Indirect Rate-Distortion Function of a Binary i.i.d Source
Abstract
The indirect source-coding problem in which a Bernoulli process is compressed in a lossy manner from its noisy observations is considered. These noisy observations are obtained by passing the source sequence through a The indirect source-coding problem in which a Bernoulli process is compressed in a lossy manner from its noisy observations is considered. These noisy observations are obtained by passing the source sequence through a binary symmetric channel so that the channel crossover probability controls the amount of information available about the source realization at the encoder. We use classic results in rate-distortion theory to compute an expression of the rate-distortion function for this model, where the Bernoulli source is not necessarily symmetric. The indirect rate-distortion function is given in terms of a solution to a simple equation. In addition, we derive an upper bound on the indirect rate-distortion function which is given in a closed. These expressions capture precisely the expected behavior that the noisier the observations, the smaller the return from increasing bit-rate to reduce distortion.
Cite
@article{arxiv.1505.04875,
title = {Indirect Rate-Distortion Function of a Binary i.i.d Source},
author = {Alon Kipnis and Stefano Rini and Andrea J. Goldsmith},
journal= {arXiv preprint arXiv:1505.04875},
year = {2015}
}