NDLI: Algebraic construction of sparse matrices with large girth

Content Provider	IEEE Xplore Digital Library
Author	O'Sullivan, M.E.
Copyright Year	1963
Abstract	In this correspondence, we present a method for constructing sparse matrices that have a compact description and whose associated bipartite graphs have large girth. Based on an arbitrary seed matrix of nonnegative integers a new matrix is constructed which replaces each entry of the seed matrix with a sum of permutation matrices. Algebraic conditions that lead to short cycles in the associated bipartite graph are analyzed and methods to achieve large girth in two special cases are presented. In one, all the permutation matrices are circulants; in the other they are all affine permutation matrices. When used to define a low-density parity-check (LDPC) code the compact description should lead to efficient implementation and the large girth to good error correction performance. The method is adaptable to a variety of rates, and a variety of row and column degrees
Sponsorship	IEEE Information Theory Society
Starting Page	718
Ending Page	727
Page Count	10
File Size	467883
File Format	PDF
ISSN	00189448
Volume Number	52
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sparse matrices Parity check codes Bipartite graph Decoding Information theory Upper bound Error correction codes Belief propagation Sum product algorithm Floors low-density parity-check (LDPC) codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

LDPC codes from generalized polygons

Partition-and-shift LDPC codes

Reversible Low-Density Parity-Check Codes

On the Girth of Quasi-Cyclic Protograph LDPC Codes

On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm

Graph-based message-passing schedules for decoding LDPC codes

Quantum Error Correction Beyond the Bounded Distance Decoding Limit

Sinkhorn Solves Sudoku

Error-Correction Capability of Column-Weight-Three LDPC Codes

Algebraic construction of sparse matrices with large girth

Similar Documents

LDPC codes from generalized polygons

Partition-and-shift LDPC codes

Reversible Low-Density Parity-Check Codes

On the Girth of Quasi-Cyclic Protograph LDPC Codes

On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm

Graph-based message-passing schedules for decoding LDPC codes

Quantum Error Correction Beyond the Bounded Distance Decoding Limit

Sinkhorn Solves Sudoku

Error-Correction Capability of Column-Weight-Three LDPC Codes

Algebraic construction of sparse matrices with large girth