lecture9 - Lecture Outline Source Encoding and Huffman...

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Lecture Outline Source Encoding and Huffman Coding Reading: Section 6.3.1. Part of 6.1 (pages 267-271) Material covered: 1. What is information? Example: M= {It rains today in Phoenix, It does not rain today in Phoenix} The fact that Phoenix rains for less than 30 days of the year implies there is not much information in this statement ( << 1 bit) Self-information of a message: If message m occurs with probability m p , then self information = m p 2 log - bits. Source Information (Source Entropy) = self information averaged over all messages m m m p p M H log ) ( - = Example : Entropy of “being rainy” in Phoenix 425 . 0 365 30 log 365 30 365 335 log 365 335 log ) ( 2 2 = - - = - = m m m p p M H bit Example : Entropy of English: M = English alphabet. If English letters are equally likely and memoryless (it is not!), then 7 . 4 26 1 log 26 1 26 log ) ( 2 = × - = - = m m m p p M H bits per letter Entropy of English = 2.6 bits/letter, found by a guessing game by Shannon. Example : Morse code (see table on page 2 of textbook) Frequent letters are assigned short codes.
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