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Neural networks, error-correcting codes, and polynomials over the binary n-cube

Bruck, Jehoshua and Blaum, Mario (1989) Neural networks, error-correcting codes, and polynomials over the binary n-cube. IEEE Transactions on Information Theory, 35 (5). pp. 976-987. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:BRUieeetit89

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Abstract

Several ways of relating the concept of error-correcting codes to the concept of neural networks are presented. Performing maximum-likelihood decoding in a linear block error-correcting code is shown to be equivalent to finding a global maximum of the energy function of a certain neural network. Given a linear block code, a neural network can be constructed in such a way that every codeword corresponds to a local maximum. The connection between maximization of polynomials over the n-cube and error-correcting codes is also investigated; the results suggest that decoding techniques can be a useful tool for solving such maximization problems. The results are generalized to both nonbinary and nonlinear codes.


Item Type:Article
Additional Information:© Copyright 1989 IEEE. Reprinted with permission. Manuscript received December 7, 1987; revised November 2, 1988. This work was supported in part by the U.S. Air Force Office of Scientific Research. This paper was presented in part at the IEEE Symposium on Information Theory, Kobe, Japan, June 1988. The authors would like to thank Dr. A. Dembo for his valuable comments on the earlier version of this manuscript and the referees for their suggestions.
Subject Keywords:decoding; error correction codes; neural nets; nonlinear programming; polynomials
Record Number:CaltechAUTHORS:BRUieeetit89
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BRUieeetit89
Alternative URL:http://dx.doi.org/10.1109/18.42215
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5701
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:29 Oct 2006
Last Modified:26 Dec 2012 09:14

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