CN107241106B

CN107241106B - Deep learning-based polar code decoding algorithm

Info

Publication number: CN107241106B
Application number: CN201710371218.1A
Authority: CN
Inventors: 张川; 徐炜鸿; 吴至臻; 尤肖虎
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2017-05-24
Filing date: 2017-05-24
Publication date: 2020-07-14
Anticipated expiration: 2037-05-24
Also published as: CN107241106A

Abstract

The invention discloses a polarization code decoding algorithm based on deep learning, and provides a multidimensional scaling Min-sum confidence propagation (Beliexpropagation) decoding algorithm for accelerating the convergence speed of the decoding algorithm; then, according to the similarity between the factor graph of the BP algorithm and the deep neural network, the deep neural network-based polar code decoder is realized, the deep neural network decoder is trained by utilizing a deep learning technology, the decoding iteration times are reduced by nearly 90% compared with the original BP decoding algorithm, and better decoding performance is obtained; finally, the invention provides the hardware realization of the basic operation module of the deep neural network polar code decoder, and the hardware folding technology is utilized to reduce the hardware consumption by 50 percent.

Description

Deep learning-based polar code decoding algorithm

Technical Field

The invention belongs to the field of deep neural networks and decoding of polarization codes, and particularly relates to a polarization code decoding algorithm based on deep learning.

Background

Polarization code (Polar code) is a paper "Channelpolarization" by ErdalArikan in 2009: a method for constructing capacity-encoding codes for systematic combining-input mechanisms channels is proposed. The channel polarization phenomenon means that when the number of channels tends to infinity, a part of the channels tends to be perfect, and a part of the channels tends to be pure noise channels. Based on the channel polarization phenomenon, a better channel in the combined channels is selected to construct a polarization code. Polar codes are one of the very important technologies in fifth generation (5G) mobile communication systems.

The two most common polar code decoding algorithms are the Successive Cancellation (SC) algorithm and the Belief Propagation (BP) algorithm. The SC decoding has low calculation complexity and good error correction performance, but has longer decoding delay due to the serial operation structure of the SC algorithm.

Compared with SC decoding, BP decoding has much shorter decoding delay than SC decoding under the condition of long codes due to the parallel structure of BP decoding; however, BP decoding requires multiple iterations, so the computation complexity of BP decoding is high, and the decoding performance has a certain gap from SC. To reduce computational complexity, the early stop algorithm and Min-sum algorithm are introduced into BP decoding, but do not speed up the convergence of BP decoding. Deep learning (deep learning) techniques and Deep Neural Networks (DNNs) have also been introduced to achieve better decoding performance, but neural network complexity grows exponentially with code length. Therefore, how to obtain a better compromise between complexity and decoding performance is one of the key points in the deep learning-based BP decoding algorithm research.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problems, the invention provides a polarization code decoding algorithm based on deep learning, which solves the problem that the existing polarization code BP decoding algorithm has low convergence speed under low signal-to-noise ratio, achieves the aim of obtaining better decoding performance with less iteration times by utilizing the deep learning technology, and reduces the decoding complexity and the decoding delay.

The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a polar code decoding algorithm based on deep learning specifically comprises the following steps:

(1) based on a BP algorithm for scaling Min-sum, an improved BP algorithm for scaling Min-sum in a multidimensional way is provided;

(2) expanding the polarization code BP decoding factor graph to form a deep neural network decoder according to the similarity of the polarization code BP decoding factor graph and the neural network structure;

(3) generating all-zero code words, and training a deep neural network decoder by utilizing backward propagation and Mini-batch stochastic gradient descent algorithm in a deep learning technology after AWGN channel transmission;

(4) the hardware architecture of the improved BP decoder is provided based on the original BP decoder, and the hardware consumption is reduced by using a hardware folding technology.

In the step (1), the BP algorithm of multidimensional scaling Min-sum is as follows:

wherein the content of the first and second substances,

and

respectively representing the log-likelihood ratio characteristic information of the jth row of the ith column of the BP factor graph in the tth iteration,

and

for scaling coefficients corresponding to left and right propagation, g (x, y) ═ sign (x) sign (y) min (| x |, | y |).

In the step (2), a polarization code factor graph is expanded by utilizing the similarity between the deep neural network and the BP factor graph, fixed iteration times are selected, and finally a Sigmoid activation function is output to form a deep neural network polarization code decoder.

In the step (3), a neural network is trained by utilizing backward propagation and Mini-batch stochastic gradient descent algorithm in deep learning to obtain the combination of optimal scaling parameters of the multidimensional scaling Min-sum algorithm, an Adam algorithm with the learning rate of 0.001 is introduced through all-zero code words of an additive white Gaussian noise channel, the learning rate is adjusted in a self-adaptive mode, and the training convergence of a deep neural network polarization code decoder is accelerated.

In the step (4), a hardware folding technology is utilized to select a proper folding set, the same module is time division multiplexed, and a basic computing module after folding comprises 1 adder, 1 g function module and 1 multiplier.

Has the advantages that: compared with the prior polarization code BP decoder, the invention has the remarkable advantages that: the convergence rate of the decoding algorithm is greatly increased, the iteration times required for achieving the convergence effect are reduced, the performance of the deep neural network polarization code decoder for 5 iterations exceeds the performance of the original polarization code BP decoder for 50 times, and the convergence rate is about 10 times; in addition, hardware consumption after the hardware folding technology processing is saved by about 50% compared with the original deep neural network decoder.

Drawings

FIG. 1 is a diagram of 8-bit polar code BP decoding factors;

FIG. 2 is a diagram of an iterative process of one complete BP decoding of an 8-bit polar code neural network decoder;

FIG. 3 is a block diagram of a 64-bit deep neural network polar code decoder for T iterations;

FIG. 4 is a block diagram of a basic operation module with multi-dimensional scaling function in a polar decoder;

FIG. 5 is a basic operation module of a polarization code decoder after hardware folding;

FIG. 6 is a multi-dimensional scaling Min-sum operation block;

fig. 7 is a graph comparing the performance of a deep neural network polar code decoder with a conventional polar code BP decoder.

Detailed Description

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

Fig. 1 shows an iterative factor graph of the polar code BP decoding, which is log likelihood ratio information iteratively propagated to the left and the right on the factor graph. Taking the polarization code with the code length N being 8 as an example, the leftmost end in the factor graph corresponds to the bit information being u, and the rightmost end corresponds to the received codeword being x.

Wherein, (i, j) represents the node of the jth row in the ith column, each node contains the log-likelihood ratio information of the left and the right, and the information propagated to the left in the t iteration is recorded as

Information propagated to the right is noted

In the initial decoding stage, the information of the leftmost end and the rightmost end is initialized as follows:

wherein A represents a set of information bits, and n is log₂N。

After the traditional polarization code BP decoding is initialized, iteration is carried out according to the following formula:

where g (x, y) ═ sign (x) sign (y) min (| x |, | y |), sign is a sign function.

After iteration is finished, if the code word is not the information bit, the code word is decoded to be 0, and if the code word is the information bit, the judgment is carried out according to the following formula:

based on the existing BP algorithm for scaling Min-sum (Scaled Min-sum), the improved multi-dimensional scaling Min-sum (Multiple Scaled Min-sum) BP algorithm is provided, and each iteration adopts different scaling coefficients for the function g, so that the decoding effect can be improved.

Wherein the content of the first and second substances,

and

corresponding to left-and right-propagating scaling factors, respectively.

And expanding the polarization code BP decoding factor graph to form a deep neural network decoder by utilizing the similarity between the polarization code BP decoding factor graph and the neural network. As shown in fig. 2, a polar code neural network decoder performs a complete BP decoding iteration process, and a complete 8-bit polar code BP iteration corresponds to a neural network, and the output of the neural network goes through a Sigmoid activation function. The structure of a 64-bit deep neural network polarization code BP decoder with T iterations is fully represented by fig. 3.

A certain number of noisy all-zero codewords are generated, and a loss function (L oss function) measures the coding performance using a cross entropy (cross entropy) function as follows:

training a neural network by utilizing Back propagation (Back propagation) and Mini-batch stochastic gradient descent (Mini-batch stochastic gradient device) algorithms in deep learning to obtain an optimal scaling parameter of the multi-dimensional scaling Min-sum algorithm

And

the training complexity is greatly reduced by only needing all-zero code words passing through an Additive White Gaussian Noise (AWGN) channel, and by introducing an Adam algorithm with the learning rate of 0.001, the learning rate can be adaptively adjusted, so that the training convergence of the deep neural network polar code decoder is accelerated.

Based on the hardware architecture of the original BP decoder given the modified BP decoder, the basic computation module in the deep neural network decoder can be represented as fig. 4, where the s-module is the g-function with scaling function as shown in fig. 6. The basic calculation module consists of 2 adders, 2 g-function modules and 2 multipliers.

By utilizing a hardware folding technology, a proper folding set is selected, the same module is subjected to time division multiplexing, only 1 adder, 1 g function module and 1 multiplier are needed, a basic computing module after folding can be represented as a graph 5, and hardware consumption in the basic computing module in the polarization code BP decoder is reduced by nearly 50%.

As shown in fig. 7, comparing the performance of the deep neural network polar code decoder with the performance of the traditional polar code BP decoder, it can be seen that the convergence rate of the decoding algorithm is greatly increased, the number of iterations required to achieve the convergence effect is reduced, the performance of the deep neural network polar code decoder with 5 iterations exceeds the performance of the original polar code BP decoder by 50 times, and the convergence rate is about 10 times.

Claims

1. A polar code decoding algorithm based on deep learning is characterized in that: the method specifically comprises the following steps:

the BP algorithm of multidimensional scaling Min-sum is as follows:

wherein the content of the first and second substances,

and

and

for scaling coefficients corresponding to left and right propagation, g (x, y) ═ sign (x) · sign (y) · min (| x |, | y |);

(2) expanding the polarization code BP decoding factor graph according to the similarity of the polarization code BP decoding factor graph and a neural network structure, selecting fixed iteration times, outputting a Sigmoid activation function, and forming a deep neural network decoder;

(3) generating all-zero code words, after the all-zero code words are transmitted through an AWGN channel, training a deep neural network decoder by utilizing backward propagation in a deep learning technology and a Mini-batch random gradient descent algorithm, obtaining the combination of optimal scaling parameters of a multidimensional scaling Min-sum algorithm, introducing an Adam algorithm with the learning rate of 0.001 through the all-zero code words of an additive white Gaussian noise channel, adaptively adjusting the learning rate, and accelerating the training convergence of the deep neural network polar code decoder;

2. The deep learning-based polar code decoding algorithm according to claim 1, wherein: in the step (4), a hardware folding technology is utilized to select a proper folding set, the same module is time division multiplexed, and a basic computing module after folding comprises 1 adder, 1 g function module and 1 multiplier.