On Sparse Regression LDPC Codes

TL;DR

This paper introduces a novel concatenated coding scheme combining LDPC and SPARC-inspired codes, achieving improved finite-length performance and steep error rate drops, supported by numerical results.

Contribution

It proposes a new concatenated coding structure with efficient AMP decoding that outperforms traditional SPARCs and LDPC codes at finite block lengths.

Findings

Performance improvements over SPARCs and LDPC codes

Steep waterfall error performance observed

Numerical results validate the proposed scheme

Abstract

Belief propagation applied to iterative decoding and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, LDPC codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs. Findings are supported by numerical results.