Extremal Properties of Rate-Distortion Functions
We will consider the following problem formulated by Csiszár in 1988 : It is true that for fixed distortion level \(\Delta \) the rate-distortion function \(R(P,\Delta )\) has in the distribution P no local maxima with value different from the global maximum? We show that in general the answer is negative. However, the answer is positive for Hamming distortion measures. Moreover, R is Schur-concave.
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