Belief Propagation Decoding of Polar Codes on Permuted Factor Graphs

TL;DR

This paper introduces a novel belief propagation decoding method for polar codes that uses permuted factor graphs and CRC-based stopping criteria, significantly improving iterative decoding performance.

Contribution

The paper proposes a new BP decoding approach for polar codes using permuted factor graphs and CRC stopping, achieving performance close to SCL decoding.

Findings

Achieves near SCL decoding performance with permuted factor graphs.

Uses CRC as an effective iteration stopping criterion.

Provides a new visualization method for polar code factor graphs.

Abstract

We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is sufficiently large. The proposed decoder is based on different realizations of the polar code factor graph with randomly permuted stages during decoding. Additionally, a different way of visualizing the polar code factor graph is presented, facilitating the analysis of the underlying factor graph and the comparison of different graph permutations. In our proposed decoder, a high rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and used as an iteration stopping criterion (i.e., genie) to even outperform the SCL decoder of the plain polar code (without the CRC-aid). Although our permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it achieves, to the best of our knowledge, the best performance of all iterative polar decoders presented thus far.