Almost-sure variable-length source coding theorems for general sources

Source coding theorems for general sources are presented. For a source /spl mu/, which is assumed to be a probability measure on all strings of an infinite-length sequence with a finite alphabet, the notion of almost-sure sup entropy rate is defined; it is an extension of the Shannon entropy rate. W...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 45; no. 1; pp. 337 - 342
Main Authors: Muramatsu, J., Kanaya, F.
Format: Journal Article
Language:English
Published: New York IEEE 01.01.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Codes
Decoding
Entropy
Extraterrestrial measurements
Information technology
Information theory
Length measurement
Mathematics
Memoryless systems
Source coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Source coding theorems for general sources are presented. For a source /spl mu/, which is assumed to be a probability measure on all strings of an infinite-length sequence with a finite alphabet, the notion of almost-sure sup entropy rate is defined; it is an extension of the Shannon entropy rate. When both an encoder and a decoder know that a sequence is generated by /spl mu/, the following two theorems can be proved: (1) in the almost-sure sense, there is no variable-rate source coding scheme whose coding rate is less than the almost-sure sup entropy rate of /spl mu/, and (2) in the almost-sure sense, there exists a variable-rate source coding scheme whose coding rate achieves the almost-sure sup entropy rate of /spl mu/.
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.746838