Adaptive Single-Trial Error/Erasure Decoding of Reed-Solomon Codes

TL;DR

This paper proposes an adaptive erasing strategy for Reed-Solomon code decoding that minimizes residual error probability by optimally utilizing reliability information, applicable across various algebraic decoding algorithms.

Contribution

It introduces a novel adaptive erasing strategy that improves error correction efficiency for Reed-Solomon codes using existing decoding algorithms.

Findings

The strategy reduces residual error probability effectively.

Applicable to multiple decoding algorithms including list decoding.

Enhances decoding performance by optimal erasure decisions.

Abstract

Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both errors and erasures. This enables the decoder to exploit binary quantized reliability information obtained from the transmission channel: Received symbols with high reliability are forwarded to the decoding algorithm while symbols with low reliability are erased. In this paper we investigate adaptive single-trial error/erasure decoding of Reed-Solomon codes, i.e. we derive an adaptive erasing strategy which minimizes the residual codeword error probability after decoding. Our result is applicable to any error/erasure decoding algorithm as long as its decoding capabilities can be expressed by a decoder capability function. Examples are Bounded Minimum Distance decoding with the Berlekamp-Massey- or the Sugiyama algorithms and the Guruswami-Sudan list decoder.