Performance Analysis of Algebraic Soft Decoding of Reed-Solomon Codes over Binary Symmetric and Erasure Channels

TL;DR

This paper analyzes the decoding capabilities of algebraic soft decoding for Reed-Solomon codes over erasure and binary symmetric channels, showing it can outperform traditional decoding methods with optimal strategies.

Contribution

It characterizes the decoding region of ASD, derives tight bounds, and demonstrates its superiority over conventional decoding across various code rates.

Findings

ASD outperforms Berlekamp Massey decoding over studied channels

Optimal multiplicity assignment strategies enhance decoding performance

Analysis extends to other channel models like RS coded modulation

Abstract

In this paper, we characterize the decoding region of algebraic soft decoding (ASD) of Reed-Solomon (RS) codes over erasure channels and binary symmetric channel (BSC). Optimal multiplicity assignment strategies (MAS) are investigated and tight bounds are derived to show the ASD can significantly outperform conventional Berlekamp Massey (BM) decoding over these channels for a wide code rate range. The analysis technique can also be extended to other channel models, e.g., RS coded modulation over erasure channels.