A Novel Graph Expansion and a Decoding Algorithm for NB-LDPC Codes

• Published in: IEEE transactions on communications Vol. 68; no. 3; pp. 1358 - 1369
• Main Authors: Wijekoon, V. B., Viterbo, Emanuele, Hong, Yi, Micheloni, Rino, Marelli, Alessia
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Binary codes; Binary system; Codes; Complexity; Computer simulation; Decoding; Error correcting codes; Fields (mathematics); graph expansion; iterative decoding; Low density parity check codes; Non-binary LDPC codes
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2019.2961884

Non-binary low-density parity-check (NB-LDPC) codes are known to offer several advantages over their binary counterparts, but the higher complexity, and the resource-hungry nature of decoding algorithms have so far restricted their practical usage. In this paper, we propose a new decoding algorithm for NB-LDPC codes over finite fields of characteristic 2, based on a novel binary expansion of the <inline-formula> <tex-math notation="LaTeX">{Q} </tex-math></inline-formula>-ary Tanner graph. While it offers substantial complexity gains, simulation results demonstrate that the performance loss of the new algorithm, in comparison to the best known decoder, is quite small. Furthermore, due to being based on a binary graph, it is particularly attractive for hardware implementations. We also suggest a simplified version of the algorithm, which offers even higher gains in complexity.