List decoding of repeated codes

TL;DR

This paper introduces a new hard-decision list decoding algorithm for repeated codes derived from linear codes, demonstrating improved performance through simulations and theoretical estimates, especially for Reed-Solomon codes.

Contribution

It presents a novel decoding algorithm for repeated codes based on soft-decision algorithms, with performance analysis and comparison to existing Reed-Solomon decoding methods.

Findings

The algorithm performs well in simulations for Reed-Solomon repeated codes.

Performance exceeds initial estimates, indicating robustness.

Repeated codes show good potential despite not being used for encoding.

Abstract

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed-Solomon code against a decoding algorithm of a Reed-Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed-Solomon codes and show that performance is somewhat better than our estimates.