Decoding Generalized Concatenated Codes Using Interleaved Reed-Solomon Codes

TL;DR

This paper introduces a modified decoding algorithm for Generalized Concatenated codes that leverages interleaved Reed-Solomon codes to improve decoding efficiency and performance beyond traditional limits.

Contribution

A novel decoding approach that groups outer Reed-Solomon codes into an interleaved code, enabling decoding beyond half the minimum distance with reduced complexity.

Findings

Decoding performance is maintained while reducing complexity.

The new algorithm can decode beyond the traditional d/2 limit.

Decoding iterations are skipped, improving efficiency.

Abstract

Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume some linear block code which can be decoded up to half its minimum distance. Decoding up to half the minimum distance of Generalized Concatenated codes is classically achieved by the Blokh-Zyablov-Dumer algorithm, which iteratively decodes by first using the inner decoder to get an estimate of the outer code words and then using an outer error/erasure decoder with a varying number of erasures determined by a set of pre-calculated thresholds. In this paper, a modified version of the Blokh-Zyablov-Dumer algorithm is proposed, which exploits the fact that a number of outer Reed-Solomon codes with average minimum distance d can be grouped into one single Interleaved Reed-Solomon code which can be decoded beyond d/2. This allows to skip a number of decoding iterations on the one hand and to reduce the complexity of each decoding iteration significantly - while maintaining the decoding performance - on the other.