# hw8 - EE 376A Information Theory Prof T Cover Handout#27...

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EE 376A Handout #27 Information Theory Thursday, February 26, 2009 Prof. T. Cover Due Tuesday, March 10, 2009 Homework Set #8 1. Source and channel. We wish to encode a Bernoulli( α ) process V 1 , V 2 , . . . for transmission over a binary symmetric channel with error probability p . V n 011011101 −→ X n ( V n ) −→ a45 a45 a8 a8 a8 a8 a8 a42 a72 a72 a72 a72 a72 a106 0 1 0 1 p p −→ Y n −→ ˆ V n 011011101 Find conditions on α and p so that the probability of error P ( ˆ V n negationslash = V n ) can be made to go to zero as n −→ ∞ . 2. Cascaded BSCs. Consider the two discrete memoryless channels ( X , p 1 ( y | x ) , Y ) and ( Y , p 2 ( z | y ) , Z ). Let p 1 ( y | x ) and p 2 ( z | y ) be binary symmetric channels with crossover probabilities λ 1 and λ 2 respectively. a45 a45 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a51 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a115 a45 a45 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a17 a51 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a81 a115 1 0 X 1 0 Z 1 0 Y 1 λ 1 1 λ 1 λ 1 λ 1 1 λ 2 1 λ 2 λ 2 λ 2 (a) What is the capacity C 1 of p 1 (

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