Fast Min-Sum Algorithms for Decoding of LDPC over GF(q)

TL;DR

This paper introduces a novel fast min-sum decoding algorithm for LDPC codes over GF(q) that employs dynamic programming to improve efficiency and simplicity over previous configuration reduction methods.

Contribution

The paper proposes a dynamic programming-based min-sum decoding algorithm for LDPC over GF(q), offering simplicity and avoiding performance degradation.

Findings

Comparable complexity to existing algorithms

Simpler design with fewer parameters

No performance degradation compared to configuration reduction

Abstract

In this paper, we present a fast min-sum algorithm for decoding LDPC codes over GF(q). Our algorithm is different from the one presented by David Declercq and Marc Fossorier in ISIT 05 only at the way of speeding up the horizontal scan in the min-sum algorithm. The Declercq and Fossorier's algorithm speeds up the computation by reducing the number of configurations, while our algorithm uses the dynamic programming instead. Compared with the configuration reduction algorithm, the dynamic programming one is simpler at the design stage because it has less parameters to tune. Furthermore, it does not have the performance degradation problem caused by the configuration reduction because it searches the whole configuration space efficiently through dynamic programming. Both algorithms have the same level of complexity and use simple operations which are suitable for hardware implementations.