Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

摘要

One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.