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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 alphabet are specified. We shall determine the families of simultaneously(More)
The role of inequalities in information theory is reviewed and the relationship of these inequalities to inequalities in other branches of mathematics is developed. I NEQUALITIES in information theory have been driven by a desire to solve communication theoretic problems. To solve such problems, especially to prove converses for channel capacity theorems,(More)
and using the fact that D is self-orthogonal, we obtain p02 l=1 right-hand side of (44) = 1 jDj (p 2) n + p02 l=0 r r r A r r r(0p) r h(l) where h(l) = (p 0 1) l(p+1) p02 s=0 rs s(p+1) = 1 jDj (p 2) n + p02 l=0 r r r Ar r r(0p) n = 1 jDj (p 2) n + (p 0 1) (0p) n and the assertion of the lemma follows. REFERENCES [1] A. Ashikhmin and S. Litsyn, " Upper(More)