Bit Level Soft Decision Decoding of Triple Parity Reed Solomon Codes through Automorphism Groups

TL;DR

This paper introduces a novel bit-level soft decoding method for triple-parity Reed-Solomon codes using automorphism groups, achieving significant performance improvements over existing algorithms.

Contribution

A new algorithm for identifying automorphism groups of RS codes and a corresponding soft-decision decoding method for general (n,n-3,4) RS codes.

Findings

Over 1 dB gain at BER of 10^-5 for (31,28,4) RS codes

Effective automorphism group identification algorithm

Enhanced decoding performance compared to existing methods

Abstract

This paper discusses bit-level soft decoding of triple-parity Reed-Solomon (RS) codes through automorphism permutation. A new method for identifying the automorphism groups of RS binary images is first developed. The new algorithm runs effectively, and can handle more RS codes and capture more automorphism groups than the existing ones. Utilizing the automorphism results, a new bit-level soft-decision decoding algorithm is subsequently developed for general $(n,n-3,4)$ RS codes. Simulation on $(31,28,4)$ RS codes demonstrates an impressive gain of more than 1 dB at the bit error rate of $10^{-5}$ over the existing algorithms.