NDLI: Variable Length Unordered Codes

Content Provider	IEEE Xplore Digital Library
Author	Pezza, L. Tallini, L.G. Bose, B.
Copyright Year	1963
Abstract	In an unordered code, no code word is contained in any other code word. Unordered codes are all unidirectional error detecting (AUED) codes. In the binary case, it is well known that among all systematic codes with k information bits, Berger codes are optimal unordered codes with r=[log₂(k+1)] ≅ log₂k check bits. This paper gives some new theory on variable length unordered codes and introduces a new class of systematic (instantaneous) unordered codes with variable length check symbols. The average redundancy of the new codes presented here is r ≅ (1/2)log₂k+c, where c ∈ (1.0470,1.1332) ⊆ IR and k ∈ IN is the number of information bits. When k is large, it is shown that such redundancy is at most 0.6069 bits off the redundancy of an optimal systematic unordered code design with fixed length information symbols and variable length check symbols; and, at most 2.8075 bits off the redundancy of an optimal variable length unordered code design. The generalization is also given for the nonbinary case and it is shown that similar results hold true.
Sponsorship	IEEE Information Theory Society
Starting Page	548
Ending Page	569
Page Count	22
File Size	617262
File Format	PDF
ISSN	00189448
Volume Number	58
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-02-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Redundancy Systematics Receivers Block codes Decoding Indexes Educational institutions unordered codes Asymmetric errors all unidirectional error detecting (AUED) codes Berger codes unidirectional errors
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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