LDPC codes based on Mobius transformations

Abstract

Recently, a class of low-density parity-check (LDPC) codes from affine permutation matrices, called APM-LDPC codes, have attracted because of some advantages rather than QC-LDPC codes in minimum-distance, girth, cycle distribution and error-rate performance. In this study, a new class of LDPC codes based on Mobius transformations, called MT-LDPC codes, are presented as a generalisation of APM-LDPC codes which have some new achievements rather than QC and APM LDPC codes in the terms of length, cycle distribution and error-rate performance. Moreover, each Mobius transformation is represented by a square matrix which is helpful to pursuing the cycles in the Tanner graph of an MT-LDPC code by the product of some square matrices. In continue, for a given base matrix, the authors propose a deterministic algorithm which efficiently produces MT-LDPC codes with the desired girth. Simulation results show that the binary and non-binary constructed MT-LDPC codes outperform APM, QC, PEG, random-like and some algebraic LDPC codes with the same rates and lengths.