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Unformatted text preview: Introduction to Information Theory (67548) December 25, 2008 Assignment 3: Channels and Coding Lecturer: Prof. Michael Werman Due: Sunday, January 11, 2009 Note: Unless specified otherwise, all entropies and logarithms should be taken with base 2 . Problem 1 Binary Channel Consider a channel with binary inputs that has both erasures and errors. Let the probability of error be , and the probability of erasure be α , so the channel is as follows: 1. Find the capacity of this channel. 2. As a special case, find the capacity of this channel when α = 0 (a binary symmetric channel). 3. As a special case, find the capacity of this channel when = 0 (a binary erasure channel). Problem 2 Joint Typicality Consider a binary symmetric channel with crossover probability 0 . 1 (namely, there is a 0 . 1 probability for a bit flip). Let the random variable X represent the input (sent bit), and let the random variable Y represent the output (received bit). The input distribution that achieves capacity is the uniformrepresent the output (received bit)....
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- Spring '08