described with reference to FIGS. 3 and 5. For example, paying attention to the order of the first row of the variable node in FIG. 3, the ratio of “0.5” is shown in FIG. As shown, the first line: “0.5 × 0.36” and the second line: “0.5 × 0.64” are divided. Note that the sum of the ratios of the variable nodes of the first and third AWGNs and the second and fourth AWGNs is equal to 0.5.

  Next, after executing steps S2 to S10 in the same process as in the first embodiment, the LDPC encoder 1 determines whether or not an order ensemble having a minimum SNR threshold value has been obtained (step S23). ). For example, when an order ensemble that minimizes the SNR threshold is obtained (step S23, Yes), the variable i is initialized to 0 (step S24), and when it is not obtained (step S23, No), The variable i is incremented (step S25). This procedure counts how many times the order ensemble with the smallest SNR threshold is compared with other order ensembles.

  Finally, the LDPC encoder 1 outputs the order ensemble that minimizes the SNR threshold when the variable i is larger than the specified number of times set (step S26, Yes), and is smaller than the specified number of times. (No in step S26), the process returns to step S22, and a new order ensemble is generated by an optimization method such as “Differential Evolution” by changing the ratio of the modulation symbol for each bit position.

  Here, as a numerical analysis example of the present embodiment, for example, the order ensemble of FIG. 3 is used in a fixed manner, and “16QAM Gray Mapping” or “64QAM Gray Mapping” is performed according to the procedure of FIG. 8 in the present embodiment. The results of obtaining the order ensemble are shown in FIG. 9 and FIG. In addition, the SNR threshold obtained from the order ensemble in FIG. 3 without using the procedure in FIG. 8 in the present embodiment and the SNR threshold obtained in the procedure in FIG. 8 of the present embodiment are compared. The results are shown in FIG. As shown in the figure, in any modulation scheme, the procedure of FIG. 8 in the present embodiment is capable of generating an order ensemble having a minimum SNR threshold with respect to the order ensemble of FIG. Recognize. In addition, in the modulation scheme having a large multi-value number, the distribution of the received signal can be classified in more detail, so that the effect of the execution of FIG.

  As described above, in the present embodiment, compared to the first embodiment, it is possible to avoid a significant increase in the amount of calculation due to an increase in parameters in the order ensemble search process, and to reduce the SNR threshold value in a short time analysis. It is possible to search for an order ensemble that minimizes.

Embodiment 3 FIG.
In Embodiment 3, in the LDPC code generation method of Embodiment 1 or 2, the LLR probability density function is calculated in accordance with the LLR calculation processing in the LDPC decoder 5, for example. Note that the configuration of the communication system of the present embodiment is the same as that of FIG. 1 of the first embodiment described above.

  12 to 17 are diagrams for explaining the LLR probability density function calculation processing according to the third embodiment. As shown in FIG. 12 (a black circle represents a reception point), for example, when the LDPC decoder 5 calculates an LLR in consideration of all modulation points, the LDPC code generation method according to the present embodiment also includes all An LLR probability density function is generated in consideration of the modulation point. In the example of “16QAM Gray Mapping” illustrated in FIG. 2, an LLR probability density function is generated in the same manner as in the first embodiment. FIG. 13 is a diagram showing a probability density function of the LLRs of the 1st and 3rd bits when the LLR is calculated using all modulation points, and FIG. 14 is a diagram when the LLR is calculated using all modulation points. It is a figure which shows the probability density function of LLR of the 2nd and 4th bit.

  On the other hand, as shown in FIG. 15, when the LDPC decoder 5 calculates the LLR using the neighboring modulation point of the reception point, the LDPC code generation method according to the present embodiment also uses each bit. An LLR probability density function is generated in consideration of neighboring modulation points of “0” and “1”. The solid line in FIG. 15 represents the first and third bit neighboring points, and the dotted line represents the second and fourth bit neighboring points. For example, in the first and third bit examples of “16QAM Gray Mapping” shown in FIG. 2, the LLR is obtained by the following equation (11), and the probability density function is obtained.

  For the second and fourth bits, the LLR probability density function is obtained by the same processing as in the first embodiment with respect to the LLR obtained by the following equation (11). FIG. 16 is a diagram illustrating a probability density function of the LLRs of the 1st and 3rd bits when the LLR is calculated using the nearby modulation points, and FIG. 17 is a diagram illustrating the case where the LLR is calculated using the nearby modulation points. It is a figure which shows the probability density function of LLR of the 2nd and 4th bit.

  Thus, in the present embodiment, in addition to the effects of the first or second embodiment, an LLR probability density function can be generated in accordance with the LLR calculation process in the LDPC decoder 5.

Embodiment 4 FIG.
In the fourth embodiment, when the modulation scheme is changed in the adaptive modulation scheme, the LDPC code generated for the modulation scheme before the change by the LDPC code generation method of the first embodiment is used. For the bit positions where the LLR probability density distribution for each bit position of the modulation scheme before the change and the LLR probability density distribution for each bit position of the modulation scheme after the change are greatly different, the parity check matrix H of the object Swap columns to generate a new code.

  FIG. 18 is a diagram showing the configuration of the fourth embodiment of the communication system including the LDPC encoder / decoder, and further includes a channel quality estimation unit 6 in addition to the configuration of FIG. In the present embodiment, when the channel quality measurement unit 6 detects deterioration or improvement in channel quality, it instructs the modulator 2 to change the modulation method, and the modulator 2 follows the instruction. The modulation method is adaptively changed. At the same time, the channel quality measurement unit 6 notifies the LDPC encoder 1 that the modulation method has been changed.

  Further, in the LDPC encoder 1, as shown in FIG. 19, the LDPC code generation unit 14a newly generates an LDPC code based on the notification of the modulation scheme change from the channel quality measurement unit 16. In this case, the generated parity check matrix H and generation matrix G are input to the encoding unit 11a, and the parity check matrix H is transmitted to the receiving side through the encoding unit 11a.

  FIG. 20 is a diagram illustrating a specific example of the LDPC code generation method of the present embodiment. In the example of FIG. 20, first, an LDPC code is generated for 64QAM (“Gray Mapping”) by the same processing as in the first embodiment. Then, based on the notification of the modulation scheme change from the channel quality measurement unit 16, the modulation scheme is changed to, for example, 16QAM (“Gray Mapping”). In such a case, for example, the third bit of 64QAM (the error rate of the fourth, fifth, and sixth bits is equivalent to the first, second, and third bits, respectively) is the bit position with the highest error probability in 6 bits. When compared with the corresponding bit positions in the later 16QAM (the error rates for the 3rd and 4th bits are equivalent to the 1st and 2nd bits, respectively), the error probabilities are significantly different before and after the change. Therefore, if the LDPC code generated for 64QAM is used as it is, it can be considered that the performance is greatly deteriorated. Therefore, in the present embodiment, as shown in FIG. 20, for bit positions (third bit of 64QAM) having greatly different error probabilities, the column of the parity check matrix H is replaced with a neighboring column, and the performance is greatly improved. An LDPC code that does not deteriorate is newly generated.

  As described above, in the present embodiment, when the modulation scheme is changed during communication, the parity check matrix H corresponding to the bit position having a greatly different error probability before and after the change is changed to the peripheral column. I decided to replace it. As a result, even in a communication system that employs an adaptive modulation scheme, it is not necessary to execute the same LDPC code generation method as in the first embodiment for each modification scheme, and the performance is greatly improved for each modulation scheme. It is possible to generate a new LDPC code without deteriorating.

Embodiment 5 FIG.
Next, the LDPC code generation method according to the fifth embodiment will be described. The fifth embodiment is the same as the second embodiment described above except that in FIG. 8, step S22, the ratio is assigned to each bit position of the modulation symbol except the order of the variable node corresponding to the parity bit. .

  The processing of the present embodiment will be supplementarily described with reference to FIG. 21, FIG. 22, and FIG. An order ensemble of an existing parity check matrix H having an LDGM (Low-Density Generation Matrix) structure as shown in FIG. 21 is prepared, and the order of the variable node corresponding to the parity bit is excluded (the order corresponding to the parity bit is equal). Probability) and a ratio for each bit position of the modulation symbol, and then an order ensemble suitable for the modulation scheme is searched. Note that the parity check matrix having the LDGM structure refers to a parity check matrix in which parity bits can be sequentially obtained by providing, for example, a Dual-Diagonal structure in a portion corresponding to a parity bit. FIG. 22 shows an example of how encoding is performed using a parity check matrix having an LDGM structure. Here, the parity is determined for each row so that the operation result becomes “0”. As a result, the code string for the input string “0110” is “01100101”.

  Then, as shown in FIG. 23, a parity check matrix suitable for the modulation scheme is obtained by replacing the columns of the existing parity check matrix H according to the obtained order ensemble. Note that the columns corresponding to the parity bits are not interchanged.

  Thus, in the present embodiment, a parity check matrix suitable for the modulation scheme can be obtained while maintaining the LDGM structure of the parity check matrix.

Embodiment 6 FIG.
Next, an LDPC code generation method according to the sixth embodiment will be described. The positioning of the LDPC encoder capable of realizing the LDPC code generation method of the present embodiment in the communication system is the same as that of the first embodiment.

  Here, the flow of encoding and decoding in the present embodiment will be described. In the LDPC encoder 1 on the transmission side, a codeword C is generated by an existing parity check matrix H described later having an LDGM structure. Further, the codeword C ′ to be transmitted to the communication path 3 is generated by changing the order of the codeword C by a method described later.

  Further, the modulation processing on the transmission side, the demodulation processing and decoding processing on the reception side are the same as those in the first embodiment described above, but the LDPC decoder 5 on the reception side uses the LDPC code generation method of the present embodiment described later. Decoding processing is performed using the parity check matrix H ′ generated in step (1).

  In this embodiment, the method for searching the degree ensemble of the parity check matrix H ′ generated for decoding is the same as in the second embodiment described above, and the column of the parity check matrix H generated by the existing order ensemble is used. By rearranging, a parity check matrix H ′ is generated.

  FIG. 24 is a diagram showing a specific image of conversion from codeword C to codeword C ′. In the present embodiment, the column rearrangement method of the parity check matrix H is stored, and the rearrangement method is made to correspond to the transmission bit sequence corresponding to the column of the parity check matrix H, whereby the codeword C is changed to the codeword C ′. Convert to That is, in the present embodiment, codewords are replaced instead of replacing columns of the parity check matrix on the encoding side.

  Thus, in the present embodiment, the encoding side adds processing for changing the order of codewords based on how the columns of the parity check matrix are rearranged. As a result, while maintaining the LDGM structure of the parity check matrix used for encoding, the encoding side can obtain a codeword suitable for the modulation scheme only by adding a process of changing the order of the codewords. Then, on the decoding side, by generating a new parity check matrix suitable for the modulation scheme, decoding can be performed by normal processing without requiring additional processing.

Embodiment 7 FIG.
Next, an LDPC code generation method according to the seventh embodiment will be described. The positioning of the LDPC encoder capable of realizing the LDPC code generation method of the present embodiment in the communication system is the same as that of the first embodiment.

  Here, the flow of encoding and decoding in the present embodiment will be described. In the LDPC encoder 1 on the transmission side, a code word C is generated by a parity check matrix H ″ described later. Further, the codeword C ′ to be transmitted to the communication path 3 is generated by changing the order of the codeword C by a method described later. Further, the modulation processing on the transmission side, the demodulation processing and decoding processing on the reception side are the same as those in the first embodiment described above, and the LDPC decoder 5 on the reception side replaces the demodulation result with the code replaced on the transmission side. The order of the words is returned to the original order, and the decoding process is performed using the parity check matrix H ″.

  First, a procedure for generating a parity check matrix H ″ and a procedure for generating a codeword C ′ are shown below. For example, a parity check matrix H ′ is generated by searching for the order ensemble and replacing the columns of the existing parity check matrix H by the same procedure as in the second embodiment. Then, for this parity check matrix H ′, the column corresponding to the parity bit in the original parity check matrix H is returned to the original position, and the vacant columns are system bits (encoders) in the original parity check matrix H. The parity check matrix H ″ is generated by moving the column corresponding to the input information sequence) to the left justified. Note that the order of the variable nodes corresponding to the parity bits needs to be the same for the order ensemble of the existing parity check matrix H.

  Next, a conversion process from the code word C to the code word C ′ will be described. FIG. 25 is a diagram showing a specific image of conversion from codeword C to codeword C ′. In the present embodiment, when the parity check matrix H ″ is generated for the parity check matrix H ′, the column positions for the replaced parity bits are stored. For the codeword C generated by the parity check matrix H ″, the parity check is performed by inserting the transmission bit corresponding to the original position returned by the above processing at the column position stored above. A code word C ′ corresponding to the matrix H ′ is generated.

  As described above, in the present embodiment, the encoding side performs processing for inserting transmission bits corresponding to parity bits at a predetermined position, and the decoding side performs processing for returning received bits corresponding to parity bits to the original positions. We decided to add each. As a result, a codeword suitable for the modulation scheme can be obtained while maintaining the LDGM structure of the parity check matrix.

  As described above, the LDPC code generation method according to the present invention is useful for communication apparatuses and communication systems that employ an LDPC code as an error correction method, and in particular, generates an optimal degree ensemble of a parity check matrix in an LDPC code. Suitable for encoder.

Claims (4)

In an LDPC (Low-Density-Parity-Check) code generation method applicable to a multi-level modulation system,
A degree ensemble generation step of classifying a distribution of received signals for each bit position of a modulation symbol to generate a parity check matrix order ensemble (an ensemble of row weights and column weights);
SNR a (Signal-to Noise Ratio) threshold value (code length value of the SNR bit error rate drops sharply when a sufficiently long) upper limit contact and low limits of the search range for searching for initializing, further, An LLR probability density function is generated for each bit position of the modulation symbol based on the average value of the upper and lower limits of the search range, and the execution result of “Density Evolution” using the generated order ensemble and the generated probability density function and SNR threshold determining step on Kilima other of said search range on the basis of determining the desired SNR threshold repeatedly performs a process of updating the lower limit, the
Including
The order when the order ensemble generation step and the SNR threshold value determination step are repeatedly performed to obtain a plurality of SNR threshold values, and the SNR threshold value having the smallest value among the plurality of SNR threshold values is determined. An LDPC code generation method characterized by generating a parity check matrix and a generation matrix based on an ensemble.   The LDPC code generation method according to claim 1, further comprising: calculating a distribution of received signals for each bit position of the modulation symbol in accordance with a likelihood calculation process of the decoder.   The column of the parity check matrix H corresponding to a bit position having a greatly different error probability before and after the change when the modulation scheme is changed during communication is replaced with a neighboring column. LDPC code generation method. In a communication apparatus that employs an LDPC (Low-Density-Parity-Check) code as an encoding method for a multi-level modulation method,
A degree ensemble generation function for classifying a distribution of received signals for each bit position of a modulation symbol and generating a parity check matrix order ensemble (an ensemble of row weights and column weights);
SNR a (Signal-to Noise Ratio) threshold value (code length value of the SNR bit error rate drops sharply when a sufficiently long) upper limit contact and low limits of the search range for searching for initializing, further, An LLR probability density function is generated for each bit position of the modulation symbol based on the average value of the upper and lower limits of the search range, and the execution result of “Density Evolution” using the generated order ensemble and the generated probability density function and SNR threshold determining function for determining a desired SNR threshold the upper Kilima other search range repeatedly executes a process of updating the lower limit on the basis of,
Have
The order when the order ensemble generation function and the SNR threshold value determination function are repeatedly executed to obtain a plurality of SNR threshold values, and the SNR threshold value having the smallest value among the plurality of SNR threshold values is determined. A communication apparatus that generates a parity check matrix and a generation matrix based on an ensemble.

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