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

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, 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. Index Terms BCH codes, block Markov superposition transmission (BMST), forward error correction (FEC), iterative decoding, optical communication. This work was supported by the 973 Program (No. 2012CB316100), the NSF of China (No. 91438101), and the NSF of Guangdong (No. 2016A030308008). This paper was presented in part at 2017 IEEE International Symposium on Information Theory. Suihua Cai and Nina Lin are with the School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510006, China (e-mail: [email protected], [email protected]). Xiao Ma is with the School of Data and Computer Science and Guangdong Key Laboratory of Information Security Technology, Sun Yat-sen University, Guangzhou 510006, China (e-mail: [email protected]).