Block Markov Superposition Transmission of BCH Codes with Iterative Erasures-and-Errors Decoders

TL;DR

This paper introduces BMST-BCH codes with a low-complexity iterative decoding algorithm, achieving near-capacity performance and low error floors, suitable for optical networks.

Contribution

It proposes a novel BMST-BCH code construction with an efficient sliding-window decoding algorithm and a fast simulation method for low error rate evaluation.

Findings

Achieves a net coding gain of 10.55 dB at BER of 10^{-15} with hard decoding.

Soft decoding improves net coding gain to 10.74 dB.

Flexible code design balances latency and performance.

Abstract

In this paper, we present the block Markov superposition transmission of BCH (BMST-BCH) codes, which can be constructed to obtain a very low error floor. To reduce the implementation complexity, we design a low complexity iterative sliding-window decoding algorithm, in which only binary and/or erasure messages are processed and exchanged between processing units. The error floor can be predicted by a genie-aided lower bound, while the waterfall performance can be analyzed by the density evolution method. To evaluate the error floor of the constructed BMST-BCH codes at a very low bit error rate (BER) region, we propose a fast simulation approach. Numerical results show that, at a target BER of $10^{-15}$, the hard-decision decoding of the BMST-BCH codes with overhead $25\%$ can achieve a net coding gain (NCG) of $10.55$ dB. Furthermore, the soft-decision decoding can yield an NCG of $10.74$ dB. The construction of BMST-BCH codes is flexible to trade off latency against performance at all overheads of interest and may find applications in optical transport networks as an attractive~candidate.