Technical Reports
HPL-2009-19
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On the rate distortion function of Bernoulli Gaussian sequences
Chang, Cheng
HP Laboratories
HPL-2009-19
Keyword(s): Rate distortion theory, duality between channel and source coding, sparse signals
Abstract: In this paper, we study 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). We use a new technique in the derivation of the lower bound in which we establish the duality between channel coding and lossy source coding in the strong sense. We improve the lower bound on the rate distortion function over the best known lower bound by 
if 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). This improvement in the lower bound shows that the lower and upper bounds are almost identical for sparse signals with small distortion because 
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32 Pages
Additional Publication Information: Submitted to IEEE Transactions on Information Theory, Allerton Conference 2009
External Posting Date: February 6, 2009 [Fulltext]. Approved for External Publication
Internal Posting Date: February 6, 2009 [Fulltext]