hw4 - ECE320 Homework 4 Cornell University Spring 2006...

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ECE320 Homework 4 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the end of lecture on Tuesday, 28 February. Use only your assigned three-digit code and not your name. Throughout, give reasons for your answers. 1. (a) Generate a prefix code C containing 6 codewords. (b) Sketch a binary tree representation for the code of (a). (c) Consider the code with the three codewords 10 , 1011 , 10011. Is this a prefix code? (d) Sketch a binary tree representation for the code of (c). (e) Is the code of (c) uniquely decodable? 2. (a) Is there a uniquely decodable code having the codeword lengths 1 , 3 , 3 , 4 , 4 , 4? (b) Is there a prefix code having the lengths of (a)? (c) Is there a prefix code having the lengths 2 , 2 , 3 , 3 , 3 , 3 , 4? 3. We wish to construct a uniquely decodable code for the values of a random variable X described by P ( X = - 1) = . 2 , P ( X = 0) = . 2 , P ( X = 4) = . 1 , P ( X = 5) = . 25 , P ( X = 7) = . 25 .
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Unformatted text preview: (a) What is EX ? (b) What is the minimum number of codewords that we need? (c) Provide good lower and upper bounds to the minimum expected length of a code for the values of X . 4. (a) Construct a Huffman code for the values of X specified in Problem 3. (b) What is the expected code word length for this code? 5. (a) Plot the entropy function H as a function of 0 ≤ p ≤ 1 when the random variable X has only two possible outcomes, the first of which occurs with probability p . (b) For what value of p is the entropy H a maximum? 6. (a) Let the domain of a system S delay=1 consist of the functions { e-α | t | : α ≥ } . What is the system response to an input with α = 0? What is the codomain of this system? (b) What is the codomain of the system S time=2 when the domain is given in (a)? 1...
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  • Spring '06
  • FINE
  • Prefix code, binary tree representation, uniquely decodable code

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