Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

In this paper, we show that over the binary erasure channel, Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding. We demonstrate that the quasi-cyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as k√k, where k is the number of source symbols.