{ "id": "1505.04875", "version": "v1", "published": "2015-05-19T05:00:23.000Z", "updated": "2015-05-19T05:00:23.000Z", "title": "Indirect Rate-Distortion Function of a Binary i.i.d Source", "authors": [ "Alon Kipnis", "Stefano Rini", "Andrea J. Goldsmith" ], "categories": [ "cs.IT", "math.IT", "stat.CO" ], "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 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 of Witsenhausen and Gallager to compute an expression of the rate-distortion function for this model. A closed form solution is obtained for the special case of a Bernoulli $1/2$ source, as well as a lower bound valid for all Bernoulli sources. These expressions capture precisely the expected behaviour that the noisier the observations, the smaller the return from increasing bit-rate to reduce distortion.", "revisions": [ { "version": "v1", "updated": "2015-05-19T05:00:23.000Z" } ], "analyses": { "keywords": [ "indirect rate-distortion function", "noisy observations", "channel crossover probability controls", "binary symmetric channel", "lower bound valid" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2015arXiv150504875K" } } }