Effects of base matrices on iterative decoding performance of irregular QC-LDPC codes

The edge connections in factor graphs of quasi-cyclic (QC) LDPC codes, which affect their iterative decoding performance, are determined by their base matrices. In this paper, the effects of base matrices on the iterative decoding performance of QC-LDPC codes are investigated by using the recently proposed EXIT chart tool for protograph LDPC codes. Extensive experiments have been carried out and iterative decoding thresholds of QC-LDPC codes with the same degree distribution pair but base matrices having different structures and different dimensions have been obtained and compared. Experimental results show that 1) the base matrix structure affects not only the waterfall performance but also the error floor performance; base matrices having good waterfall performance may exhibit rather poor error floor performance. 2) by increasing the dimensions of base matrices for a given degree distribution, the threshold means are reduced while the ranges of threshold distributions are increased. 3) similar to the case of detailed represented LDPC codes, base matrices with sufficiently large dimensions may have thresholds surpassing the conventional ensemble threshold with the same degree distribution pair. Moreover, as a concrete example, an improved base matrix is designed for a rate-1/2 WiMax LDPC code.