# 2 - EE 478 Multiple User Information Theory Handout#5...

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EE 478 Handout #5 Multiple User Information Theory Thursday, October 2, 2008 Homework Set #2 Due: Thursday, October 9, 2008. 1. Capacity with input cost. Consider a DMC denoted by ( X ,p ( y | x ) , Y ), and assume that nonnegative cost b ( x ) is associated with each input symbol x ∈ X . The capacity of such channel with input cost constraint B is given by C ( B ) = max X :E( b ( X )) B I ( X ; Y ) . (a) Show that the function C ( B ) is concave in B . (b) The proof of the achievability is outlined in the lecture note. Complete the details of the proof. 2. Mutual information game. Consider the following channel: aA ±² a a A X Y Z Throughout this problem, assume that X and Z are independent, E( X ) = 0, E( X 2 ) = P , E( Z ) = 0, and E( Z 2 ) = 1. The channel capacity is given by I ( X ; Y ) = I ( X ; X + Z ). Now for the game. The noise player chooses a distribution on Z to minimize I ( X ; X + Z ) , while the signal player chooses a distribution on X to maximize I

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2 - EE 478 Multiple User Information Theory Handout#5...

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