Iterative Bounded Distance Decoding with Random Flipping for Product-Like Codes

Product-like codes are widely used in high-speed communication systems since they can be decoded with low-complexity hard decision decoders (HDDs). To meet the growing demand of data rates, enhanced HDDs are required. In this paper, we propose a novel soft-aided HDD (SA-HDD), termed iterative bounded distance decoding with random flipping (iBDD-RF), for product-like codes. In iBDD-RF, the soft reliability of a bit is a weighted sum of the output of bounded distance decoder (BDD) and the channel log-likelihood ratio (LLR). When the amplitude of the soft reliability of a bit is less than a given threshold, it is flipped with a given probability. This random flipping may make the decoder escape from the local optimum. To optimize the threshold and the flipping probability, we derive the density evolution (DE) equations of iBDD-RF for product codes (PCs) and staircase codes (SCs). Our extensive numerical results show that iBDD-RF outperforms iBDD with scaled reliability (iBDD-SR) over the binary-input additive white Gaussian noise (Bi-AWGN) channel. Particularly, for a PC with (255,239,2) Bose-Chaudhuri-Hocquenghem (BCH) code and an SC with (254,230,3) BCH code, iBDD-RF performs about 0.25 dB and 0.28 dB better than iBDD-SR, respectively.