This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 sourcechannel 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 57 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 ≤...
View
Full
Document
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.
 Spring '11
 Kelly

Click to edit the document details