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Unformatted text preview: EE376B/Stat 376B Handout #9 Information Theory Thursday, April 27, 2006 Prof. T. Cover Due Thursday, May 4, 2006 Homework Set #4 1. Multiple layer waterfilling Let C ( x ) = 1 2 log(1 + x ) denote the channel capacity of a Gaussian channel with signal to noise ratio x . Show C P 1 N + C P 2 P 1 + N = C P 1 + P 2 N . This suggests that the first signal power P 1 acts as self noise for the second layer P 2 . 2. Parallel channels and waterfilling Consider a pair of parallel Gaussian channels, i.e., Y 1 Y 2 = X 1 X 2 + Z 1 Z 2 , where Z 1 Z 2 ∼ N , σ 2 1 σ 2 2 , and there is a power constraint E ( X 2 1 + X 2 2 ) ≤ P . Assume that σ 2 1 > σ 2 2 . (a) At what power does the channel stop behaving like a single channel with noise variance σ 2 2 , and begin behaving like a pair of channels, ie., at what power does the worst channel become useful? (b) What is the capacity C ( P ) for large P ?...
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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.
- Spring '05