CN110661532B - Symbol flipping decoding method based on multivariate LDPC code noise enhancement - Google Patents

Abstract

The invention discloses a multivariate low-density parity-check LDPC code symbol flip decoding N-SFDP method based on noise enhancement. The information of the verification node; calculate the soft reliability of each codeword symbol; obtain its corresponding flip value; update the hard decision symbol sequence; decode and stop the judgment, if the condition is not met, update the current information of each verification node. The present invention introduces random noise disturbance into the objective function of the SFDP decoding method by changing the flipping mechanism of the SFDP decoding method, thereby increasing the probability that the SFDP decoding method of the prior art escapes from the local maximum, so that the present invention can reduce a certain The error floor of these multivariate LDPC codes greatly improves the BER performance of the decoder.

Description

Sign Inversion Decoding Method Based on Multivariate LDPC Code Noise Enhancement

technical field

The invention belongs to the technical field of communication, and further relates to a symbol flipping decoding SFD (Symbol Flipping Decoding) method based on multiple low-density parity check LDPC (Low-Density Parity-Check Codes) code noise enhancement in the technical field of channel coding. The invention can realize the symbol flip decoding of the multivariate low-density parity check LDPC code predicted by the logic of large numbers.

Background technique

Low-density parity-check LDPC codes with low decoding complexity and good performance close to the Shannon limit have been widely used in deep space communication, wireless communication and other fields of modern communication, and have been adopted by 802.11n, 802.16e, 10GBASE-T, etc. Adoption of various modern communication standards. Therefore, low-density parity-check LDPC codes and their decoding methods have become a research hotspot in the field of channel coding in recent years. For low-density parity-check LDPC codes with short to medium packet lengths, the BER (Bit Error Rate) performance of multivariate LDPC codes is better than that of binary LDPC codes. However, the disadvantages of traditional multivariate low-density parity-check LDPC decoding methods are: high decoding complexity, or low decoding complexity but a certain degree of loss in decoding performance.

Guangxi University disclosed in its patent document "A Multivariate LDPC Code Decoding Method Based on Hard Reliability Information" (application publication date: February 14, 2016, application publication number: CN 105763203A, application number: 2016100846156) A decoding method for multivariate low-density parity-check LDPC codes is proposed. In this method, the reliability of each binary hard-decision symbol in the hard-decision symbol vector is integerized in bits, and the value of each binary hard-decision symbol is determined according to the reliability of each hard-decision symbol in each iteration. And perform decoding verification, after updating the external information and reliability of the variable nodes in a bit-weighted manner, the next iteration is performed, thereby reducing the complexity and storage load of multivariate low-density parity check LDPC decoding. The disadvantage of this method is: for each variable node in the decoding process, the reliability of each binary hard-decision symbol is determined according to the Hamming distance between the external information it receives and the binary representation corresponding to the hard-decision symbol. The degree is weighted by bit, which makes the complexity of updating the information outside the variable node higher.

Qin Huang et al. proposed a Sign flipping decoding SFDP (Symbol Flipping Decoding algorithm based on Prediction) method of multivariate low-density parity-check LDPC code based on large number logic prediction. In this method, by constructing a symbol flip objective function including soft reliability information from the channel and check-based hard reliability information from the check node, the flip metric of the symbol flip decoding SFD method takes into account both the pre-symbol flip and the symbol flip The reversed information greatly improves the error performance of decoding. The shortcomings of this method are: for multi-element low-density parity-check LDPC codes with a ring length of 6, the sign-flip decoding SFDP method based on large-number logic prediction has a high SNR (Signal-to-Noise Ratio) There will be an error level under the region, and the method does not specify how to choose the weight coefficients related to the logic of large numbers.

Contents of the invention

The purpose of the present invention is to address the above-mentioned deficiencies in the prior art, propose a kind of symbol flip decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement, for solving low decoding performance, low bit error rate, And how to choose the weight coefficients related to the logic of large numbers.

The train of thought of realizing the object of the present invention is: by changing the inversion measure of SFDP decoding method, random noise perturbation is introduced in the objective function of SFDP decoding method, thereby increases the probability that SFDP decoding method escapes from the undesired local maximum, greatly improves decoding performance. Change the flip metric of the sign flip decoding SFDP method based on large number logic prediction, introduce random noise disturbance into the objective function of the sign flip decoding SFDP method based on large number logic prediction, and dynamically select the sign flip based on large number logic prediction Decoding the weight coefficients related to large number logic in the SFDP method, thereby increasing the probability of the target function escaping from the unexpected local maximum in the prior art sign flip decoding SFDP method based on large number logic prediction, greatly improving the decoding The bit error rate performance of the device, while overcoming when the flipped hard-decision symbols have a small binary Hamming distance, the prior art SFDP method of symbol flip decoding based on large number logic prediction is easy to use at medium and high SNR Falling into the shortcoming of the local trap set, thereby reducing the error floor of the multivariate low-density parity-check LDPC code with a ring length of 6, and improving the decoding performance.

The realization of the inventive method comprises the steps:

Step 1, according to the following formula, calculate the hard decision value of each codeword symbol received by the additive Gaussian white noise channel during the initial iteration:

表示加性高斯白噪声信道接收的第j个码字符号在初始迭代时的硬判决值，j的取值范围为[0，N-1]，N表示多元低密度奇偶校验LDPC码的码字长度，d表示以二进制表示的第j个码字符号的比特数，Σ表示求和操作，r表示在初始迭代时以二进制表示的第j个码字符号的硬判决值

比特位数，r的取值范围为[0，d-1]，

表示在初始迭代时由加性高斯白噪声信道接收的以二进制表示的第j个码字符号信息进行非线性量化后的第t个比特值，t与r的取值对应相等；in,

Indicates the hard decision value of the jth codeword symbol received by the additive Gaussian white noise channel at the initial iteration, the value range of j is [0, N-1], and N represents the code of the multivariate low-density parity-check LDPC code word length, d represents the number of bits of the jth codeword symbol in binary, Σ represents the summation operation, and r represents the hard decision value of the jth codeword symbol in binary representation at the initial iteration

The number of bits, the value range of r is [0, d-1],

Represents the t-th bit value after nonlinear quantization of the j-th codeword symbol information received by the additive Gaussian white noise channel received by the additive Gaussian white noise channel during the initial iteration, and the values of t and r are correspondingly equal;

Step 2, update the information of each check node:

The first step is to calculate the sum of external information passed from the check node to the variable node during the current iteration according to the following formula:

表示在第k次迭代时从第i个校验节点传递给第j个变量节点的外信息和，i的取值范围为[0，M-1]，M表示奇偶校验矩阵的行数，j的取值范围为j∈N_v，∈表示属于符号，N_v表示与第v个校验节点相邻的变量节点的序号集合，v的取值范围为[0，N-1]，h_m,n表示奇偶校验矩阵中第m行第n列的非二元元素的值，

表示非二元元素h_m,n在GF(Q＝2^d)有限域内的乘法逆元，GF(Q)表示Q个非二元元素的集合，GF(Q)有限域内元素的取值范围为[0，Q-1]，·表示GF(Q)有限域乘法操作，j'表示码字符号的序号，N_w表示与第w个校验节点相邻的变量节点的序号集合，\表示不包含符号，q表示码字符号的序号，h_m,n'表示奇偶校验矩阵中第m行第n'列的非二元元素的值，

表示第j'个码字符号在第k次迭代时的硬判决值，i、m与w的取值对应相等，j、n与q的取值对应相等，j'与n'的取值对应相等；in,

Indicates the sum of external information passed from the i-th check node to the j-th variable node at the k-th iteration, the value range of i is [0, M-1], and M represents the number of rows of the parity check matrix, The value range of j is j∈N _v , ∈ means belonging to a symbol, N _v means the sequence number set of variable nodes adjacent to the vth check node, the value range of v is [0, N-1], h _{m, n} represent the value of the non-binary element in the mth row and nth column in the parity check matrix,

Indicates the multiplicative inverse of the non-binary elements h _{m, n} in the finite field of GF(Q=2 ^d ), GF(Q) represents the set of Q non-binary elements, and the value range of the elements in the finite field of GF(Q) is [0, Q-1], represents GF(Q) finite field multiplication operation, j' represents the sequence number of the codeword symbol, N _w represents the sequence number set of variable nodes adjacent to the wth check node, \ represents not Contains symbols, q represents the serial number of the codeword number, h _{m, n'} represents the value of the non-binary element in the mth row and n'th column in the parity check matrix,

Indicates the hard decision value of the j'th codeword symbol at the kth iteration, the values of i, m and w are correspondingly equal, the values of j, n and q are correspondingly equal, and the values of j' and n' are corresponding equal;

The second step is to update the information of each check node in the current iteration by using the sum of external information passed from the check node to the variable node in the current iteration;

Step 3, using the soft reliability formula, according to the information received by the additive Gaussian white noise channel, calculate the soft reliability of each codeword symbol of the multivariate low density parity check LDPC code in the current iteration;

Step 4, obtain the inversion value corresponding to each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration:

In the first step, according to the following formula, calculate the flip metric of each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration:

表示第a个码字符号在第k次迭代时的翻转度量，a的取值范围为[0，N-1]，

表示第q个码字符号在第k次迭代时更新后的值，

表示第s个码字符号在第k次迭代时的硬判决值，

表示与第q个码字符号在第k次迭代时更新后的值

对应的加性高斯白噪声信道的软可靠度，

表示与第q个码字符号更新后的值

对应的大数逻辑权重系数，

表示来自校验节点的外信息中与第q个码字符号更新后的值

相等的外信息个数，

的取值范围为[0，v]，v表示多元低密度奇偶校验LDPC码的列重，

表示与第t个码字符号在第k次迭代时更新后的值对应的扰动噪声，

表示与第a个码字符号在第k次迭代时更新前的值对应的加性高斯白噪声信道的软可靠度，

表示与第s个码字符号在第k次迭代时的硬判决值

对应的大数逻辑权重系数，

表示来自校验节点的外信息中与第s个码字符号的硬判决值

相等的外信息个数，

的取值范围为[0，v]，

表示在与第t个码字符号在第k次迭代时的硬判决值对应的扰动噪声，a、q、s、w与t的取值对应相等；in,

Indicates the flip metric of the a-th codeword symbol at the k-th iteration, and the value range of a is [0, N-1],

Indicates the updated value of the qth codeword symbol at the kth iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration,

Indicates the updated value of the qth codeword symbol at the kth iteration

The soft reliability of the corresponding additive white Gaussian noise channel,

Indicates the value updated with the qth codeword symbol

The corresponding large number logic weight coefficient,

Indicates the updated value of the qth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v], and v represents the column weight of the multivariate low-density parity-check LDPC code,

Denotes the perturbation noise corresponding to the updated value of the t-th codeword symbol at the k-th iteration,

Indicates the soft reliability of the additive white Gaussian noise channel corresponding to the value of the a-th codeword symbol before the update at the k-th iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration

The corresponding large number logic weight coefficient,

Indicates the hard decision value of the sth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v],

Indicates the disturbance noise corresponding to the hard decision value of the t-th codeword symbol at the k-th iteration, and the values of a, q, s, w and t are correspondingly equal;

The second step is to select the maximum value of the flipping measure of each codeword symbol as the reliability of the codeword symbol in the current iteration of the multivariate low density parity check LDPC code;

The third step is to use the flip objective function to calculate the flip objective function value of each codeword symbol in the current iteration of the multivariate low-density parity check LDPC code;

The fourth step is to use the flipping formula to calculate the flipping value of each codeword symbol of the multivariate low density parity check LDPC code in the current iteration;

Step 5, update the hard-decision symbol sequence of the multivariate low-density parity-check LDPC code in the current iteration:

The first step is to take the sequence number of the codeword symbol corresponding to the maximum flip objective function value of each codeword symbol in the current iteration, as the sequence number of the codeword symbol to be flipped in the current iteration, if the sequence number is different from that in the previous iteration If the sequence numbers of the flipped codeword symbols are equal, the sequence number of the codeword symbol corresponding to the second largest value among the flipping objective function values of each codeword symbol during the current iteration is taken as the sequence number of the codeword symbol to be flipped during the current iteration ;

In the second step, the hard decision value corresponding to the sequence number is updated with the flip value corresponding to the sequence number of the codeword symbol to be flipped during the current iteration;

Step 6, judging whether the codeword vector of the current iteration satisfies the condition for stopping decoding, if so, then perform step 7, otherwise, perform step 2;

Step 7, the decoding is successful.

Compared with the prior art, the present invention has the following advantages:

First, because the present invention introduces random noise disturbance into the objective function of the SFDP decoding method by changing the calculation formula of the flip metric of the SFDP decoding method, it overcomes the high or low decoding complexity of the prior art However, there is a disadvantage of a certain degree of loss in decoding performance, which increases the probability of escaping from an undesired local maximum in the SFDP decoding method of the prior art, so that the present invention greatly improves the decoding performance.

Second, because the present invention uses random noise perturbation to dynamically change the weight coefficients related to large number logic in the SFDP decoding method, it overcomes the relatively high complexity of updating the information outside the variable node during the decoding process, thereby increasing the The probability of the target function escaping from an undesired local maximum in the sign flip decoding SFDP method based on large number logic prediction in the prior art makes the present invention greatly improve the bit error rate performance of the decoder.

The 3rd, because the present invention adopts the dynamic random noise perturbation mode, for different multiple LDPC codes, under different signal-to-noise ratios SNR, select corresponding different weight coefficients, overcome prior art SFDP method in high signal-to-noise ratio SNR ( Signal-to-Noise Ratio) region, there will be an error flat layer, and it is easy to fall into a local trap set under the situation of medium and high signal-to-noise ratios, and there is no specific description of how to select the shortcoming of the weight coefficient relevant to the logic of large numbers, so that the present invention can be used in In some multivariate LDPC codes, the error floor is reduced, and better weight coefficients are selected, which reduces the error performance of decoding.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a comparison diagram of decoding results between the present invention and the existing method at SNR=5.0dB;

Fig. 3 is a comparison diagram of the decoding performance and a decoding convergence speed comparison diagram of the present invention and the existing method for code _C1 ;

Fig. 4 is a comparison diagram of decoding performance and decoding convergence speed of code C ₂ between the present invention and the existing method.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

Below in conjunction with accompanying drawing 1, the specific steps of the present invention will be further described.

Step 1, according to the following formula, calculate the hard decision value of each codeword symbol received by the additive Gaussian white noise channel during the initial iteration:

表示加性高斯白噪声信道接收的第j个码字符号在初始迭代时的硬判决值，j的取值范围为[0，N-1]，N表示多元低密度奇偶校验LDPC码的码字长度，d表示以二进制表示的第j个码字符号的比特数，Σ表示求和操作，r表示在初始迭代时以二进制表示的第j个码字符号的硬判决值

比特位数，r的取值范围为[0，d-1]，

表示在初始迭代时由加性高斯白噪声信道接收的以二进制表示的第j个码字符号信息进行非线性量化后的第t个比特值，t与r的取值对应相等。in,

Indicates the hard decision value of the jth codeword symbol received by the additive Gaussian white noise channel at the initial iteration, the value range of j is [0, N-1], and N represents the code of the multivariate low-density parity-check LDPC code word length, d represents the number of bits of the jth codeword symbol in binary, Σ represents the summation operation, and r represents the hard decision value of the jth codeword symbol in binary representation at the initial iteration

The number of bits, the value range of r is [0, d-1],

Indicates the t-th bit value after the nonlinear quantization of the j-th codeword symbol information received by the additive Gaussian white noise channel received by the additive Gaussian white noise channel during the initial iteration, and the values of t and r are correspondingly equal.

Step 2, update the information of each check node:

The first step is to calculate the sum of external information passed from the check node to the variable node during the current iteration according to the following formula:

表示在第k次迭代时从第i个校验节点传递给第j个变量节点的外信息和，i的取值范围为[0，M-1]，M表示奇偶校验矩阵的行数，j的取值范围为j∈N_v，∈表示属于符号，N_v表示与第v个校验节点相邻的变量节点的序号集合，v的取值范围为[0，N-1]，h_m,n表示奇偶校验矩阵中第m行第n列的非二元元素的值，

表示非二元元素h_m,n在GF(Q＝2^d)有限域内的乘法逆元，GF(Q)表示Q个非二元元素的集合，GF(Q)有限域内元素的取值范围为[0，Q-1]，·表示GF(Q)有限域乘法操作，j'表示码字符号的序号，N_w表示与第w个校验节点相邻的变量节点的序号集合，\表示不包含符号，q表示码字符号的序号，h_m,n'表示奇偶校验矩阵中第m行第n'列的非二元元素的值，

表示第j'个码字符号在第k次迭代时的硬判决值，i、m与w的取值对应相等，j、n与q的取值对应相等，j'与n'的取值对应相等。in,

Indicates the sum of external information passed from the i-th check node to the j-th variable node at the k-th iteration, the value range of i is [0, M-1], and M represents the number of rows of the parity check matrix, The value range of j is j∈N _v , ∈ means belonging to a symbol, N _v means the sequence number set of variable nodes adjacent to the vth check node, the value range of v is [0, N-1], h _{m, n} represent the value of the non-binary element in the mth row and nth column in the parity check matrix,

Indicates the multiplicative inverse of the non-binary elements h _{m, n} in the finite field of GF(Q=2 ^d ), GF(Q) represents the set of Q non-binary elements, and the value range of the elements in the finite field of GF(Q) is [0, Q-1], represents GF(Q) finite field multiplication operation, j' represents the sequence number of the codeword symbol, N _w represents the sequence number set of variable nodes adjacent to the wth check node, \ represents not Contains symbols, q represents the serial number of the codeword number, h _{m, n'} represents the value of the non-binary element in the mth row and n'th column in the parity check matrix,

Indicates the hard decision value of the j'th codeword symbol at the kth iteration, the values of i, m and w are correspondingly equal, the values of j, n and q are correspondingly equal, and the values of j' and n' are corresponding equal.

The second step is to update the information of each check node at the current iteration with the sum of extrinsic information passed from the check node to the variable node at the current iteration.

Step 3, using the following soft reliability formula, according to the information received by the additive Gaussian white noise channel, calculate the soft reliability of each codeword symbol of the multivariate low-density parity check LDPC code in the current iteration:

表示第i个码字符号在第k次迭代时的硬判决值，i的取值范围为[0，N-1]，⊙表示非对称二进制操作，y_w表示加性高斯白噪声信道接收的第w个码字符号信息，t表示以二进制表示的第i个码字符号在第k次迭代时的硬判决值

的比特位数，t的取值范围为[0，d-1]，

表示以二进制表示的第i个码字符号在第k次迭代时第t个比特值，y_r,s表示加性高斯白噪声信道接收的以二进制表示的第r个码字符号第s个比特的软可靠度，i、w与r的取值对应相等，s与t的取值对应相等。in,

Indicates the hard decision value of the i-th codeword symbol at the k-th iteration, the value range of i is [0, N-1], ⊙ indicates an asymmetric binary operation, y _w indicates the additive Gaussian white noise channel received The wth codeword symbol information, t represents the hard decision value of the ith codeword symbol expressed in binary at the kth iteration

The number of bits, the value range of t is [0, d-1],

Represents the t-th bit value of the i-th codeword in binary representation at the k-th iteration, y _r,s represents the s-th bit of the r-th codeword in binary representation received by the additive Gaussian white noise channel The soft reliability of , the values of i, w and r are correspondingly equal, and the values of s and t are correspondingly equal.

Step 4, obtaining the inversion value corresponding to each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration.

In the first step, according to the following formula, calculate the flip metric of each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration:

表示第a个码字符号在第k次迭代时的翻转度量，a的取值范围为[0，N-1]，

表示第q个码字符号在第k次迭代时更新后的值，

表示第s个码字符号在第k次迭代时的硬判决值，

表示与第q个码字符号在第k次迭代时更新后的值

对应的加性高斯白噪声信道的软可靠度，

表示与第q个码字符号更新后的值

对应的大数逻辑权重系数，

表示来自校验节点的外信息中与第q个码字符号更新后的值

相等的外信息个数，

的取值范围为[0，v]，v表示多元低密度奇偶校验LDPC码的列重，

表示与第t个码字符号在第k次迭代时更新后的值对应的扰动噪声，

表示与第a个码字符号在第k次迭代时更新前的值对应的加性高斯白噪声信道的软可靠度，

表示与第s个码字符号在第k次迭代时的硬判决值

对应的大数逻辑权重系数，

表示来自校验节点的外信息中与第s个码字符号的硬判决值

相等的外信息个数，

的取值范围为[0，v]，

表示在与第t个码字符号在第k次迭代时的硬判决值对应的扰动噪声，a、q、s、w与t的取值对应相等。in,

Indicates the flip metric of the a-th codeword symbol at the k-th iteration, and the value range of a is [0, N-1],

Indicates the updated value of the qth codeword symbol at the kth iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration,

Indicates the updated value of the qth codeword symbol at the kth iteration

The soft reliability of the corresponding additive white Gaussian noise channel,

Indicates the value updated with the qth codeword symbol

The corresponding large number logic weight coefficient,

Indicates the updated value of the qth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v], and v represents the column weight of the multivariate low-density parity-check LDPC code,

Denotes the perturbation noise corresponding to the updated value of the t-th codeword symbol at the k-th iteration,

Indicates the soft reliability of the additive white Gaussian noise channel corresponding to the value of the a-th codeword symbol before the update at the k-th iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration

The corresponding large number logic weight coefficient,

Indicates the hard decision value of the sth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v],

Indicates the disturbance noise corresponding to the hard decision value of the t-th codeword symbol at the k-th iteration, and the values of a, q, s, w are correspondingly equal to t.

和

可以考虑两种类型的随机噪声：Among them, the added noise perturbation

and

Two types of random noise can be considered:

The first is a uniform random variable with a mean of 0 and a distribution interval of [-a, a].

The second type is a Gaussian random variable with a mean of 0 and a variance of σ ² =λ ² N ₀ /2. Among them, σ ² represents the variance, λ represents the noise scale parameter, the value range of λ is 0<λ≤1, and N ₀ /2 represents the bilateral power spectral density of the Gaussian function. All Gaussian random variables are independent and identically distributed.

In the second step, the maximum value of the flipping measure of each codeword symbol in the current iteration of the multivariate low-density parity-check LDPC code is selected as the reliability of the codeword symbol.

The third step is to use the following flipping objective function to calculate the flipping objective function value of each codeword symbol of the multivariate low-density parity check LDPC code in the current iteration:

表示第w个码字符号在第k次迭代中的翻转目标函数值，w的取值范围为[0，N-1]，max表示取最大值操作，∈为属于符号，Γ表示集合符号，

表示除第q个码字符号在第k次迭代时的硬判决值以外其他有限域元素构成的集合，w、q、a与s的取值对应相等。in,

Indicates the flip objective function value of the w-th codeword symbol in the k-th iteration, the value range of w is [0, N-1], max means the maximum value operation, ∈ is the belonging symbol, Γ means the set symbol,

Indicates the set of other finite field elements except the hard decision value of the qth codeword symbol at the kth iteration, and the values of w, q, a and s are correspondingly equal.

The fourth step is to use the following inversion formula to calculate the inversion value of each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration:

表示第w个码字符号在第k次迭代时的翻转值，w的取值范围为[0，N-1]，arg max表示当目标函数取最大值时自变量的值，q、a、s与w的取值对应相等。in,

Indicates the flip value of the wth codeword symbol at the kth iteration, the value range of w is [0, N-1], arg max indicates the value of the independent variable when the objective function takes the maximum value, q, a, The values of s and w are correspondingly equal.

Step 5, update the hard-decision symbol sequence of the multivariate low-density parity-check LDPC code in the current iteration:

The first step is to take the sequence number of the codeword symbol corresponding to the maximum flip objective function value of each codeword symbol in the current iteration, as the sequence number of the codeword symbol to be flipped in the current iteration, if the sequence number is different from that in the previous iteration If the sequence numbers of the flipped codeword symbols are equal, the sequence number of the codeword symbol corresponding to the second largest value among the flipping objective function values of each codeword symbol during the current iteration is taken as the sequence number of the codeword symbol to be flipped during the current iteration .

The second step is to update the hard decision value corresponding to the sequence number of the codeword symbol to be flipped with the flip value corresponding to the sequence number of the codeword symbol to be flipped in the current iteration.

Step 6, judging whether the codeword vector of the current iteration satisfies the condition for stopping decoding, if so, execute step 7, otherwise, execute step 2.

The described stop decoding condition refers to any one of the following two conditions:

Condition 1: The product of the codeword vector and the transpose of the parity check matrix of the multivariate low-density parity-check LDPC code is a zero vector.

Condition 2: The number of N-SFDP decoding iterations based on noise-enhanced sign flip decoding reaches 100.

Step 7, the decoding is successful.

Effect of the present invention is described further below in conjunction with simulation experiment:

1. Simulation experiment conditions:

The hardware platform of the emulation experiment of the present invention is: processor is Intel i75930k CPU, main frequency is 3.5GHz, memory 16GB.

The software platform of the simulation experiment of the present invention is: Windows 7 operating system, Microsoft Visual C++6.0, MATLAB 2017.

The noise perturbations used in the simulation experiment of the present invention are respectively Gaussian noise and uniform noise. Under the additive Gaussian white noise channel, the 16-element LDPC code C ₁ and the code rate of 1/2 length of 204 are utilized for SFDP decoding. Simulation is carried out for the 64-element LDPC code C ₂ whose 1/2 length is 384, and the decoding adopts the existing SFDP decoding method and the N-SFDP decoding method proposed by the present invention respectively.

2. Simulation content and result analysis:

The emulation experiment of the present invention is to adopt the present invention and a prior art (based on the multivariate LDPC code symbol reversal decoding SFDP method of prediction) to carry out three emulation experiments respectively:

Experiment 1, adopting the present invention and the prior art method to emulate the 16-element LDPC code C ₁ that is 204 to the code rate 1/2 length respectively when SNR=5.0dB, obtain the decoding result contrast chart, as shown in Figure 2 Show.

Experiment two, adopt the present invention and prior art method respectively to carry out emulation to the 16 yuan LDPC code _C1 that length is 204 for code rate 1/2, obtain decoding performance comparison diagram and decoding convergence speed comparison diagram, as shown in Figure 3 shown.

Experiment three, the method of the present invention and the prior art are respectively used to emulate the 64-element LDPC code _C2 whose code rate is 1/2 and the length is 384, and obtain a decoding performance comparison diagram and a decoding convergence speed comparison diagram, as shown in Figure 4 shown.

In the simulation experiment, an existing technology adopted refers to:

Qin Huang et al. proposed a Sign flipping decoding SFDP (Symbol Flipping Decoding algorithm based on Prediction) method of multivariate low-density parity-check LDPC code based on large number logic prediction.

The effects of the present invention will be further described below in conjunction with FIG. 2 .

Fig. 2 is a comparison diagram of the decoding results of the present invention and the existing method for code _C1 at SNR=5.0dB. Fig. 2 shows a comparison of decoding results between the prior art SFDP decoding method and the N-SFDP decoding method of the present invention when uniform noise disturbance is introduced for code C ₁ at SNR=5.0dB. The abscissa in Figure 2 represents the position index of code C ₁ decoding error symbols in the 16-element finite field, and the corresponding position index range is [0, 203], and the ordinate represents the error in the code word obtained by the two decoding methods The hard decision value of the symbol. The dots marked with solid circles in FIG. 2 represent error symbols in codewords decoded by the existing SFDP decoding method. The points marked with squares in FIG. 2 indicate the error symbols in the codeword obtained by decoding the N-SFDP decoding method proposed by the present invention for the code _C1 when SNR=5.0dB.

It can be seen from Fig. 2 that the hard decision values of the error symbols in the code word obtained by decoding the code C ₁ when SNR=5.0dB by the SFDP decoding method of the existing method are mostly {1, 2, 4, 8} , and their corresponding binary representations are (1) ₁₆ ＝(0001) ₂ , (2) ₁₆ ＝(0010) ₂ , (4) ₁₆ ＝(0100) ₂ , (8) ₁₆ ＝(1000) ₂ , these four Each value has a binary Hamming weight of 1. This shows that when the symbols with relatively small Hamming weights are flipped to other symbols, the SFDP decoding method of the existing method is easy to fall into a local error set. The N-SFDP decoding method proposed by the present invention only has a small number of error symbols in the codeword obtained by decoding the code _C1 when SNR=5.0dB. Figure 2 illustrates the impact of random noise on the error correction capability of the SFDP decoding method. The noise perturbation of the flip metric can effectively correct symbols trapped in local error sets.

The effects of the present invention will be further described below in conjunction with FIG. 3 .

Fig. 3(a) is a comparison diagram of decoding performance for code C ₁ between the present invention and the existing method. Fig. 3(a) shows the performance comparison of BER between the SFDP decoding method of the prior art and the N-SFDP decoding method of the present invention when different noise disturbances are introduced. The noise introduced by N-SFDP decoding is Gaussian noise and uniform noise respectively. The abscissa in Fig. 3(a) represents the signal-to-noise ratio SNR, and the ordinate represents the bit error rate BER. The curve marked with a triangle in FIG. 3( a ) represents the BER performance of the SFDP decoding method in the prior art for code C ₁ . The curve marked with a five-pointed star in Fig. 3(a) represents the BER performance of the code C ₁ when the N-SFDP decoding method proposed by the present invention introduces Gaussian noise. In Fig. 3 (a), the curve marked with a rice-shaped character represents the BER performance of the code C ₁ when the N-SFDP decoding method proposed by the present invention introduces uniform noise.

It can be seen from Fig. 3(a) that, compared with the SFDP decoding method in the prior art, the N-SFDP decoding method proposed in the present invention can significantly improve the decoding performance when introducing different noise perturbations, especially in high signal-to-noise lower than the area. For example, when the bit error rate BER≈10 ^-6 , compared with the SFDP decoding method of the prior art, the N-SFDP decoding method proposed by the present invention can obtain a SNR gain of 0.95dB when Gaussian noise is introduced, and the uniform A 0.9dB signal-to-noise ratio gain can be obtained when there is noise.

It can be seen from Fig. 3(a) that compared with the SFDP decoding method in the prior art, the N-SFDP decoding method proposed by the present invention can reduce the error floor in the high SNR region when introducing different noise disturbances. For example, when the bit error rate BER≈10 ^-7 , the SFDP decoding method in the prior art has an error floor, but the N-SFDP decoding method proposed by the present invention has no obvious error floor when Gaussian noise or uniform noise is introduced .

Fig. 3(b) is a comparison diagram of decoding convergence speeds for code C ₁ between the present invention and the existing method. Fig. 3(b) shows the comparison of the average number of iterations (Average Number of Iterations, ANIs) of the SFDP decoding method in the prior art and the N-SFDP decoding method corresponding to different BER performances when different noise perturbations are introduced in the present invention. The noise introduced by N-SFDP decoding is Gaussian noise and uniform noise respectively. The abscissa in Figure 3(b) represents the bit error rate BER, and the ordinate represents the average number of iterations ANIs. The curve marked with a triangle in FIG. 3( b ) represents the average number of iterations ANIs for the code C ₁ in the SFDP decoding method of the prior art. The curve marked with a five-pointed star in Fig. 3(b) represents the average number of iterations ANIs for code _C1 when the N-SFDP decoding method proposed by the present invention introduces Gaussian noise. The curve marked in the shape of a rice in Fig. 3(b) represents the average number of iterations ANIs for code _C1 when the N-SFDP decoding method proposed by the present invention introduces uniform noise.

It can be seen from Fig. 3(b) that, compared with the SFDP decoding method of the prior art, under the same bit error rate BER performance, the N-SFDP decoding method proposed by the present invention introduces Gaussian noise or uniform noise when decoding The average number of iterations of the code is relatively high. However, the N-SFDP decoding method proposed by the present invention can significantly reduce the signal-to-noise ratio (SNR) at a low bit error rate BER value, that is, when the decoding method is at a similar computational complexity, the N-SFDP decoding method proposed by the present invention The method usually has a lower BER performance. For example, when the average number of iterations is equal to 30, the bit error rate BER of the SFDP decoding method in the prior art is approximately equal to 10 ^-5 , while the N-SFDP decoding method proposed by the present invention can reduce the bit error rate BER when different noises are introduced to approximately equal to 10 ^-7 .

The effects of the present invention will be further described below in conjunction with the simulation diagram of FIG. 4 .

Fig. 4(a) is a comparison diagram of the decoding performance of the present invention and the existing method for code _C2 . Fig. 4(a) shows the performance comparison of BER between the SFDP decoding method of the prior art and the N-SFDP decoding method of the present invention when different noise disturbances are introduced. The noise introduced by N-SFDP decoding is Gaussian noise and uniform noise respectively. The abscissa in Fig. 4(a) represents the signal-to-noise ratio SNR, and the ordinate represents the bit error rate BER. The curve marked with a triangle in FIG. 4( a ) represents the BER performance of the SFDP decoding method in the prior art for code C ₂ . The curve marked with a five-pointed star in Fig. 4(a) shows the BER performance for code _C2 when the N-SFDP decoding method proposed by the present invention introduces Gaussian noise. In Fig. 4 (a), the curve marked with a rice-shaped character represents the BER performance of the code _C2 when the N-SFDP decoding method proposed by the present invention introduces uniform noise.

As can be seen from Figure 4(a), compared with the SFDP decoding method of the prior art, the N-SFDP decoding method proposed by the present invention can improve the decoding performance when introducing different noise perturbations, especially at high SNR under the area. For example, when the bit error rate BER≈10 ^-6 , compared with the SFDP decoding method of the prior art, the N-SFDP decoding method proposed by the present invention can obtain a SNR gain of 0.6dB when Gaussian noise is introduced, and the uniform When there is noise, a 0.5dB SNR gain can be obtained.

Fig. 4(b) is a comparison diagram of decoding convergence speeds for code C ₂ between the present invention and the existing method. Fig. 4(b) shows a comparison chart of the average number of iterations ANIs of the SFDP decoding method in the prior art and the N-SFDP decoding method corresponding to different bit error rate BER performances when different noise perturbations are introduced in the present invention. The noise introduced by N-SFDP decoding is Gaussian noise and uniform noise respectively. The abscissa in Figure 4(b) represents the bit error rate BER, and the ordinate represents the average number of iterations ANIs. The curve marked with a triangle in FIG. 4( b ) represents the average number of iterations ANIs for the code C ₂ in the SFDP decoding method of the prior art. The curve marked with a five-pointed star in FIG. 4(b) represents the average number of iterations ANIs for code _C2 when the N-SFDP decoding method proposed by the present invention introduces Gaussian noise. The curve marked with a rice in Fig. 4(b) represents the average number of iterations ANIs for code _C2 when the N-SFDP decoding method proposed by the present invention introduces uniform noise.

It can be seen from Fig. 4(b) that, compared with the SFDP decoding method of the prior art, under the same bit error rate BER performance, the N-SFDP decoding method proposed by the present invention introduces Gaussian noise or uniform noise when decoding The average number of iterations of the code is relatively high. However, the N-SFDP decoding method proposed by the present invention can significantly reduce the signal-to-noise ratio SNR at a low bit error rate BER value, that is, when the decoding method is at a similar computational complexity, the N-SFDP decoding method proposed by the present invention The method usually has a lower BER performance. For example, when the average number of iterations is equal to 40, the bit error rate BER of the SFDP decoding method in the prior art is approximately equal to 10 ^-5 , while the N-SFDP decoding method proposed by the present invention can reduce the bit error rate BER when different noises are introduced to approximately equal to 10 ^-7 .

The above simulation experiments show that: the method of the present invention utilizes random noise to perturb the noise of the flip metric, and can effectively correct symbols trapped in local error sets, especially in areas with high SNR, by introducing different noise perturbations, the decoding performance can be significantly improved , to obtain the SNR gain, by introducing different noise perturbations, the error floor can be reduced in the high SNR region, so that the average number of iterations of decoding is higher under the same bit error rate BER performance, which solves the problem of the existing technology In the method, the decoding complexity is high, or the decoding performance is low, and there will be an error floor in the area of high SNR, and it is easy to fall into the problem of local trap set in the case of medium and high SNR. It is a very practical multivariate Noise-enhanced sign-flip decoding method for LDPC codes.

Claims (5)

1. A kind of symbol flipping decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement, it is characterized in that, calculate the reversal value corresponding to each codeword number of multivariate low-density parity check LDPC code in current iteration, Using this flip value to update the hard-decision symbol sequence during the current iteration, the steps of the method include the following: Step 1, according to the following formula, calculate the hard decision value of each codeword symbol received by the additive Gaussian white noise channel during the initial iteration:

in,

Indicates the hard decision value of the jth codeword symbol received by the additive Gaussian white noise channel at the initial iteration, the value range of j is [0, N-1], and N represents the code of the multivariate low-density parity-check LDPC code word length, d represents the number of bits of the jth codeword symbol in binary, Σ represents the summation operation, and r represents the hard decision value of the jth codeword symbol in binary representation at the initial iteration

The number of bits, the value range of r is [0, d-1],

Represents the t-th bit value after nonlinear quantization of the j-th codeword symbol information received by the additive Gaussian white noise channel received by the additive Gaussian white noise channel during the initial iteration, and the values of t and r are correspondingly equal; Step 2, update the information of each check node: The first step is to calculate the sum of external information passed from the check node to the variable node during the current iteration according to the following formula:

in,

Indicates the sum of external information passed from the i-th check node to the j-th variable node at the k-th iteration, the value range of i is [0, M-1], and M represents the number of rows of the parity check matrix, The value range of j is j∈N _v , ∈ means belonging to a symbol, N _v means the sequence number set of variable nodes adjacent to the vth check node, the value range of v is [0, N-1], h _{m, n} represent the value of the non-binary element in the mth row and nth column in the parity check matrix,

Indicates the multiplicative inverse of the non-binary elements h _{m, n} in the finite field of GF(Q=2 ^d ), GF(Q) represents the set of Q non-binary elements, and the value range of the elements in the finite field of GF(Q) is [0, Q-1], represents GF(Q) finite field multiplication operation, j' represents the sequence number of the codeword symbol, N _w represents the sequence number set of variable nodes adjacent to the wth check node, \ represents not Contains symbols, q represents the serial number of the codeword number, h _{m, n'} represents the value of the non-binary element in the mth row and n'th column in the parity check matrix,

Indicates the hard decision value of the j'th codeword symbol at the kth iteration, the values of i, m and w are correspondingly equal, the values of j, n and q are correspondingly equal, and the values of j' and n' are corresponding equal; The second step is to update the information of each check node in the current iteration by using the sum of external information passed from the check node to the variable node in the current iteration; Step 3, using the soft reliability formula, according to the information received by the additive Gaussian white noise channel, calculate the soft reliability of each codeword symbol of the multivariate low density parity check LDPC code in the current iteration; Step 4, obtain the inversion value corresponding to each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration: In the first step, according to the following formula, calculate the flip metric of each codeword symbol of the multivariate low-density parity-check LDPC code in the current iteration:

in,

Indicates the flip metric of the a-th codeword symbol at the k-th iteration, and the value range of a is [0, N-1],

Indicates the updated value of the qth codeword symbol at the kth iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration,

Indicates the updated value of the qth codeword symbol at the kth iteration

The soft reliability of the corresponding additive white Gaussian noise channel,

Indicates the value updated with the qth codeword symbol

The corresponding large number logic weight coefficient,

Indicates the updated value of the qth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v], and v represents the column weight of the multivariate low-density parity-check LDPC code,

Denotes the perturbation noise corresponding to the updated value of the t-th codeword symbol at the k-th iteration,

Indicates the soft reliability of the additive white Gaussian noise channel corresponding to the value of the a-th codeword symbol before the update at the k-th iteration,

Indicates the hard decision value of the s-th codeword symbol at the k-th iteration

The corresponding large number logic weight coefficient,

Indicates the hard decision value of the sth codeword symbol in the external information from the check node

Equal number of extrinsic information,

The value range of is [0, v],

Indicates the disturbance noise corresponding to the hard decision value of the t-th codeword symbol at the k-th iteration, and the values of a, q, s, w and t are correspondingly equal; The second step is to select the maximum value of the flipping measure of each codeword symbol as the reliability of the codeword symbol in the current iteration of the multivariate low density parity check LDPC code; The third step is to use the flip objective function to calculate the flip objective function value of each codeword symbol in the current iteration of the multivariate low-density parity check LDPC code; The fourth step is to use the flipping formula to calculate the flipping value of each codeword symbol of the multivariate low density parity check LDPC code in the current iteration; Step 5, update the hard-decision symbol sequence of the multivariate low-density parity-check LDPC code in the current iteration: The first step is to take the sequence number of the codeword symbol corresponding to the maximum flip objective function value of each codeword symbol in the current iteration, as the sequence number of the codeword symbol to be flipped in the current iteration, if the sequence number is different from that in the previous iteration If the sequence numbers of the flipped codeword symbols are equal, the sequence number of the codeword symbol corresponding to the second largest value among the flipping objective function values of each codeword symbol during the current iteration is taken as the sequence number of the codeword symbol to be flipped during the current iteration ; In the second step, the hard decision value corresponding to the sequence number is updated with the flip value corresponding to the sequence number of the codeword symbol to be flipped during the current iteration; Step 6, judging whether the codeword vector of the current iteration satisfies the condition for stopping decoding, if so, then perform step 7, otherwise, perform step 2; Step 7, the decoding is successful. 2. the sign reversal decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement according to claim 1, is characterized in that, the soft reliability formula described in step 3 is as follows:

in,

Indicates the hard decision value of the i-th codeword symbol at the k-th iteration, the value range of i is [0, N-1], ⊙ indicates an asymmetric binary operation, y _w indicates the additive Gaussian white noise channel received The wth codeword symbol information, t represents the hard decision value of the ith codeword symbol expressed in binary at the kth iteration

The number of bits, the value range of t is [0, d-1],

Represents the t-th bit value of the i-th codeword in binary representation at the k-th iteration, y _r,s represents the s-th bit of the r-th codeword in binary representation received by the additive Gaussian white noise channel The soft reliability of , the values of i, w and r are correspondingly equal, and the values of s and t are correspondingly equal. 3. the symbol reversal decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement according to claim 1, it is characterized in that, the reversal objective function described in the third step of step 4 is as follows:

in,

Indicates the flip objective function value of the w-th codeword symbol in the k-th iteration, the value range of w is [0, N-1], max means the maximum value operation, ∈ is the belonging symbol, Γ means the set symbol,

Indicates the set of other finite field elements except the hard decision value of the qth codeword symbol at the kth iteration, and the values of w, q, a and s are correspondingly equal. 4. the symbol reversal decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement according to claim 1, is characterized in that, the reversal formula described in the 4th step of step 4:

in,

Indicates the flip value of the w-th codeword symbol at the k-th iteration, the value range of w is [0, N-1], argmax indicates the value of the independent variable when the objective function takes the maximum value, q, a, s Correspondingly equal to the value of w. 5. the sign reversal decoding N-SFDP method based on multivariate low-density parity check LDPC code noise enhancement according to claim 1, is characterized in that, the stop decoding condition described in step 6 refers to satisfying following two Either of the conditions: Condition 1: the product of the transpose of the codeword vector and the parity check matrix of the multivariate low-density parity-check LDPC code is a zero vector; Condition 2: The number of N-SFDP decoding iterations based on noise-enhanced sign flip decoding reaches 100.

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