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Explicit bounds to R(D) for a binary symmetric Markov source

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1 Author(s)

A new upper houndR_{u}(D)and lower houndR_{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 intervalD_{c} < D < 1/2 = D_{max}, whereD_{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 boundR_{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 allD leq 1/2and therefore eventually rises above all the Wyner-Ziv lower bounds asDapproaches1/2. Some generalizations suggested by the analytical and geometrical techniques employed to deriveR_{u}(D)andR_{ell}(D)are discussed.

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Information Theory, IEEE Transactions on  (Volume:23 ,  Issue: 1 )