Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/79962
Title: An approach to evaluating the number of closed paths in an all-one base matrix
Authors: Jiang, S 
Lau, FCM 
Keywords: All-one base matrix
Closed path
Cycles
Low-density parity-check code
Issue Date: 2018
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE access, 2018, v. 6 How to cite?
Journal: IEEE access 
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.
URI: http://hdl.handle.net/10397/79962
ISSN: 2169-3536
DOI: 10.1109/ACCESS.2018.2819981
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

1
Citations as of Feb 18, 2019

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.