Towards optimal edge weight distribution and construction of field‐compatible low‐density parity‐check codes over GF(q). Issue 18 (1st December 2014)

• Record Type: Journal Article
• Authors: Han, Guojun; Guan, Yong Liang; Kong, Lingjun; Chan, Kheong Sann; Cai, Kui
• Is Part Of: IET communications. Volume 8:Issue 18(2014)
• Page Start: 3215
• Page End: 3222
• Publication Date: 2014-12-01
• Subjects: parity check codes -- graph theory -- particle swarm optimisation -- matrix algebra -- algebraic codes -- decoding; optimal edge weight distribution -- optimal edge weight construction -- field‐compatible low‐density parity‐check codes -- nonbinary low‐density parity‐check codes -- algebraic methods -- binary parity‐check matrices -- nonbinary parity‐check matrices -- Tanner graph -- NB‐LDPC code -- TG -- EWD parameter -- particle swarm optimisation -- PSO -- two‐element distribution -- variable‐node degree -- fleld‐compatible LDPC codes -- GF(q) -- decoding -- FC‐LDPC codes; Telecommunication systems -- Periodicals; Speech processing systems -- Periodicals; 621.38205
• DOI: 10.1049/iet-com.2014.0216
• Languages: English
• ISSNs: 1751-8628

Abstract

Abstract : 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 ).