Writing on dirty paper (Corresp.)

Author

Costa, Max H M

Volume

Issue

fYear

1983

fDate

5/1/1983 12:00:00 AM

Firstpage

439

Lastpage

441

Abstract

A channel with output $Y = X + S + Z$ is examined, The state $S \\sim N(0, QI)$ and the noise $Z \\sim N(0, NI)$ are multivariate Gaussian random variables ( $I$ is the identity matrix.). The input $X \\in R^{n}$ satisfies the power constraint $(l/n) \\sum _{i=1}^{n}X_{i}^{2} \\leq P$ . If $S$ is unknown to both transmitter and receiver then the capacity is $frac{1}{2} \\ln (1 + P/( N + Q))$ nats per channel use. However, if the state $S$ is known to the encoder, the capacity is shown to be $C^{\\ast } =frac{1}{2} \\ln (1 + P/N)$ , independent of $Q$ . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio $P/N$ . Therefore, the state $S$ does not affect the capacity of the channel, even though $S$ is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state $S$ rather than attempting to cancel it.

Keywords

Error-correction coding; Binary codes; Electrons; Gaussian channels; Gaussian noise; Network address translation; Notice of Violation; Optimization methods; Random variables; Transmitters; Writing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1983.1056659

Filename

1056659

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=936331