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# Hw8sol - EE 376B/Stat 376B Information Theory Prof T Cover Handout#27 Tuesday June 6 2006 Solutions to Homework Set#8 1 Universal data compression

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EE 376B/Stat 376B Handout #27 Information Theory Tuesday, June 6, 2006 Prof. T. Cover Solutions to Homework Set #8 1. Universal data compression. Consider three possible source distributions on X , P a = (0 . 7 , 0 . 2 , 0 . 1) , P b = (0 . 1 , 0 . 7 , 0 . 2) , P c = (0 . 2 , 0 . 1 , 0 . 7) . (a) Find the minimum incremental cost of compression D * = min P max θ D ( P θ || P ) , the associated mass function P = ( p 1 ,p 2 ,p 3 ), and ideal codeword lengths l i = log(1 /p i ). (b) What is the channel capacity of a channel matrix with rows P a , P b , P c ? Solution: Universal data compression. Since D * = C, where C is the capacity of a channel deﬁned by a channel matrix with rows P a ,P b ,P c , and the uniform input distribution p * = (1 / 3 , 1 / 3 , 1 / 3) achieves the capacity C , D * = C = log 3 - H (0 . 1 , 0 . 7 , 0 . 2) . 4282 . Thus, the cost of not knowing the true source distribution is slightly less than half a bit per symbol. 2.

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## This note was uploaded on 06/10/2008 for the course ECE 376B taught by Professor Tomcover during the Spring '05 term at Stanford.

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Hw8sol - EE 376B/Stat 376B Information Theory Prof T Cover Handout#27 Tuesday June 6 2006 Solutions to Homework Set#8 1 Universal data compression

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