Open AccessTowards optimal edge weight distribution and construction of field‐compatible low‐density parity‐check codes over GF( q )
Author(s) -
Han Guojun,
Guan Yong Liang,
Kong Lingjun,
Chan Kheong Sann,
Cai Kui
Publication year - 2014
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2014.0216
Subject(s) - low density parity check code , mathematics , weight distribution , binary number , discrete mathematics , parity (physics) , degree distribution , combinatorics , algorithm , decoding methods , arithmetic , physics , thermodynamics , particle physics , complex network
Non‐binary low‐density parity‐check (NB‐LDPC) codes can be directly constructed by using algebraic methods, or indirectly constructed by mapping well‐designed binary parity‐check matrices to non‐binary parity‐check matrices. Given the Tanner graph (TG) of a NB‐LDPC code, the selection of edge weights in the TG significantly affects the performance of the NB‐LDPC code. The authors introduce an edge weight distribution (EWD) parameter for the TG of NB‐LDPC codes. By utilising particle swarm optimisation (PSO), the EWD is optimised and it has been demonstrated that the optimal EWD approaches a two‐element distribution for large field size and high average variable‐node degree. With the optimised EWD, the authors construct a class of field‐compatible LDPC (FC‐LDPC) codes over GF( q ) whose parity‐check matrices only include elements 0, 1 and 2, and can be encoded and decoded over different field sizes. The simulations demonstrate that the performance of the proposed FC‐LDPC codes improves monotonically with increasing field size, and significantly outperforms that of the corresponding algebraic NB‐LDPC codes or NB‐LDPC codes generated with uniform distribution of non‐zero elements over GF( q ).