A Comparative Study of Ensemble Decoding Methods for Short Length LDPC Codes

TL;DR

This paper qualitatively and quantitatively compare different realizations of the ensemble decoder, namely multiple-bases belief propagation (MBBP), automorphism ensemble decoding (AED), scheduling ensemble decoding (SED), noise-aided ensemble decoding (NED) and saturated belief propagation (SBP).

Abstract

To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be described using the same general framework, which we call ensemble decoding: A set of independent constituent decoders works in parallel on the received sequence, each proposing a codeword candidate. From this list, the maximum likelihood (ML) decision is designated as the decoder output. In this paper, we qualitatively and quantitatively compare different realizations of the ensemble decoder, namely multiple-bases belief propagation (MBBP), automorphism ensemble decoding (AED), scheduling ensemble decoding (SED), noise-aided ensemble decoding (NED) and saturated belief propagation (SBP). While all algorithms can provide gains over traditional BP decoding, ensemble methods that exploit the code structure, such as MBBP and AED, typically show greater performance improvements.

Figures (7)

• Figure 1: Block diagram of ensemble decoding of the channel LLR $\mathbf{L}_\mathrm{ch}$ with $M$ constituent hard-output decoders. Only valid codeword candidates are considered in the final ML-in-the-list decision.
• Figure 2: Illustration of how the decoding regions interact with the received vector ($\boldsymbol{\times}$) for different ensemble decoding variants. In each scenario, the initial decoder $\operatorname{Dec}_1$ fails, but the ensemble of two decoders can successfully decode.
• Figure 3: BLER performance comparison for the $(63,6)$ simplex code. $\mathbf{H}_\mathrm{sys}$ indicates the use of the systematic parity-check matrix.
• Figure 4: BLER performance comparison for the $(273,191)$ PG LDPC Code.
• Figure 5: BLER performance comparison for the $(132,66)$ 5G LDPC code.