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- W109812615 abstract "The following is a short introduction to some aspects of that part of coding and decoding theory which uses algebraic tools, and is therefore called algebraic coding theory. If the channel over which information is to be transmitted from source to user is noisy, and if it is not possible to modify the channel itself, then coding and decoding can help the user receive a better (i.e. less corrupted) reproduction of the channel input. Our basic assumption will be that inform ation consists of a (potentially infinite) sequence of symbols (or digits) belonging to a finite alphabet (often binary). The input alphabet of a channel need not coincide with the output alphabet, but this is often the case. The effect of the noise is then of transforming, with some positive probability, every input symbol into a different symbol, and the mathematical description of the channel consists precisely of the set of all conditional probabilities of an output given an input. If the channel is memoryless, i.e. if past history has no influence on the current noise effect, the channel description is simplified enormously." @default.
- W109812615 created "2016-06-24" @default.
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- W109812615 date "1976-01-01" @default.
- W109812615 modified "2023-09-23" @default.
- W109812615 title "An Introduction to Algebraic Coding Theory" @default.
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- W109812615 doi "https://doi.org/10.1007/978-3-642-48895-5_20" @default.
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