02-Homework.01

02-Homework.01 - ECE 154C Homework #1 Due: Wednesday, April...

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ECE 154C – Homework #1 Due: Wednesday, April 7, 2009 1. Consider a source which produces an i.i.d. sequence of symbols from the alphabet {A,B,C} with probabilities {0.4, 0.35, 0.25} respectively. For n=1, 2, and 3, find binary Huffman codes for taking n source symbols at a time. In each case compute the average number of binary code symbols per source symbol and compare it to the entropy (base 2). 2. Repeat problem 1, except find Shannon Fano codes instead of Huffman codes. 3. The purpose of this problem is to see what happens when you design a code for the wrong set of probabilities. Assume that you design a Huffman code for the second extension of a source where the probabilities of the source letters {A,B,C,D} are {0.5, 0.3, 0.1, 0.1} but that the actual source probabilities for {A,B,C,D}are {0.05, 0.1 0.2, 0.65} respectively. Find the average number of binary code symbols per source symbol and compare it with the entropy of the source. 4.
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