The approximate capacity for the 3-receiver writing on random dirty paper channel

Stefano Rini, Shlomo Shamai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper, the approximate capacity of the 3-receiver 'writing on random dirty paper' (WRDP) channel is derived. In the M-receiver WRDP channel, the channel output is obtained as the sum of the channel input, white Gaussian noise and a channel state sequence randomly selected among a set of M independent Gaussian sequences. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which one is selected to produce the channel output. In the following, we derive upper and lower bounds to the capacity of the 3-receiver WRDP channel which are to within a distance of at most 3 bits-per-channel-use (bpcu) for all channel parameters. In the achievability proof, the channel input is composed of the superposition of three codewords: the receiver opportunistically decodes a different set of codewords, depending on the variance of the channel state appearing in the channel output. Time-sharing among multiple transmission phases is employed to guarantee that transmitted message can be decoded regardless of the state realization. In the converse proof, we derive a novel outer bound which matches the pre-log coefficient arising in the achievability proof due to time-sharing. Although developed for the case of three possible state realizations, our results can be extended the general WRDP.

Original languageEnglish
Title of host publication2017 IEEE Information Theory Workshop, ITW 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509030972
StatePublished - 31 Jan 2018
Event2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, Taiwan
Duration: 6 Nov 201710 Nov 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2017 IEEE Information Theory Workshop, ITW 2017


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