Abstract
Shannon’s theory of information [1] and subsequent generalizations to multiple users (for a survey see [2]) consider the situation of a small number of users each with an unlimited amount of information. The users communicate over a noisy channel with the goal of exchanging their information reliably. Here, we consider a complementary model. We assume a very large number of users, each with a small amount of information. We also assume that the communication takes place over a noisy channel but assume that the goal of the users is to compute a function reliably. This highly distributed information model is motivated by problems of decision making in a network. The users could be either a large number of processors, human beings, or simply the components of a logic circuit. In all cases, the noise is an inevitable physical limitation.
See contribution by Gallager in Chapter VI for more on this.
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References
C.E. Shannon, “A Mathematical Theory of Communications,” Bell Syst. Tech. J., 27, pp. 379–423 and 623–656 (July and Oct. 1948).
A. El Gamal and T. Cover, “Multiple User Information Theory,” Proc. IEEE, 68, No. 12, pp. 1466–1483 (Dec. 1980).
R. Gallager, “Computing Parity in a Broadcast Network,” in this book.
A. Orlitsky and A. El Gamal, “Broadcast Complexity,” in preparation.
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© 1987 Springer-Verlag New York Inc.
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El Gamal, A. (1987). Reliable Communication of Highly Distributed Information. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_14
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DOI: https://doi.org/10.1007/978-1-4612-4808-8_14
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