Class-5-12-10

# Class-5-12-10 - BINARY TREES next Morse Code 7 Problem on...

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Morse Code Problem on Morse code: a) The integer following each code gives number of time units needed to send that code b) Assume letters are produced by a wheel with english probabilities c) compute the expected time to send a letter in Morse code d) Compare this with the entropy of the random letter produced by the english wheel 7 next
Solution of the Morse code problem english = {73, 9, 30, 44, 130, 28, 16, 35, 74, 2, 3, 35, 25, 78, 74, 27, 3, 77, 63, 93, 27, 13, 16, 5, 19, 1} english letter frequencies morse = {5, 7, 8, 6, 3, 7, 7, 6, 4, 9, 7, 7, 6, 5, 8, 8, 9, 6, 5, 4, 6, 7, 7, 8, 9, 8} morse code lengths Since the english letters frequencies add up to 1000 we take the scalar product of english and morse and divide by 1000 (english , morse) /1000 = 5.528 On the other hand computing the entropy of english by the formula Gives entropy of english letter = 4.1621 Take the letter frequencies of the emancipation proclamation eman = {306, 42, 94, 162, 457, 110, 46, 175, 235, 11, 10, 130, 61, 277, 249, 68, 2,

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## This note was uploaded on 09/22/2010 for the course MATH MATH187 taught by Professor Math187 during the Spring '10 term at UCSD.

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Class-5-12-10 - BINARY TREES next Morse Code 7 Problem on...

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