Error-and-Erasure Decoding of Product and Staircase Codes

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 0.6dB are possible by ternary decoding, at only a small additional increase in complexity compared to traditional binary message passing.

Automated summary

This paper investigates the performance of high-rate product codes and staircase codes in high-speed optical communication on a channel with ternary output and ternary message passing. The analysis is based on density evolution and shows that using even-weight BCH subcodes as component codes can improve decoding performance at high rates. Monte-Carlo simulations verify the results of the analysis.