Thomas M. Cover

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The case of n unity-variance random variables x1, XZ,. * *, x, governed by the joint probability density w(xl, xz, * * * x,) is considered, where the density depends on the (normalized) cross-covariances pii = E[(xi jzi)(xi li)]. It is shown that the condition holds for an “arbitrary” function f(xl, x2, * * * , x,) of n variables if and only if the(More)
A relay channel consists of an input x,, a relay output yl, a cJmnnel output y, and a relay sender x2 (whose trasmission is allowed to depend on the past symbols y,). l%e dependence of the received symbols upm the inpnts is given by p(y,y,lx,,x,). ‘l%e channel is assumed to be memoryless. In this paper the following capacity theorems are proved. 1)(More)
This paper develops the separating capacities of families of nonlinear decision surfaces by a direct application of a theorem in classical combinatorial geometry. It is shown that a family of surfaces having d degrees of freedom has a natural separating capacity of 2d pattern vectors, thus extending and unifying results of Winder and others on the(More)
We introduce the problem of a single source attempting to communicate information simultaneously to several receivers. The intent is to model the situation of a broadcaster with multiple receivers or a lecturer with many listeners. Thus several different channels with a common input a lphabet are specified. W e shall determine the families of simultaneously(More)
Consider a sequence of independent identically distributed (i.i.d.) random variables X,, X,, . ., X, and a distortion measure d( 4, ,$) on the estimates X, of X,. Two descriptions i(X) E { 1,2; , 2flRl) and j(X) E (1,2,...,2”R2] are given of the sequenceX=(X1,X2;..,Xn). From these two descriptions, three estimates J%?((i(X)), X,(j(X)), and X,( i( X), j(X))(More)
Abslruct-The successive refinement of information consists of first approximating data using a few hits of information, then iteratively improving the approximation as more and more information is supplied. The goal is to achieve an optimal description at each stage. In general an ongoing description is sought which is rate-distortion optimal whenever it is(More)
The minimum complexity or minimum description-length criterion developed by Kolmogorov, Rissanen, Wallace, So&in, and others leads to consistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplicity. A related issue is the compromise between accuracy of approximations and(More)
Manuscript received November 28, 1978; revised February 28, 1980. This work was supported in part by the National Science Foundation under Grant ENG 76-23334, in part by the Stanford Research Institute under International Contract D/&C-15-C-0187, and in part by the Joint Scientific Enaineerina Program under Contracts NO001475-C-0601 and F44620-76-C&01. This(More)