List-based Optimization of Proximal Decoding for LDPC Codes

TL;DR

This paper improves proximal decoding for LDPC codes over AWGN channels by adding a correction step that targets oscillating errors, resulting in up to 1 dB gain.

Contribution

It introduces an empirical correction step to proximal decoding, enhancing error correction by addressing oscillations and refining decoding accuracy.

Findings

Achieves up to 1 dB gain over conventional proximal decoding.

Identifies oscillation behavior as a key factor in decoding errors.

Proposes an empirical rule for correcting likely erroneous bits.

Abstract

In this paper, the proximal decoding algorithm is considered within the context of additive white Gaussian noise (AWGN) channels. An analysis of the convergence behavior of the algorithm shows that proximal decoding inherently enters an oscillating behavior of the estimate after a certain number of iterations. Due to this oscillation, frame errors arising during decoding can often be attributed to only a few remaining wrongly decoded bit positions. In this letter, an improvement of the proximal decoding algorithm is proposed by establishing an additional step, in which these erroneous positions are attempted to be corrected. We suggest an empirical rule with which the components most likely needing correction can be determined. Using this insight and performing a subsequent ``ML-in-the-list'' decoding, a gain of up to 1 dB is achieved compared to conventional proximal decoding, depending on the decoder parameters and the code.