On the Asymptotic Performance of Iterative Decoders for Product Codes

TL;DR

This paper analyzes the asymptotic failure probability of iterative hard-decision decoders for product codes over erasure channels, considering various error correction capabilities and decoding rounds.

Contribution

It provides exact asymptotic failure probabilities for iterative decoding of product codes, accounting for different error correction strengths and decoding iterations.

Findings

Exact asymptotic failure probability formulas derived.

Performance insights for codes correcting constant errors or fractions.

Analysis applicable to multiple decoding rounds.

Abstract

We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function of the error-correction capabilities of the row and column codes, the number of decoding rounds, and the channel erasure probability. We examine both the case of codes capable of correcting a constant amount of errors, and the case of codes capable of correcting a constant fraction of their length.