IEEE Transactions on Communications

Maximum-Girth Cylinder-Type Block-Circulant LDPC Codes

Mohammad Gholami, Morteza Esmaeili

Published Mar 6, 2012• 8 citations

Abstract

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.

DOI: 10.1109/tcomm.2012.022912.100419

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