# moedB - The Hebrew University of Jerusalem Introduction to...

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Unformatted text preview: The Hebrew University of Jerusalem Introduction to Information Theory Course 67548, winter 2007-2008. Final examination, moed B. Lecturer: Prof. Michael Werman June 15, 2008 Instructions: There are 4 questions (some of which are subdivided into parts). You can get at most 100 points (1 point is a free bonus). You are to answer 3 questions out of 4. If you answer all 4 questions please specify clearly which three to grade. Otherwise, the answer appearing last will be ignored. There are some helpful formulas on the last page. Justify your answers, but be brief. 1. 33 points Consider a k-input-erasure channel. I.e. supposing that input X takes values in { 1 ,..,k } , then output Y takes values in { 1 ,..,k } ∪ { e } , and p ( Y = i | X = i ) = 1- , p ( Y = e | X = i ) = . if X = i then Y = i with propability (1- ) and Y = e with probability . (a) [11 points] For a given distibution p ( x ) of X what is the mutual information I ( X ; Y ) expressed in terms of H ( X )?...
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moedB - The Hebrew University of Jerusalem Introduction to...

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