hw4 - EE596A Introduction to Information Theory Winter 2004...

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Unformatted text preview: EE596A Introduction to Information Theory Winter 2004 University of Washington Dept. of Electrical Engineering Handout 7: Problem Set 4: (due Wednesday. March 10th in class) Prof: Jeff A. Bilmes <bilmes@ee.washington.edu> Lecture 17, March 1st, 2004 Book Problems Do problems 7.4(abcd),7.6,7.9,8.8,8.10,8.12,9.1,10.2 For problem 7.4d, compute the probability of the sequence quence, where halts and Also, do not do 7.4e. (note: a good break in this problem set is to be done with all chapter 7 problems, problem 1 and 2 below, and 1/2 of the chapter 8 problems by Friday). Other Problems Problem 1: (The Ternary Confusion Channel): Consider a discrete memoryless channel with input alphabet and output alphabet , where and . The stochastic matrix given by if or if , and if or if . Compute the capacity of this channel, and determine the maximizing mass function over the input alphabet. Problem 2: In class and above, we defined the amazing incredible and unknowable number . In this problem, you are to choose a normally unsolvable problem (it can be one from mathematics, or even any general world problem you wish you could solve), and show how that if you have available to you, you can compute a (guaranteed halting) solution to this problem. Be as precise as possible, in that you give a explicit algorithm for how, when is given, you can compute an answer to your problem. Argue why your algorithm is correct, and why the problem you choose is normally unsolvable. 7-1 5 U G 5 ( T  Q 17 YY 7 ba`5 R I GE SQ PHFD ¦¦¦ ¨¨¦ ¤ ¡ ¦  ¦¦¦ ¤ ¡ ¥©¨¨§¥£¢  0 which is then followed by any arbitrary se- G Q 7  D V9  ( (" & $ )¨! '%#  G Q R I GE G Q # B7  'Q PHFD 5 X V9  ( W 7  1 V7  ( 2 @7 53 C( BA 2 @9(7 53 8)8¨( 64 "¨!       ...
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