3assignment

3assignment - of this HuFman code? (b) Let Y = ( X a ,X b )...

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ECEN 455: Assignment 3 Problems: 1. A discrete-time source generates three independent symbols A , B , and C with probabilities 0 . 9, 0 . 08, and 0 . 02, respectively. Determine the entropy of the source. 2. Design a binary HuFman code for a discrete-time source that generates three independent symbols A , B , and C with probabilities 0 . 9, 0 . 08, and 0 . 02, respectively. Determine the average code length. 3. Show that { 01 , 100 , 101 , 1110 , 1111 , 0011 , 0001 } cannot be a HuFman code for any source probability distribution. 4. ±ind the Lempel-Ziv source code for the binary source sequence 00010010000001100001000000010000001010000100000011010000000110 Recover the original sequence back from the Lempel-Ziv source Code. Hint: You require two passes of the binary sequence to decide on the size of the dictionary. 5. Let X be a random variable such that { x 1 ,x 2 ,x 3 } have probabilities { 1 2 , 1 3 , 1 6 } , respectively. (a) What is the entropy of X ? Design a HuFman code for X . What is the expected length
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Unformatted text preview: of this HuFman code? (b) Let Y = ( X a ,X b ) be a vector random variable, where X 1 and X 2 are independent realizations of the source X . What is the entropy of Y ? Design a HuFman code for Y = ( X 1 ,X 2 ).(Hint: Y has 9 possible outcomes of the form ( x i ,x j ), each with probability p ( x i ) p ( x j ).) What is the expected length of this new HuFman code? (c) Is it useful to code over increasingly long vectors of independent random variables? 6. Assume that in a binary digital communication system, the signal component out of the correlator receiver is a i ( T ) = +1 or-1 V with equal probability. If the Gaussian noise at the correlator output has unit variance, ²nd the probability of bit error. Optional Problems: 1. If X and Y are independent and identically distributed with mean μ and variance σ 2 , ²nd E b ( X-Y ) 2 B . 1...
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This note was uploaded on 11/13/2011 for the course ECEN 455 taught by Professor Staff during the Spring '08 term at Texas A&M.

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