Polar code bit-flip BP decoding method based on recurrent neural network

Abstract

The present invention discloses a polarization code bit flipping BP decoding algorithm based on a recurrent neural network. The present invention designs a recurrent neural network architecture and performs bit flipping in combination with a key set, selects a candidate bit from the key set according to the index in descending order of the corresponding error rate in the key set, and improves the BP decoding algorithm based on the BP algorithm by using the minimum offset and approximate OMS. According to the similarity between the polarization code BP decoding factor graph and the neural network structure, the polarization code BP decoding factor graph is expanded on the basis of the DNN architecture to form a recurrent neural network decoder, generates all-zero codewords, and uses the back propagation and Adam gradient descent optimization algorithm in deep learning technology to train the recurrent neural network decoder. The algorithm of the present invention greatly accelerates the convergence speed of the decoding algorithm, reduces the number of iterations required to achieve the convergence effect, and improves the computing resource consumption and additional memory overhead of the traditional BP decoding algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of deep learning and polarization code decoding, and relates to a polarization code bit flip BP decoding method based on a recurrent neural network. Background Art

[0002] In 2008, Professor E. Arikan first proposed polar codes, which have attracted much attention because they have been proven to be able to achieve Shannon capacity under low encoding and decoding complexity. Polar codes have now been adopted as the control channel coding scheme for the fifth generation mobile communication technology (5th Generation Mobile Networks, 5G).

[0003] The basic decoding algorithms of polar codes mainly include Successive Cancellation (SC) decoding algorithm and Belief Propagation (BP) decoding algorithm. Compared with BP decoding, SC decoding can achieve better channel capacity and lower block error rate (BLER) through the improved SC algorithm. However, SC decoding has a low throughput due to its sequential processing characteristics, while the BP algorithm performs well in parallelization. The parallel decoding process of the BP decoding algorithm has higher throughput and lower latency, so it can better meet the communication requirements of 5G scenarios.

[0004] In recent years, the research on BP decoding has been working hard to improve the decoding performance of BP while maintaining its advantages. One way to optimize the performance of BP decoding algorithm is to add neural network to assist the BP decoding process. The BP decoding algorithm based on deep neural network (DNN) reduces the total number of iterations and overall complexity before convergence by scaling the messages of trainable weights. However, there are still problems with the deep neural network architecture. First, the scaling factor set by the algorithm to reduce the approximation loss adds a large number of multiplication operations to the algorithm, resulting in a significant increase in the computational complexity of the BP decoding algorithm based on deep neural network. In addition, the storage space is occupied by the storage of a large number of scaling factors in the deep neural network architecture, which makes it difficult to deploy in real communication systems. Moreover, the BP decoding algorithm based on DNN does not solve the error propagation problem existing in the BP decoding algorithm. Incorrect decoding of the information bit of the BP decoding message passing algorithm may cause error propagation, which has a negative impact on the reliability and accuracy of many other bits. Summary of the invention

[0005] The purpose of the present invention is to provide a polar code bit flipping BP decoding method based on a recurrent neural network, which solves the problems of large computational memory overhead and error propagation in the polar code BP decoding algorithm in the prior art. To address this problem, the present invention designs a recurrent neural network architecture and combines a critical set (CS) to perform bit flipping, thereby reducing the BLER of the BP decoding algorithm and improving the computational resource consumption and additional memory overhead of the traditional BP decoding algorithm.

[0006] The technical solution adopted by the present invention is

[0007] A polar code bit flip BP decoding method based on recurrent neural network specifically comprises the following steps:

[0008] (1) Establish the bit flip set key set CS;

[0009] (2) If the CRC decoding fails after the cyclic redundancy check, a candidate bit is selected from the key set according to the index in the key set sorted in descending order of the corresponding error rate to be flipped;

[0010] (3) Based on the minimum and approximate BP algorithm, the offset minimum and approximate OMS is used to improve the BP decoding algorithm;

[0011] (4) Based on the similarity between the polar code BP decoding factor graph and the neural network structure, the polar code BP decoding factor graph is expanded on the basis of the DNN architecture to form a recurrent neural network decoder;

[0012] (5) Generate an all-zero codeword, transmit it through the AWGN channel, and then use the back propagation and Adam gradient descent optimization algorithm in deep learning technology to train the recurrent neural network decoder.

[0013] In step (1), the key set needs to be the index of the first bit in each node with a coding rate of 1 in the binary tree structure of polar codes where the leaf nodes are all information bits:

[0014]

[0015] In step (3), the BP algorithm with the minimum deviation and approximation is:

[0016]

[0017] and They represent the left information log-likelihood ratio in the tth iteration process respectively. and right information log-likelihood ratio The offset added during the calculation, where g(x,y) is expressed as follows:

[0018] g(x,y)≈sgn(x)sgn(y)×max(min(|x|,|y|)-β,0)

[0019] In step (4), based on the deep neural network decoder, the polar code factor graph is expanded, a fixed number of iterations is selected, and finally the output uses the Sigmoid activation function to form a recurrent neural network polar code decoder.

[0020] In step (5), the neural network is trained using the back propagation and Mini-batch stochastic gradient descent algorithms in deep learning to obtain a combination of offset parameters with the minimum offset and the best approximation algorithm. After passing through an all-zero codeword of an additive white Gaussian noise channel, the Adam algorithm with a learning rate of 0.0001 is introduced to adaptively adjust the learning rate to accelerate the training convergence of the recurrent neural network polar code decoder.

[0021] The beneficial effects of the present invention are as follows:

[0022] Compared with the original polar code BP decoder, the present invention has the following significant advantages: greatly accelerating the convergence speed of the decoding algorithm, reducing the number of iterations required to achieve the convergence effect, effectively reducing the BLER of the BP decoding algorithm, and improving the computing resource consumption and additional memory overhead of the traditional BP decoding algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the 8-bit polar code BP decoding factor graph;

[0024] Figure 2 This is a complete decoding iteration diagram of a 4-bit polar code in a recurrent neural network;

[0025] Figure 3 There are 3 types of neurons in the recurrent neural network architecture;

[0026] Figure 4 It is a polar code bit-flip BP decoder based on recurrent neural network;

[0027] Figure 5 This is a comparison chart of the BLER performance of the RNN-BPF decoder at different bit rates and different code lengths;

[0028] Figure 6 This is a comparison chart of the BLER performance of the RNN-BPF decoder and other decoders;

[0029] Figure 7 This is a comparison chart of the delay of different decoders. DETAILED DESCRIPTION

[0030] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] like Figure 1 The figure shows the iterative factor graph of polar code BP decoding. Polar code BP decoding is the log-likelihood ratio information that propagates leftward and rightward iteratively on the factor graph. The factor graph of (N,K) polar code consists of N×(n+1) nodes and n=log2N stages. Taking the polar code with code length N=8 as an example, the leftmost bit information in the factor graph is u, and the rightmost bit information is x.

[0032] The BP decoding process is related to two types of information at the node (i, j): the log-likelihood ratio of the right information from left to right and the left information log-likelihood ratio from right to left Where t represents the tth iteration. and Information is transferred between adjacent nodes in the factor graph and iteratively updated. The update formula of information in each iteration process is expressed as follows:

[0033]

[0034] in, In order to reduce the computational complexity of the BP decoding algorithm, the minimum sum (Min-Sum, MS) approximation is used to approximate g(c, y) as:

[0035] g(x,y)≈sign(x)×sign(y)min(|x|,|y|)

[0036] When the iteration starts, the initial log-likelihood ratio can obtain the initial values ​​of the right information log-likelihood ratio and the left information log-likelihood ratio respectively. and It is expressed as follows:

[0037]

[0038] Where A represents the information bit set, A c represents the frozen bit set. After T iterations, the jth estimated information bit can be obtained by comparing the left information log-likelihood ratio of the last iteration output Making a hard decision yields:

[0039]

[0040] Based on the existing minimum sum approximate BP algorithm, an improved offset minimum sum approximate algorithm is used to calculate the left information log-likelihood ratio in each iteration. and right information log-likelihood ratio Adding offsets during calculations and Different scaling factors are used for the function g in each iteration. Simple symbol, comparison and subtraction operations are used instead of multiplication operations to solve the problem of high computational complexity caused by setting the scaling factor of the previous DNN-BP and improve the decoding effect.

[0041]

[0042] Taking advantage of the similarity between the polar code BP decoding factor graph and the neural network, based on the deep neural network architecture, the polar code BP decoding factor graph is expanded to form a recurrent neural network decoder. Figure 2 The figure shows a complete BP decoding iteration process of the polar code neural network decoder. The input layer consists of N neurons and the initial value of the input channel log-likelihood ratio. The transmission process of right information from left to right and left information from right to left is expanded into (n-1) layers and n layers of hidden layers consisting of N neurons respectively. Therefore, a complete iteration is converted into (2n-1) layers of hidden layers. The last hidden layer of information transmission from right to left calculates the output of the leftmost node of the original factor graph. At the end of T iterations, in order to make the codeword estimation range obtained by the neural network decoder [0,1], the output layer of the last layer of the network needs to use the sigmoid function to readjust the output to the [0,1] range, as shown below:

[0043]

[0044] In order to evaluate the decoding performance, the cross entropy loss function is used to evaluate the error between the predicted information bit o output by the neural network through the activation function and the transmitted information bit u:

[0045]

[0046] like Figure 4 As shown in Figure 1, if the RNN-assisted BP decoder fails to decode after the cyclic redundancy check (CRC), a candidate bit is selected from the key set according to the index in descending order of the corresponding error rate in the key set for flipping, that is, the candidate bit with a larger P e (u i ) value of u i First, it is flipped. Such sorting can be done offline without introducing delays caused by sorting. After bit flipping, RNN-based BP decoding is performed. If the result satisfies the CRC, the decoding process is completed. Otherwise, other candidate nodes in the key set will be tried until the CRC passes successfully.

[0047] The loss function is minimized by the back propagation algorithm and the stochastic gradient descent (SGD) algorithm, and the Adam gradient descent optimization algorithm with a learning rate of 0.0001 is used for training to determine the optimal offset value.

[0048] Example

[0049] Polar codes of (16,8), (32,16), (64,32) and (128,64) are selected respectively, and all-zero codewords are selected as training data. The data is obtained by transmitting through a Gaussian channel, and 3600 codewords are selected as the size of the mini-batch. The test data is random binary information obtained after polarization coding, binary phase shift keying modulation and transmission on a Gaussian channel.

[0050] (1) Performance comparison

[0051] from Figure 5 The simulation results show that when the code length is constant, the smaller the code rate, the better the BLER performance of the polar code bit-flip BP decoding, which is more significant when the signal-to-noise ratio is small. When the code rate remains unchanged, in the low signal-to-noise ratio range, the BLER performance of the short code length is better than that of the long code length, and in the high signal-to-noise ratio range, the performance of the long code length is better. When the code length and code rate are the same, the BLER performance of the original BP, RNN-BP and RNN-BPF decoding algorithms under different numbers of iterations are compared. It can be observed that for the (64,32) polar code, the RNN-BP and RNN-BPF decoding algorithms only need about 7 iterations to converge and obtain good performance. On the other hand, the traditional CS-BF decoding algorithm requires more than 30 iterations to achieve a BLER performance similar to that of the RNN-BPF decoder with 7 iterations.

[0052] (2) Delay comparison

[0053] The delay analysis of different decoders under different code lengths is as follows Figure 7 As shown in Figure 2, the RNN-BPF decoder achieves lower decoding latency compared to other decoders.

Claims

1. A polar code bit-flip BP decoding method based on a recurrent neural network, characterized in that: The specific steps include: (1) Establish the bit flip set key set CS; (2) If the CRC decoding fails after the cyclic redundancy check, a candidate bit is selected from the key set according to the index in the key set sorted in descending order of the corresponding error rate to be flipped; (3) Based on the minimum and approximate BP algorithm, the offset minimum and approximate OMS is used to improve the BP decoding algorithm; (4) Based on the similarity between the polar code BP decoding factor graph and the neural network structure, the polar code BP decoding factor graph is expanded on the basis of the DNN architecture to form a recurrent neural network decoder; (5) Generate all-zero codewords, transmit them through the AWGN channel, and train the recurrent neural network decoder using the back propagation and Adam gradient descent optimization algorithms in deep learning technology; In step (3), the BP algorithm with the minimum deviation and approximation is: and They represent the left information log-likelihood ratio in the tth iteration process respectively. and right information log-likelihood ratio The offset added during the calculation, where g(x,y) is expressed as follows: g(x,y)≈sgn(x)sgn(y)×max(min(|x|,|y|)-β,0).

2. The polar code bit-flip BP decoding method based on recurrent neural network according to claim 1, characterized in that: In step (1), the key set needs to be the index of the first bit in each node with a coding rate of 1 in the binary tree structure of polar codes where the leaf nodes are all information bits:

3. The polar code bit-flip BP decoding method based on recurrent neural network according to claim 2, characterized in that: In step (4), based on the deep neural network decoder, the polar code factor graph is expanded, a fixed number of iterations is selected, and finally the output uses the Sigmoid activation function to form a recurrent neural network polar code decoder.

4. The polar code bit-flip BP decoding method based on recurrent neural network according to claim 3, characterized in that: In step (5), the neural network is trained using the back propagation and Mini-batch stochastic gradient descent algorithms in deep learning to obtain a combination of offset parameters with the minimum offset and the best approximation algorithm. After passing through an all-zero codeword of an additive white Gaussian noise channel, the Adam algorithm with a learning rate of 0.0001 is introduced to adaptively adjust the learning rate to accelerate the training convergence of the recurrent neural network polar code decoder.

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