Quasi Cyclic LDPC Codes Based on Finite Set Systems
This work addresses the need for efficient error-correcting codes in communication systems, offering incremental improvements in code design for specific applications.
The paper tackles the problem of designing Quasi-cyclic LDPC codes with large girth and arbitrary column-weight distributions by using finite set systems, resulting in codes that achieve higher rates than existing geometric and cylinder-type codes for column weight-2 and show significantly large coding gains over random-like LDPC codes in simulations over the AWGN channel.
A finite set system (FSS) is a pair (V; B) where V is a finite set whose members are called points, equipped with a finite collection of its subsets B whose members are called blocks. In this paper, finite set systems are used to define a class of Quasi-cyclic low- density parity-check (LDPC) codes, called FSS codes, such that the constructed codes possess large girth and arbitrary column-weight distributions. Especially, the constructed column weight-2 FSS codes have higher rates than the column weight-2 geometric and cylinder-type codes with the same girths. To find the maximum girth of FSS codes based on (V; B), inevitable walks are defined in B such that the maximum girth is determined by the smallest length of the inevitable walks in B. Simulation results show that the constructed FSS codes have very good performance over the AWGN channel with iterative decoding and achieve significantly large coding gains compared to the random-like LDPC codes of the same lengths and rates.