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# hw6 - EE 376B/Stat 376B Information Theory Prof T Cover...

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EE 376B/Stat 376B Handout #14 Information Theory Thursday, May 11, 2006 Prof. T. Cover Due Thursday, May 18, 2006 Homework Set #6 1. Slepian-Wolf for deterministically related sources. Find and sketch the Slepian-Wolf rate region for the simultaneous data compression of ( X, Y ) , where y = f ( x ), and f is a given deterministic function. 2. Slepian-Wolf. Three cards from a three-card deck are dealt, one to sender X 1 , one to sender X 2 , and one to sender X 3 . At what rates do X 1 , X 2 , and X 3 need to communicate to some receiver so that their card information can be recovered? Decoder - - - - - - X n 3 X n 2 X n 1 k ( X n 3 ) j ( X n 2 ) i ( X n 1 ) - ˆ X n 1 , ˆ X n 2 , ˆ X n 3 · Assume that ( X 1 i , X 2 i , X 3 i ) are i.i.d. from a uniform distribution over the permutations of { 1 , 2 , 3 } . 3. Broadcast channel. (a) For the degraded broadcast channel X Y 1 Y 2 , find the points a and b where the capacity region hits the R 1 and R 2 axes. (b) Show that b a. 4. Slepian-Wolf.

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