Low decoding complexity of LDPC Codes over the Binary Erasure Channel

In this paper, we present a new low complexity decoding algorithm outperforming existing schemes. When the Belief Propagation fails and cannot solve all the erased bits, the guessing algorithm makes assumptions on a set of erased bits. However, in our new algorithm instead of guessing the values of a set of message bits, the decoder selects a set of check nodes and makes assumption on bits connected to them. The number of possibilities is reduced by half because the field is binary resulting in lower decoding complexity. The proposed decoding algorithm is applied to two regular half rate LDPC codes with lengths of 1000 and 2000. The theoretical belief propagation (BP) threshold for these two codes is 0.429. It is shown that the actual BP threshold is improved using the new algorithm. Setting the number of possibilities to two, we achieve a threshold of 0.43 which is higher than the BP theoretical.