ELEC1010 assignment4.pdf

# ELEC1010 assignment4.pdf - Name Fung Chun Sing 1 1 Entropy...

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Name: Fung Chun Sing 20200230 1. 1) Entropy = 7 280 log 280 7 + 5 280 log 280 5 + 23 280 log 280 23 + 245 280 log 280 245 = 0.701499642 bits/symbol By Shannon’s entropy formula , the minimum is 0.701 bits/symbol. 2) i) Number of Symbols Symbol Set Possible Codewords 4 {20, 30, 40 ,60} 00, 01, 10, 11 ii) Average = 7 280 *2 + 5 280 *2+ 23 280 *2+ 245 280 *2 = 2 bits/symbol 3) i) Four symbols with probabilities: 20: 7 280 , 30: 5 280 , 40: 23 280 , 60: 245 280 Grade (Symbol) Codewords 20 110 30 111 40 10 60 0 ii) Avg. bit/sym = 7 280 *3 + 5 280 *3+ 23 280 *2+ 245 280 *1 = 1.168 bits

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Name: Fung Chun Sing 20200230 2. 1) Input bit = 10111101110001001010 Encoded bit sequence = 10111 11011 11000 01001 10100 2) Encoded = 11101000011010101001 = 11101 00001 10101 01001 We can see that only the second(00001) and the third block(10101) have odd
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