hw6 - IST 1 Handout #35 Introduction to Information...

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Unformatted text preview: IST 1 Handout #35 Introduction to Information Wednesday, 5/9/7 Prof. M. Effros Homework Set #6 Due: Wednesday, May 16 1. Determine if each of the following channels is weakly symmetric, or not. Find the capacity of each weakly symmetric channel. (a) For 0 < p < 1, P Y | X = 1 − p p p 1 − p 1 − p p p 1 − p . (b) For 0 < p,q < 1, p negationslash = q , P Y | X = 1- p 2 p 2 q 2 1- q 2 p 2 1- p 2 q 2 1- q 2 1- p 2 p 2 1- q 2 q 2 p 2 1- p 2 1- q 2 q 2 . (c) For 0 < p,q < 1, p negationslash = q , P Y | X = 1- p 2 p 2 q 2 1- q 2 p 2 1- p 2 q 2 1- q 2 1- q 2 q 2 1- p 2 p 2 q 2 1- q 2 1- p 2 p 2 . 2. Consider the composition of two BSCs as follows (0 ≤ p,q ≤ 1). 1 1 1 q q 1 − q 1 − q 1 − p p p 1 − p Z Y 1 X 1 (a) What is the capacity of the channel with input X and output Z and transition probabilities governed by the given composition?...
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This note was uploaded on 12/01/2010 for the course ADLAC 1023 at Stanford.

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hw6 - IST 1 Handout #35 Introduction to Information...

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