This preview shows page 1. Sign up to view the full content.
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....
View
Full
Document
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.
 Spring '11
 Kelly

Click to edit the document details