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On the Rate Distortion Function of Bernoulli Gaussian Sequences

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Executive Summary

This paper studies the rate distortion function of the i.i.d sequence of multiplications of a Bernoulli p random variable and a gaussian random variable ~ N (0,1). The paper uses a new technique in the derivation of the lower bound in which they establish the duality between channel coding and lossy source coding in the strong sense. The paper improves the lower bound on the rate distortion function over the best known lower bound by plog21/2if distortion D is small. This has some interesting implications on sparse signals where p is small since the known gap between the lower and upper bound is H (p).

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