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The hardness of decoding linear codes with preprocessing

Bruck, Jehoshua and Naor, Moni (1990) The hardness of decoding linear codes with preprocessing. IEEE Transactions on Information Theory, 36 (2). pp. 381-385. ISSN 0018-9448. doi:10.1109/18.52484.

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The problem of maximum-likelihood decoding of linear block codes is known to be hard. The fact that the problem remains hard even if the code is known in advance, and can be preprocessed for as long as desired in order to device a decoding algorithm, is shown. The hardness is based on the fact that existence of a polynomial-time algorithm implies that the polynomial hierarchy collapses. Thus, some linear block codes probably do not have an efficient decoder. The proof is based on results in complexity theory that relate uniform and nonuniform complexity classes.

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Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© Copyright 1990 IEEE. Reprinted with permission. Manuscript received October 10, 1988; revised July 12, 1989. The material in this paper was partially presented at the 1990 IEEE Information Theory Symposium, San Diego, CA, January 14-19. The authors thank Dr. Mario Blaum for useful discussions and the Associate Editor, Dr. Don Coppersmith, for his comments.
Subject Keywords:decoding; error correction codes; complexity theory
Issue or Number:2
Record Number:CaltechAUTHORS:BRUieeetit90b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5703
Deposited By: Archive Administrator
Deposited On:29 Oct 2006
Last Modified:08 Nov 2021 20:28

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