A comparative study of BMST-LDPC codes and staircase-LDPC codes

In this paper, we conduct a comparative study of two classes of convolutional low-density parity-check (LDPC) codes: block Markov superposition transmission (BMST) codes and staircase codes, which are both constructed by incorporating spatial coupling between LDPC coded blocks. By examining the differences and similarities between the two classes of codes in coding, decoding, performance, and complexity, we demonstrate that the BMST-LDPC codes exhibit lower complexity and superior waterfall performance, but have higher error floors. We present two approaches to reduce the error floors. One approach is to use conventional concatenated codes with Bose–Chaudhuri–Hocquenghem (BCH) codes as outer codes, which allows for the prediction of error floors. The other approach is to use free-ride coding for cyclic redundancy check (CRC) bits, which is applicable to staircase-LDPC codes and does not result in any loss of code rate. Additionally, we propose double-check to reduce effectively the mis-correction probability, enabling the decoder to stop the iterative decoding process early without error propagation, thereby reducing complexity. Simulation results show that the proposed scheme can improve the performance of the staircase code, constructed using a variant of the 5G LDPC code, by achieving a gain of about $0.2\mathrm{dB}$ at a bit error rate (BER) of $10^{-7}$ without any loss of code rate, and reduce the decoding complexity by approximately 40%.