On the Multiple Threshold Decoding of LDPC codes over GF(q)

TL;DR

This paper proposes a modified LDPC decoding algorithm over GF(q) using multiple thresholds, improving decoding radius estimates without increasing complexity.

Contribution

It introduces a multi-threshold modification to the majority decoding algorithm for LDPC codes over GF(q), enhancing decoding performance.

Findings

Improved decoding radius estimate with multiple thresholds

Maintained low complexity of the decoding process

Demonstrated better performance over single-threshold decoders

Abstract

We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new algorithm is derived. The estimate is shown to be better than the estimate for a single threshold majority decoder. At the same time the transition to multiple thresholds does not affect the order of complexity.