Published March 1, 1990
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Journal Article
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The hardness of decoding linear codes with preprocessing
- Creators
-
Bruck, Jehoshua
- Naor, Moni
Abstract
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.
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.Files
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- CaltechAUTHORS:BRUieeetit90b
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