S. Hanly and D. Tse, "Not known yet." Check with Stephen and David, 1995.  Home/Search   Document Not in Database   Summary   Related Articles

....; Y jX S ) I(X S ; Y ) The last step in the above inequality follows from the chain rule I(XL ; Y ) I(XM ; Y ) I(X LnM ; Y jXM ) Chain Rule) 3 A few basic facts on convex polytopes may be found in Section 3B. 4 This follows from the fact that, as observed by Hanly, Tse, and Whiting [16, 17], R is actually a convex polytope of a special kind called bounded polymatroid. One of the properties of bounded polymatroids is that they have a face that dominates every point. which holds for any M L [M ] Notice that if X 1 ; Delta Delta Delta ; XM are independent random variables ....

.... i 2 [M ] gets assigned, where (i) 1 ( i) M) corresponds to the position at the very top (bottom) In this way, each 2 Pi defines a rate tuple R 2 D with R i = I(X i ; Y j [ j2 Gamma1 (f1; Delta Delta Delta; i) Gamma1g) X j ) 38) It was observed by Hanly, Tse, and Whiting [16, 17] that R is in fact a bounded polymatroid. Polymatroids were introduced by Edmonds [20] who also derived their basic properties. For an introduction into polymatroid theory see, e.g. 21] The following lemma is a direct consequence of the fact that R is a bounded polymatroid. Lemma 14 (See ....

S. Hanly and D. Tse, "Not known yet." Check with Stephen and David, 1995.

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