h5 - # 18 ECE 253a Digital Image Processing Pamela Cosman...

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Unformatted text preview: # 18 ECE 253a Digital Image Processing Pamela Cosman 11/17/10 HOMEWORK 5 Due Monday Nov 29 in class 1. Huffman coding In class weve talked about only binary Huffman codes, but one can use different output alphabets. For example, a ternary Huffman code is a code over an output alphabet with 3 symbols, which we could call a , b , and c . The design is done by combining, at each step, the three least probable symbols in the input alphabet, and assigning them the output symbols a , b and c . Consider a random variable X that takes six values with probabilities 0.5, 0.25, 0.1, 0.05, 0.05, 0.05. (a) Construct a binary Huffman code for this random variable. What is its average length? (b) Construct a quaternary Huffman code for this random variable. A quaternary code has 4 symbols in the output alphabet (call them a , b , c , and d ). What is the average length of the code? (c) One way to construct a binary code for the random variable is to start with a quaternary code and convert the symbols into binary using the mapping a 00, b 01, c 10, and d 11. What is the average length of the binary code for the random variable above constructed by this process? (d) For any random variable, X , let L H be the average length of the binary Huffman code for the random variable, and let L QB be the average length constructed by first building a quaternary Huffman code and converting it to binary. It can be shown thatbuilding a quaternary Huffman code and converting it to binary....
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h5 - # 18 ECE 253a Digital Image Processing Pamela Cosman...

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