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

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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.

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