Gamal_Multi user information theory

Gamal_Multi user information theory - 1466 PROCEEDINGS OF...

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Unformatted text preview: 1466 PROCEEDINGS OF THE IEEE, VOL. 68, NO. 12, DECEMBER 1980 Multiple User Information Theory DBAS EL MEMBER, IEEE, AND THOMAS M. COVER, FELLOW, IEEE Invited Paper Abstract-A u d i i framework is given for multiple user information networks. These networks consist of several users communicating to one another in the preaence of arbitrary inteflerence and noise. The presence of many senders necessitates a tradeoff in the achievable in- formation tmmnisdoa tptes. The god is the characterization of the capacity region consicting of dl achievabh? rata The focus is on broad- wt, multiple axes, day, and other channels for which the recent theory is relatively well developed. A discussion of the Gaussian version of these channels dem0nstmte.s the concreteness of the encoding and decoding necesmry to achieve optimal information flow. We aka offer speculations about the form of a gend theory of information flow in networks. I. INTRODUCTION HE SHANNON theory of channel capacity has been ex- tended successfully to many interesting communication networks in the past 10 years. We shall attempt to achieve three goals in our exposition of this theory: (i) make the theory accessible to researchers in communication theory, (ii) provide conditionally novel proofs of the theory for re- searchers in information theory, and (iii) present an overview of the basic problems in constructing a theory of information flow in networks. The primary ideas can be obtained by reading the introduc- tion and the sections on the Gaussian examples, the Shannon’s theorem, and the summary. The heretofore unpublished in- formation theoretic proofs are those for the sections on the multiple access channel, Slepian-Wolf data compression, and the degraded broadcast channel. All proofs, both new and old, are based on the idea of jointly typical sequences. No claim for comprehensive coverage is given. For that the reader is referred to van der Meulen [I]. Rather, we are concerned with providing a unified approach to the theory. This leads naturally to a discussion of some of the major re- sults. We begin by discussing some of the building blocks for networks. Suppose m ground stations are simultaneously communica- ting to a common satellite as in Fig. 1. This is known as the multiple access channel. What are the achievable rates of com- munication? Does the total amount of information flow tend to infinity with the number of stations-or does the interfer- ence put an upper limit on the total communication? Does of A. El Gamal was partiaUy supported by the Joint Services Elec- Manuscript received June 2, 1980; revised July 25, 1980. The work tronics Rogram through the Air Force Office of Scientific Research (AFSC) under Contract F44620-76-C-0061 and NSF ENG 79-08948....
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This note was uploaded on 10/16/2010 for the course ECE 380 taught by Professor Baltazar during the Spring '10 term at Rice.

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Gamal_Multi user information theory - 1466 PROCEEDINGS OF...

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