TY - GEN

T1 - The approximate capacity for the 3-receiver writing on random dirty paper channel

AU - Rini, Stefano

AU - Shamai, Shlomo

PY - 2018/1/31

Y1 - 2018/1/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85046354643&partnerID=8YFLogxK

U2 - 10.1109/ITW.2017.8277990

DO - 10.1109/ITW.2017.8277990

M3 - Conference contribution

AN - SCOPUS:85046354643

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 364

EP - 368

BT - 2017 IEEE Information Theory Workshop, ITW 2017

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 6 November 2017 through 10 November 2017

ER -