Universal noiseless coding. (English) Zbl 0283.94005

Summary: The paper deals with universal coding (any asymptotically optimum method of block-to-block memoryless source coding for sources with unknown parameters). There is assumed variable-length coding, which is noiseless with performance measured as a function of the coding redundancy relative to the per-letter conditional source entropy given the unknown parameter. Necessary and sufficient conditions are found for universal coding, for maximin universal codes, and for minimax ones; the using of the words “maximin” and “minimax”” is directly analogous to their well-known decision-theoretical sense. For conditionally stationary ergodic sources, it is shown that weighted universal codes always exist if the alphabet (or only the entropy) is finite. It holds, that minimax universal codes result if an additional entropy stability constraint is applied. There are discussed some implications of the work to fixed length codes. Several examples are given to illustrate the ideas of this paper. The author proposes as well some open problems.
Reviewer: J. Lisá


94A15 Information theory (general)
94B99 Theory of error-correcting codes and error-detecting codes
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