AVN-based Elimination of Short Cycles in Tanner Graphs of QC LDPC Codes

One of the most efficient approaches to improving the frame error rate (FER) performance of low-density parity-check (LDPC) codes is based on adding both auxiliary variable nodes (AVN) and the corresponding redundant parity checks (RPC) to the binary parity-check matrices of the code. It is known that for the LDPC codes, whose Tanner graphs contain length four cycles, this technique allows for substantial improvement in the FER performance of the belief-propagation (BP) decoding on the binary erasure channel (BEC) channel. The AVN-based technique followed by adding orthogonal redundant parity-checks is known to be efficient for both the BEC and additive white Gaussian noise (AWGN) channels. In this paper, firstly, the AVN-based approach is generalized to efficiently removing cycles of length larger than four. Secondly, the AVN-based technique is reformulated in terms of labeled base matrices of quasi-cyclic (QC) LDPC codes. An improved iterative decoding of QC LDPC codes is proposed, which is applied to the labeled base matrices of QC LDPC codes extended by the AVN-RPC technique.