An approach to evaluating the number of closed paths in an all-one base matrix

Jiang, S; Lau, FCM

Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/79962

DC Field	Value	Language
dc.contributor	Department of Electronic and Information Engineering	-
dc.creator	Jiang, S	-
dc.creator	Lau, FCM	-
dc.date.accessioned	2018-12-21T07:14:03Z	-
dc.date.available	2018-12-21T07:14:03Z	-
dc.identifier.issn	2169-3536	en_US
dc.identifier.uri	http://hdl.handle.net/10397/79962	-
dc.language.iso	en	en_US
dc.publisher	Institute of Electrical and Electronics Engineers	en_US
dc.rights	© 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.	en_US
dc.rights	Posted with permission of the publisher.	en_US
dc.rights	The following publication Jiang, S., & Lau, F. C. M.(2018). An approach to evaluating the number of closed paths in an all-one base matrix. IEEE Access, 6, - is available at https://dx.doi.org/10.1109/ACCESS.2018.2819981	en_US
dc.subject	All-one base matrix	en_US
dc.subject	Closed path	en_US
dc.subject	Cycles	en_US
dc.subject	Low-density parity-check code	en_US
dc.title	An approach to evaluating the number of closed paths in an all-one base matrix	en_US
dc.type	Journal/Magazine Article	en_US
dc.identifier.spage	22332	-
dc.identifier.epage	22340	-
dc.identifier.volume	6	-
dc.identifier.doi	10.1109/ACCESS.2018.2819981	en_US
dcterms.abstract	Given an all-one base matrix of size M x N, a closed path of different lengths can be formed by starting at an arbitrary element and moving horizontally and vertically alternatively before terminating at the same "starting" element. When the closed-path length is small, say 4 or 6, the total number of combinations can be evaluated easily. When the length increases, the computation becomes non-trivial. In this paper, a novel method is proposed to evaluate the number of closed paths of different lengths in an all-one base matrix. Theoretical results up to closed paths of length 10 have been derived and are verified by the exhaustive search method. Based on the theoretical work, results for closed paths of length larger than 10 can be further derived. Note that each of such closed paths may give rise to one or more cycles in a low-density parity-check (LDPC) code when the LDPC code is constructed by replacing each "1" in the base matrix with a circulant permutation matrix or a random permutation matrix. Since LPDC codes with short cycles are known to give unsatisfactory error correction capability, the results in this paper can be used to estimate the amount of effort required to evaluate the number of potential cycles of an LDPC code or to optimize the code.	-
dcterms.accessRights	open access	en_US
dcterms.bibliographicCitation	IEEE access, 2018, v. 6, p. 22332-22340	-
dcterms.isPartOf	IEEE access	-
dcterms.issued	2018	-
dc.identifier.isi	WOS:000431977800001	-
dc.identifier.scopus	2-s2.0-85044870374	-
dc.identifier.rosgroupid	2017003613	-
dc.description.ros	2017-2018 > Academic research: refereed > Publication in refereed journal	-
dc.description.validate	201812 bcrc	en_US
dc.description.oa	Version of Record	en_US
dc.identifier.FolderNumber	OA_IR/PIRA	en_US
dc.description.pubStatus	Published	en_US
Appears in Collections:	Journal/Magazine Article

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