NDLI: Ultra-small block-codes for binary discrete memoryless channels

Content Provider	IEEE Xplore Digital Library
Author	Po-Ning Chen Hsuan-Yin Lin Moser, S.M.
Copyright Year	2011
Description	Author affiliation: Department of Electrical Engineering, National Chiao Tung University (NCTU), Hsinchu, Taiwan (Po-Ning Chen; Hsuan-Yin Lin; Moser, S.M.)
Abstract	Block-codes with a very small number of codewords are Investigated for the two special binary memoryless channels, the binary symmetric channel (BSC) and the Z-channel (ZC). The optimal (In the sense of minimum average error probability, using maximum likelihood decoding) code structure Is derived for the cases of two, three, and four codewords and an arbitrary blocklength. It Is shown that for two possible messages, on a BSC, the so-called flip codes of type t are optimal for any t, while on a ZC, the flip code of type 0 Is optimal. For codes with three or four messages It Is shown that the so-called weak flip codes of some given type are optimal where the type depends on the blocklength. For all cases an algorithm Is presented that constructs an optimal code for blocklength n recursively from an optimal code of length n — 1. For the ZC a recursive optimal code design Is conjectured In the case of live possible messages. The derivation of these optimal codes relies heavily on a new approach of constructing and analyzing the code-matrix not row-wise (codewords), but column-wise. Moreover, these results also prove that the minimum Hamming distance might be the wrong design criterion for optimal codes even for very symmetric channels like the BSC.
Starting Page	175
Ending Page	179
File Size	328200
Page Count	5
File Format	PDF
ISBN	9781457704383
e-ISBN	9781457704376
DOI	10.1109/ITW.2011.6089371
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-16
Publisher Place	Brazil
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Hamming distance Error probability Vectors Memoryless systems Linear code
Content Type	Text
Resource Type	Article

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