Multiple-Bases Belief-Propagation Decoding of High-Density Cyclic Codes

TL;DR

This paper presents a novel multiple-bases belief-propagation decoding method for cyclic codes, leveraging diverse parity-check matrices to improve error correction performance over standard BP decoding.

Contribution

The paper introduces MBBP, a decoding scheme utilizing multiple parity-check matrices of cyclic form, enhancing decoding accuracy for high-density cyclic codes.

Findings

MBBP outperforms standard BP decoding in simulations.

Decoding performance approaches maximum-likelihood decoding.

Analytical methods guide the selection of effective parity-check matrices.

Abstract

We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of the fact that a code has many structurally diverse parity-check matrices, capable of detecting different error patterns. We show that this inherent code property leads to decoding algorithms with significantly better performance when compared to standard BP decoding. Furthermore, we describe how to choose sets of parity-check matrices of cyclic form amenable for multiple-bases decoding, based on analytical studies performed for the binary erasure channel. For several cyclic and extended cyclic codes, the MBBP decoding performance can be shown to closely follow that of maximum-likelihood decoders.