LDPC codes based on Mobius transformations
Mohammad Reza Gholami, Akram Nassaj · IET Communications · 2019
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.