MIT16_36s09_lec05

MIT16_36s09_lec05 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 16.36 Communication Systems Engineering Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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16.36: Communication Systems Engineering Lecture 5: Source Coding Eytan Modiano Eytan Modiano Slide 1
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Source coding Source Encode Channel Alphabet Alphabet {a 1 ..a N } {c 1 ..c N } Source symbols Letters of alphabet, ASCII symbols, English dictionary, etc. .. Quantized voice Channel symbols In general can have an arbitrary number of channel symbols Typically {0,1} for a binary channel Objectives of source coding Unique decodability Compression Encode the alphabet using the smallest average number of channel symbols Eytan Modiano Slide 2
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Compression Lossless compression Enables error free decoding Unique decodability without ambiguity Lossy compression Code may not be uniquely decodable, but with very high probability can be decoded correctly Eytan Modiano Slide 3
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Prefix (free) codes A prefix code is a code in which no codeword is a prefix of any other codeword Prefix codes are uniquely decodable Prefix codes are instantaneously decodable The following important inequality applies to prefix codes and in general to all uniquely decodable codes Kraft Inequality Let n 1 …n k be the lengths of codewords in a prefix (or any Uniquely decodable) code. Then, 2 ! n i i = 1 k " # 1 Eytan Modiano Slide 4
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Proof of Kraft Inequality Proof only for prefix codes Can be extended for all uniquely decodable codes Map codewords onto a binary tree Codewords must be leaves on the tree A codeword of length n i is a leaf at depth n i Let n k n k-1 n 1 depth of tree = n k In a binary tree of depth n k , up to 2 nk leaves are possible (if all leaves
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This note was uploaded on 11/07/2011 for the course AERO 16.38 taught by Professor Alexandremegretski during the Spring '09 term at MIT.

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MIT16_36s09_lec05 - MIT OpenCourseWare http:/ocw.mit.edu...

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