Error-and-Erasure Decoding of Product and Staircase Codes

TL;DR

This paper extends density evolution analysis for high-rate product and staircase codes to ternary channels with erasures, demonstrating improved decoding performance with minimal complexity increase.

Contribution

It introduces a density evolution analysis for ternary message passing in product and staircase codes, enabling optimized component code configurations and showing performance gains with ternary decoding.

Findings

Ternary decoding yields up to 0.6 dB coding gain.

Analysis guides component code and quantizer design.

Monte-Carlo simulations confirm theoretical predictions.

Abstract

High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative decoding algorithms that require very little complexity. In this paper, we extend the density evolution (DE) analysis for PCs and SCs to a channel with ternary output and ternary message passing, where the third symbol marks an erasure. We investigate the performance of a standard error-and-erasure decoder and of its simplification using DE. The proposed analysis can be used to find component code configurations and quantizer levels for the channel output. We also show how the use of even-weight BCH subcodes as component codes can improve the decoding performance at high rates. The DE results are verified by Monte-Carlo simulations, which show that additional coding gains of up to 0.6 dB are possible by ternary decoding, at only a small additional increase in complexity compared to traditional binary message passing.