Wrap-Around Sliding-Window Near-ML Decoding of Binary LDPC Codes Over the BEC

A novel method of low-complexity near-maximum-likelihood (ML) decoding of quasi-cyclic (QC) low-density paritycheck (LOPC) codes over the binary erasure channel is presented. The idea is similar to wrap-around decoding of tail-biting convolutional codes. ML decoding is applied to a relatively short window which is cyclically shifted along the received sequence. The procedure is repeated until either all erasures have been corrected, or no new erasures are corrected at a certain round. A new upper bound on the ensemble-average ML decoding error probability for a finite-length row-regular LOPC code family is derived and presented. Furthermore, a few examples of regular and irregular QC LOPC codes are studied by simulations and their performance is compared with the ensemble-average performance. Finally, the impact of the codeword weight and stopping set size spectra on the ML and belief-propagation decoding performance is discussed.