hw6-2011 - University of Illinois Fall 2011 ECE 563:...

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Unformatted text preview: University of Illinois Fall 2011 ECE 563: Homework 6 Issued: October 16th, 2011; Due: October 27th, 2011 1. Let C 1 be a code with codelengths l i = log 2 ( i ) and let C 2 be a code with codelengths l i = log 2 ( i 2 ), where i ∈ { 2 , 3 ,... } . Can C 1 and C 2 be prefix codes for a binary output alphabet? For a ternary output alphabet? If your answer to all the above questions is no, find the smallest power j such that l i = log 2 ( i j )’s represent lengths of a prefix code, with i > 1. 2. A prefix code C is called full if it loses its prefix property by adding any new codeword to it. A string x is called undecodable if it is impossible to construct a sequence of codewords such that x is a prefix of their concatenation. Show that the following three statements are equivalent: (a) C is full; (b) there is no undecodable string with respect to this code; (c) the codelengths of the code satisfy Kraft’s inequality with equality....
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This note was uploaded on 10/24/2011 for the course ELECTRICAL ECE 571 taught by Professor Kelly during the Spring '11 term at University of Illinois, Urbana Champaign.

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