Approaching Miscorrection-free Performance of Product and Generalized Product Codes

TL;DR

This paper introduces a new iterative decoding algorithm for product codes that detects and avoids most miscorrections, significantly improving performance and lowering error floors over traditional methods.

Contribution

A novel decoding algorithm for product and generalized product codes that effectively detects and prevents miscorrections, enhancing decoding accuracy and performance.

Findings

Up to 0.4 dB increase in net coding gain.

Error floor reduced by orders of magnitude.

Decoder performs nearly as well as a genie-aided decoder.

Abstract

Product codes (PCs) protect a two-dimensional array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the component codes. For this coding scheme, undetected errors in the component decoding-also known as miscorrections-significantly degrade the performance. In this paper, we propose a novel iterative decoding algorithm for PCs which can detect and avoid most miscorrections. The algorithm can also be used to decode many recently proposed classes of generalized PCs such as staircase, braided, and half-product codes. Depending on the component code parameters, our algorithm significantly outperforms the conventional iterative decoding method. As an example, for double-error-correcting Bose-Chaudhuri-Hocquenghem component codes, the net coding gain can be increased by up to 0.4 dB. Moreover, the error floor can be lowered by orders of magnitude, up to the point where the decoder performs virtually identical to a genie-aided decoder that avoids all miscorrections. We also discuss post-processing techniques that can be used to reduce the error floor even further.