Maximum-Girth Cylinder-Type Block-Circulant LDPC Codes

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 proper...

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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
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ISSN	0090-6778
DOI	10.1109/TCOMM.2012.022912.100419

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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.
AbstractList	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.
Author	Esmaeili, M. Gholami, M.
Author_xml	– sequence: 1 givenname: M. surname: Gholami fullname: Gholami, M. email: gholami-m@sci.sku.ac.ir organization: Dept. of Math. Sci., Shahrekord Univ., Shahrekord, Iran – sequence: 2 givenname: M. surname: Esmaeili fullname: Esmaeili, M. email: emorteza@cc.iut.ac.ir organization: Dept. of Math. Sci., Isfahan Univ. of Technol., Isfahan, Iran
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Keywords	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
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SubjectTerms	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
Title	Maximum-Girth Cylinder-Type Block-Circulant LDPC Codes
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