final - University of Toronto F R Kschischang ECE 1502S...

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University of Toronto ECE 1502S Department of Electrical F. R. Kschischang Information Theory & Computer Engineering Final Examination — April 17, 2006 Instructions : You have approximately 2 hours of “in-class” time, followed by two days of “take-home” time to complete this test. Complete as much as possible during the in-class time; your grade will be computed as a weighted average of your “in-class” grade and your “take-home” grade. (Weights to be determined later.) Answer all five [5] questions. All questions have equal value. Show all steps and present all results clearly. Please start each question on a new page. Take-home due date: Wednesday, April 19, 2006, 5:00 p.m. , or earlier. Please hand in to the instructor (BA4132), to his assistant, Margaret Hewer, or to the teaching assistant, Karen Su. All work is to be done independently. Consultation with others is not permitted. Good luck! 1 . Short Snappers —The parts of this question all have short answers that require a minimum of computation, though some may rely on the assigned homework. In all cases, justify your answer briefly. (a) True or false?: a variable-length source code that satisfies the Kraft inequality is uniquely decodable. (b) True or false?: if H ( X ) = H ( Y ) then H ( X | Y ) = H ( Y | X ). (c) True or false?: to achieve the capacity of a weakly symmetric discrete memoryless chan- nel, it is necessary to use a channel input distribution that makes the channel output distribution uniform.
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