fall08-exam2 - University of Illinois at Urbana-Champaign...

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Unformatted text preview: University of Illinois at Urbana-Champaign ECE 563: Information Theory Fall 2008 Midterm 2 Wednesday, November 19, 2008 Name: This is a closed-book exam. You may consult both sides of two sheets of notes, typed in font size 10 or equivalent handwriting size. Calculators, laptop computers, Palm Pilots, two-way email pagers, etc. may not be used. Write your answers in the space provided. Please show all of your work. Answers without appropriate justification will receive very little credit. Score: 1. (20 points) 2. (50 points) 3. (30 points) Total. (100 points) 1 1. Consider optimally compressing a source X X where each x X is equally likely. a) Suppose |X| = 2 k and the optimal Huffman code tree is constructed. Consider a new source Y , also equally likely, with |Y| = 2 k + 1. How do the huffman codes differ in the two cases? What is the expected length of the latter? (Feel free to think graphically). b) Give the exact expected Huffman code length for the scenario where X = 100. 2 2. Consider trying to communicate a message in W W = ' 1 ,..., 2 nR at rate R across a memoryless noisy channel, with feedback. We assume W is uniformly distributed over W ....
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fall08-exam2 - University of Illinois at Urbana-Champaign...

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