NDLI: Energy-Minimizing Error-Correcting Codes

Content Provider	IEEE Xplore Digital Library
Author	Cohn, H. Yufei Zhao
Copyright Year	1963
Abstract	We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length. Examples of these universally optimal codes include Hamming, Golay, and Reed-Solomon codes, among many others, and this helps to explain their robustness as the channel model varies. Universal optimality of these codes is equivalent to minimality of their binomial moments, which has been proved in many cases by Ashikhmin and Barg. We highlight connections with mathematical physics and the analogy between these results and previous work by Cohn and Kumar in the continuous setting, and we develop a framework for optimizing the linear programming bounds. Furthermore, we show that if these bounds prove a code is universally optimal, then the code remains universally optimal even if one codeword is removed.
Sponsorship	IEEE Information Theory Society
Starting Page	7442
Ending Page	7450
Page Count	9
File Size	669535
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Linear programming Potential energy Physics Vectors Minimization Maximum likelihood decoding Error correction codes Combinatorial mathematics. combinatorial mathematics
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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