Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

TL;DR

This paper presents a method to design polar codes compatible with standard LDPC decoders that reduces performance loss and achieves error rates comparable to established LDPC codes, especially at high SNR.

Contribution

It introduces a joint design approach for polar codes and LDPC parity-check matrices that mitigates performance degradation in LDPC-style decoding.

Findings

Polar codes under LDPC-style decoding match performance of standard LDPC codes.

The proposed design reduces the gap between LDPC-style and BP decoding of polar codes.

Performance gains are observed in high SNR regions.

Abstract

Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this loss can be mitigated; in particular, we demonstrate how the gap between LDPC-style decoding and Arikan's Belief Propagation (BP) decoding of polar codes can be closed by taking into account the underlying graph structure of the LDPC decoder while jointly designing the polar code and the parity-check matrix of the corresponding LDPC-like code. The resulting polar codes under conventional LDPC-style decoding are shown to have similar error-rate performance when compared to some well-known and standardized LDPC codes. Moreover, we obtain performance gains in the high SNR region.