Research On Polar Code Encoding And Decoding Algorithm With Variable Code Length

Arikan first proposed polar codes in 2009 and provided a rigorous theoretical proof that polar codes can "achieve" Shannon capacity under binary input symmetric discrete memoryless channels.This has significant implications for channel coding and decoding techniques in realizing high-capacity communication transmission.Polar codes exhibit relatively low complexity in encoding and decoding algorithms,and their performance is excellent within certain code lengths.Consequently,since their introduction,they have attracted considerable attention and found widespread application.However,in practical applications,the channel conditions change.To adapt to these changes,it is necessary to flexibly adjust parameters such as the code length and code rate of polar codes.Therefore,it is essential to study encoding and decoding algorithms for variable-length polar codes.In this context,the present study analyzes the existing problems in the current variable-length polar code encoding and decoding schemes,and proposes an improved variable-length polar code encoding algorithm to address the performance degradation of polar codes after adjusting the code length.Under the traditional puncturing method for adjusting the polar code length,the error probability of each polar sub-channel is calculated based on the channel reliability estimation method,and the polar sub-channels with relatively low reliability are punctured.To ensure better performance,the initial log-likelihood ratio of the punctured bits is set to infinity(or negative infinity).Simulation results show that the improved encoding algorithm proposed in this paper has better performance than the traditional encoding algorithm.To further improve the performance of the encoding algorithm,this paper introduces deep neural network technology into the research of variable-length polar code decoding.Deep learning technology is increasingly mature and stable,demonstrating excellent performance in addressing classification problems.Polar code channel decoding is a high-dimensional classification problem in practice,making deep neural network technology suitable for handling and solving decoding issues,and has gradually become the focus of current research.Based on this,the study compares and analyzes the decoding performance of several common deep neural networks under irregular code lengths.In terms of decoding system structure,this paper presents a variable-length polar code decoding algorithm that achieves better decoding performance by changing the learning objectives through modifying the system framework.Traditional neural network decoding systems require the neural network to learn not only the noise characteristics but also the codeword structure mapping from the codeword position to the data information position.Research and analysis reveal that the codeword structure is a distribution composed of N-bit parity-check problems in practice,which is difficult for deep neural networks to learn efficiently.By altering the learning objective of the neural network decoder,a variable-length polar code neural network decoding system structure is proposed,which avoids forcing the neural network to learn the codeword structure mapping and applies the highly generalizable neural network to conduct variable-length polar code decoding learning.The final simulation results show that the improved neural network’s generalization ability has been significantly enhanced,requiring only a small part of the codebook space to independently learn the spatial dispersion characteristics of the codewords and achieve performance close to the MAP decoding algorithm.