Using List Decoding to Improve the Finite-Length Performance of Sparse Regression Codes

TL;DR

This paper enhances the finite-length performance of sparse superposition codes over complex AWGN channels by using list decoding with concatenated CRC codes, and introduces novel circulant design matrices for improved flexibility.

Contribution

It proposes a concatenated coding scheme with list decoding for SPARCs, and introduces new circulant matrices for encoding, improving finite-length performance and design flexibility.

Findings

Concatenated coding with CRC and list decoding significantly improves performance.

The proposed scheme exhibits steep waterfall behavior in bit-error rate curves.

New circulant matrices offer comparable performance with more design options.

Abstract

We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves. Furthermore, we apply our proposed concatenated coding scheme to spatially coupled SPARCs. Besides that, we also introduce a novel class of design matrices, i.e., matrices that describe the encoding process, based on circulant matrices derived from Frank or from Milewski sequences. This class of design matrices has comparable encoding and decoding computational complexity as well as very close performance with the commonly-used class of design matrices based on discrete Fourier transform (DFT) matrices, but gives us more degrees of freedom when designing SPARCs for various applications.