Application of Beam Search for the decoding of one class of LDPC codes

Abstract

For one class of Low-Density Parity-Check (LDPC) codes with low row weight in their parity check matrix, a new Syndrome Decoding (SD) based on the heuristic Beam Search (BS), labeled as SD-BS, is put forward to improve the error performance. First, two observations are made and verified by simulation results. One is that in the SNR region of interest, the hard-decision on the corrupted sequence yields only a handful of erroneous bits. The other is that the true error pattern for the nonzero syndrome has a high probability to survive the competition in the BS, provided sufficient beam width. Bearing these two points in mind, the decoding of LDPC codes is transformed into seeking an error pattern with the known decoding syndrome. Secondly, the effectiveness of SD-BS depends closely on how to evaluate the bit reliability. Enlightened by a bit-flipping definition in the existing literature, a new metric is employed in the proposed SD-BS. The strength of SD-BS is demonstrated via applying it on the corrupted sequences directly and the decoding failures of the Belief Propagation (BP), respectively.