Capacity theorems for the relay channel

Author

Cover, Thomas M. ; Gamal, Abbas El

Volume

Issue

fYear

1979

fDate

9/1/1979 12:00:00 AM

Firstpage

572

Lastpage

584

Abstract

A relay channel consists of an input $x_{l}$ , a relay output $y_{1}$ , a channel output $y$ , and a relay sender $x_{2}$ (whose transmission is allowed to depend on the past symbols $y_{1}$ . The dependence of the received symbols upon the inputs is given by $p(y,y_{1}|x_{1},x_{2})$ . The channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)If $y$ is a degraded form of $y_{1}$ , then $C : = : \\max !_{p(x_{1},x_{2})} \\min ,{I(X_{1},X_{2};Y), I(X_{1}; Y_{1}|X_{2})}$ . 2)If $y_{1}$ is a degraded form of $y$ , then $C : = : \\max !_{p(x_{1})} \\max _{x_{2}} I(X_{1};Y|x_{2})$ . 3)If $p(y,y_{1}|x_{1},x_{2})$ is an arbitrary relay channel with feedback from $(y,y_{1})$ to both $x_{1} and x_{2}$ , then $C: = : \\max _{p(x_{1},x_{2})} \\min ,{I(X_{1},X_{2};Y),I ,(X_{1};Y,Y_{1}|X_{2})}$ . 4)For a general relay channel, $C \\leq \\hbox{max}_{p(x_{1},x_{2})} \\hbox{ min} \\{ I(X_{1}, X_{2};Y),I(X_{1};Y,Y_{1}|X_{2})$ . Superposition block Markov encoding is used to show achievability of $C$ , and converses are established. The capacities of the Gaussian relay channel and certain discrete relay channels are evaluated. Finally, an achievable lower bound to the capacity of the general relay channel is established.

Keywords

Information rates; Repeaters; Chaotic communication; Error correction; Error correction codes; Fast Fourier transforms; Feedback; Information theory; Relays; Signal representations; Spectroscopy; Statistics;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1979.1056084

Filename

1056084

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=930554