DocumentCode :
1779592
Title :
Codes for tasks and Rényi entropy rate
Author :
Bunte, Christoph ; Lapidoth, Amos
Author_Institution :
ETH Zurich, Zurich, Switzerland
fYear :
2014
fDate :
June 29 2014-July 4 2014
Firstpage :
346
Lastpage :
350
Abstract :
A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum ρ-th moment of the number of performed tasks are derived. The key is an analog of the Kraft Inequality for partitions of finite sets. When a sequence of tasks is produced by a source of a given Rényi entropy rate of order 1=(1 + ρ) and n tasks are jointly described using nR bits, it is shown that for R larger than the Rényi entropy rate, the ρ-th moment of the ratio of performed tasks to n can be driven to one as n tends to infinity, and that for R less than the Rényi entropy rate it tends to infinity. This generalizes a recent result for IID sources by the same authors. A mismatched version of the direct part is also considered, where the code is designed according to the wrong law. The penalty incurred by the mismatch can be expressed in terms of a divergence measure that was shown by Sundaresan to play a similar role in the Massey-Arikan guessing problem.
Keywords :
codes; entropy; IID sources; Kraft Inequality; Massey-Arikan guessing problem; Rényi entropy rate; divergence measure; finite set partitions; minimum ρ-th moment; task codes; Electronic mail; Entropy; Fasteners; Information theory; Markov processes; Q measurement; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory (ISIT), 2014 IEEE International Symposium on
Conference_Location :
Honolulu, HI
Type :
conf
DOI :
10.1109/ISIT.2014.6874852
Filename :
6874852
Link To Document :
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