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Arithmetic codes have been studied in the context of compression coding, i.e., transformations to code strings which take up less storage space or require less transmission time over a communications link. Another application of coding theory is that of noiseless channel coding, where constraints on strings in the channel symbol alphabet prevent an obvious mapping of data strings to channel strings. An interesting duality exists between compression coding and channel coding. The source alphabet and code alphabet of a compression system correspond, respectively, to the channel alphabet and data alphabet of a constrained channel system. The decodability criterion of compression codes corresponds to the representability criterion of constrained channel codes, the generalized Kraft Inequality has a dual inequality due to the senior author.
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