A Polar Subcode Approach to Belief Propagation List Decoding

TL;DR

This paper introduces a novel permutation decoding method for pre-transformed polar codes using belief propagation subdecoders, achieving near-CRC-aided SCL performance with improved error rates and lower latency.

Contribution

It extends permutation decoding to pre-transformed polar codes like CRC-aided codes by leveraging polar subcodes, enabling effective belief propagation decoding.

Findings

Performance close to CRC-aided SCL decoding

Outperforms previous iterative CRC-aided BP list decoders

Reduces decoding latency

Abstract

Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.