DocumentCode :
926156
Title :
Explicit bounds to R(D) for a binary symmetric Markov source
Author :
Berger, Toby
Volume :
23
Issue :
1
fYear :
1977
fDate :
1/1/1977 12:00:00 AM
Firstpage :
52
Lastpage :
59
Abstract :
A new upper hound R_{u}(D) and lower hound R_{\\ell }(D) are developed for the rate-distortion function of a binary symmetric Markov source with respect to the frequency of error criterion. Both hounds are explicit in the sense that they do not depend on a blocklength parameter. In the interval D_{c} < D < 1/2 = D_{\\max } , where D_{c} is Gray\´s critical value of distortion, R_{u}(D) is convex downward and possesses the correct value and the correct slope at both endpoints. The new lower bound R_{\\ell }(D) diverges from the Shannon lower bound at the same value of distortion as does the second-order Wyner-Ziv lower bound. However, it remains strictly positive for all D \\leq 1/2 and therefore eventually rises above all the Wyner-Ziv lower bounds as D approaches 1/2 . Some generalizations suggested by the analytical and geometrical techniques employed to derive R_{u}(D) and R_{\\ell }(D) are discussed.
Keywords :
Markov processes; Rate-distortion theory; Frequency; Hamming distance; Iterative algorithms; Probability distribution; Rate-distortion; Upper bound; White noise;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1977.1055654
Filename :
1055654
Link To Document :
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