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Abstract: We derive a simple general parametric representation of the rate-distortionfunction of a memoryless source, where both the rate and the distortion aregiven by integrals whose integrands include the minimum mean square errorMMSE of the distortion $\Delta=dX,Y$ based on the source symbol $X$, withrespect to a certain joint distribution of these two random variables. At firstglance, these relations may seem somewhat similar to the I-MMSE relations dueto Guo, Shamai and Verd\-u, but they are, in fact, quite different. The newrelations among rate, distortion, and MMSE are discussed from several aspects,and more importantly, it is demonstrated that they can sometimes be ratheruseful for obtaining non-trivial upper and lower bounds on the rate-distortionfunction, as well as for determining the exact asymptotic behavior for very lowand for very large distortion. Analogous MMSE relations hold for channelcapacity as well.



Autor: Neri Merhav

Fuente: https://arxiv.org/







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