hw9 - Problem 3 The code you constructed in Problem 2 can...

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ECE220 Signals and Information Spring 2008 Homework 8: Due Monday, April 28th, at 10:08pm Drop your homework in the collection box marked ”ECE220 Spring 2008, homework” , located on the second floor of Phillips at the south entrance to 219 Phillips. Print your name, NetId, and lab section in the top right corner on all pages. NOTE: This homework is based on lecture notes that can be found on Blackboard. Problem 1 Consider the following binary codes: letter code 1 code 2 code 3 code 4 A 0 0 00 00 B 1 11 01 01 C 01 01 10 1 (a) Which of the codes are prefix codes? Expalin. (b) Which of the codes are uniquely decodable? Explain. (c) How will the sequence 0111 be decoded by each of the codes? Problem 2 Consider the alphabet { A,B,C } with probabilities of occurence P = { 0 . 1 , 0 . 2 , 0 . 7 } . (a) Compute the entropy of the alphabet. (b) Construct a Hoffman code for this alphabet. (c) Calculate the average length of codewords in (b).
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Unformatted text preview: Problem 3 The code you constructed in Problem 2 can be improved by considering pairs oF letters. Assume that the source generating letters is memoryless. Thus the probability oF occurence, For example, oF the sequence AB is 0.02, which is the product oF probailities oF occurence oF A and oF B separately. (a) Construct a new alphabet consisting of all possible pairs of letters from Problem 1. (b) Compute the entropy of the alphabet. (c) Construct a HoFman code for this new alphabet. (d) Calculate the average length of codewords in (c). (e) De±ne the e²ciency of the code as the ratio of the entropy of the alphabet and the average length of codewords. Compare the e²ciency of the code from Problem 2 with the e²ciency of the code in (c). 2...
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