Maximum-Girth Cylinder-Type Block-Circulant LDPC Codes

• Published in: IEEE transactions on communications Vol. 60; no. 4; pp. 952 - 962
• Main Authors: Gholami, M., Esmaeili, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2012; Institute of Electrical and Electronics Engineers
• Subjects: Algorithm design and analysis; Applied sciences; Arrays; AWGN channels; block-structure graph; Coding, codes; cylinder form matrix; Encoding; Exact sciences and technology; Information, signal and communications theory; LDPC codes; maximum girth; Parity check codes; Partitioning algorithms; Phase change materials; Signal and communications theory; Telecommunications and information theory; Performance evaluation; Block code; Partition method; Algorithm; Random codes; LDPC codes; AWGN channels; block-structure graph; Error correcting code; Parity check codes; maximum girth; Parity check; cylinder form matrix
• ISSN: 0090-6778
• DOI: 10.1109/TCOMM.2012.022912.100419

In this paper, a particular class of block-circulant low-density parity-check (BC-LDPC) codes referred to as cylinder-type BC-LDPC (CTBC-LDPC) codes is studied. We represent a cylinder-type parity-check matrix H by a graph called the block-structure graph of H and denoted by BSG(H). Using the properties of BSG(H) we show that CTBC matrices with column-weight two and girth an arbitrary multiple of 8 can be constructed, while for a CTBC matrix H with column-weight ℓ ≥ 3 this girth cannot exceed 12. An algorithm generating CTBC-LDPC codes of arbitrary possible girth is given. The algorithm produces a large group of codes with flexible rate, length and girth. From performance perspective over AWGN channel, the maximum girth-12 CTBC-LDPC codes with column-weight at least three generated by the given algorithm are at least as good as their random-like counterpart codes and outperform the codes of the same size constructed by successive-level-growth, progressive-edge-growth, and partition-and-shift methods.