Semi-Analytical Solutions for Rate Distortion Bounds and OPTA for Sources with Arbitrary Distributions

Authors:

Rüngeler, M. ,  Schotsch, B. ,  Vary, P.

Book Title:

Proceedings of International ITG Conference on Source and Channel Coding (SCC)

Organization:

ITG

Publisher:

VDE

Address:

Siegen

Date:

Jan. 2010

ISBN:

978-3-80073-211-1

Language:

English

Abstract

The rate distortion bound is a widely used theoretical bound which describes the minimum mean square error (MMSE) distortion for a given number of quantization bits when quantizing a scalar random variable. An analytical solution for this bound is only available for a small number of probability density functions (pdf), such as the Gaussian pdf. For arbitrary pdfs, the Blahut-Arimoto algorithm [1], [2] needs to be applied to iteratively estimate the rate distortion bound. We propose a novel method to (semi-)analytically calculate the rate distortion bound for sources with arbitrary pdfs. This method is based on the Guo-Shamai-Verdú (GSV) theorem [3]. Furthermore, it is possible to apply the proposed method for calculating the Optimum Performance Theoretically Attainable (OPTA) for arbitrarily distributed input symbols observed through an AWGN channel.

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