# 4 - EE 478 Handout#12 Multiple User Information Theory...

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Unformatted text preview: EE 478 Handout #12 Multiple User Information Theory Thursday, October 16, 2008 Homework Set #4 Due: Thursday, October 23, 2008. 1. Sending correlated sources over a MAC. Consider the joint source-channel coding theorem in Lecture Notes #4. Complete the proof of the theorem by providing details of the analysis of the probability of error that yields the stated inequalities: H ( U 1 | U 2 ) < I ( X 1 ; Y | X 2 ,U 2 ) , H ( U 2 | U 1 ) < I ( X 2 ; Y | X 1 ,U 1 ) , H ( U 1 ,U 2 ) < I ( X 1 ,X 2 ; Y ) . 2. Binary symmetric broadcast channel. Consider the binary symmetric broadcast channel de- scribed on pages 5-7 of Lecture Notes #5 with 0 ≤ p 1 ≤ p 2 ≤ 1 / 2. Express the outputs as Y 1 = X + Z 1 (mod 2) and Y 2 = Y 1 + Z ′ 2 (mod 2), where Z 1 ∼ Bern( p 1 ) and Z ′ 2 ∼ Bern( α ) are independent and α is such that p 2 = p 1 ∗ α = α (1 − p 1 ) + (1 − α ) p 1 . In this problem, we derive that the capacity region is given by the set of all rate pairs ( R 1 ,R 2 ) such that R 2 ≤ 1 − H ( β ∗ p 2 ) , R 1 ≤ H ( β ∗ p 1 ) − H ( p 1 ) , for some β ∈ [0 , 1]. We start with the general capacity region expression for the degraded broadcast channel, go through the following steps, and use the fact that for 0 ≤ u ≤ 1, H ( H − 1 ( u ) ∗ α ) is a convex function, where H and 0 ≤ H − 1 ≤...
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## This note was uploaded on 10/24/2011 for the course ELECTRICAL ECE 571 taught by Professor Kelly during the Spring '11 term at University of Illinois, Urbana Champaign.

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4 - EE 478 Handout#12 Multiple User Information Theory...

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