List Decoding of 2-Interleaved Binary Alternant Codes

TL;DR

This paper introduces a novel list decoding algorithm for 2-interleaved binary alternant codes, combining Reed-Solomon and alternant code decoding techniques, achieving decoding beyond the Johnson radius with high probability.

Contribution

It proposes a new decoding algorithm for 2-interleaved binary alternant codes and derives an upper bound on decoding radius, with empirical results surpassing traditional bounds.

Findings

Decoding radius exceeds the binary Johnson radius.

List size scales polynomially with code parameters.

High probability of successful decoding beyond known bounds.

Abstract

This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for (non-interleaved) alternant codes. A new upper bound on the decoding radius is derived and the list size is shown to scale polynomially in the code parameters. While it remains an open problem whether this upper bound is achievable, the provided simulation results show that a decoding radius exceeding the binary Johnson radius can be achieved with a high probability of decoding success by the proposed algorithm.