An attempt is made to determine whether it is true that for a fixed distortion level Delta the rate-distortion function R(P, Delta ) has in the distribution P no local maxima with values different from the global maximum. It is shown that, in general, the answer is negative. However, the answer is positive for Hamming distortion measures. Moreover their R is Schur-concave.>
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Rudolf Ahlswede (1990) studied this question.
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