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**Unformatted text preview: **EE 376A/Stat 376A Information Theory Prof. T. Weissman Friday, March 17, 2006 Practice Final Problems These problems are sampled from a couple of the actual finals in previous years. 1. ( 20 points) Errors and erasures. Consider a binary symmetric channel (BSC) with crossover probability p .-- 3 Q Q Q Q Q Q Q Qs 1 1 1- p 1- p p p A helpful genie who knows the locations of all bit flips offers to convert flipped bits into erasures. In other words, the genie can transform the BSC into a binary erasure channel. Would you use his power? Be specific. 2. (20 points) Code constraint. What is the capacity of a BSC( p ) under the constraint that each of the codewords has a proportion of 1s less than or equal to , i.e., 1 n n X i =1 X i ( w ) , for w { 1 , 2 ,..., 2 nR } . (Pay attention when > 1 / 2.) 1 3. ( 20 points) Partition. Let ( X,Y ) denote height and weight. Let [ Y ] be Y rounded off to the nearest pound. (a) Which is greater I ( X ; Y ) or I ( X ;[ Y ]) ? (b) Why? 4. ( 20 points) Amplify and forward. We cascade two Gaussian channels by feeding the (scaled) output of the first channel into the second....

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