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hw7_09 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering The Johns Hopkins University 520.137 Introduction to Electrical and Computer Engineering – Fall 2009 Homework Assignment VII Reading Assignment: Kuc Chapter 7 1. Let’s explore the encoding of a binary source with skewed statistics: P [ 1 ] = 1 8 and P [ 0 ] = 7 8 . (a) What is the entropy H of this bit-stream? (b) What is the average code-word length for the fixed-length code in this case? What is the average code-word length if we apply Huffman code directly? (c) One solution to this problem is to combine two consecutive binary symbols to form a new symbol. Find the probabilities of occurrence for the “new” symbols: P [ 00 ] , P [ 01 ] , P [ 10 ] , P [ 11 ]. (d) What is the entropy of the modified source in Part c ? How does it compare to the original entropy? (e) Construct the Huffman code for the modified source of Part c . Show the Huffman tree as well as the Huffman code table. (f) What is the average Huffman code-word length now and how does it compare to the two entropy figures computed earlier?
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