On the Decoding of Polar Codes on Permuted Factor Graphs

TL;DR

This paper proposes a method to improve polar code decoding by using a single decoder for multiple permutations, resulting in better error correction performance suitable for 5G applications.

Contribution

It introduces a way to map factor graph permutations to codeword permutations, enabling a unified decoder and a set of predetermined permutations for enhanced error correction.

Findings

Error-correction performance improved by over 0.25 dB at FER of 10^{-4}

Single decoder can handle multiple permutations effectively

Predetermined permutations enhance decoding success

Abstract

Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications. However, the error-correction performance of polar codes under BP decoding is far from the requirements of 5G. It has been shown that the error-correction performance of BP can be improved if the decoding is performed on multiple permuted factor graphs of polar codes. However, a different BP decoding scheduling is required for each factor graph permutation which results in the design of a different decoder for each permutation. Moreover, the selection of the different factor graph permutations is at random, which prevents the decoder to achieve a desirable error-correction performance with a small number of permutations. In this paper, we first show that the permutations on the factor graph can be mapped into suitable permutations on the codeword positions. As a result, we can make use of a single decoder for all the permutations. In addition, we introduce a method to construct a set of predetermined permutations which can provide the correct codeword if the decoding fails on the original permutation. We show that for the 5G polar code of length $1024$, the error-correction performance of the proposed decoder is more than $0.25$ dB better than that of the BP decoder with the same number of random permutations at the frame error rate of $10^{-4}$.