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Lecture 4

# SFWRENG 4J03 Lecture 4: Lecture 2016-02-02 Premium

5 Pages
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Department
Software Engineering
Course Code
SFWRENG 4J03
Professor
Rong Zheng

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Description
Lecture 2016-02-02 Author: Kemal Ahmed Instructor: Dr. Gowri Krishnasamy Course: SFWR ENG 4J03 Math objects made using MathType. Table of Contents Huffman Coding ............................................................................................................................. 1 enciphering.................................................................................................................................. 1 Algorithm.................................................................................................................................... 2 e.g. 1) .......................................................................................................................................... 2 Pulse Code Modulation................................................................................................................... 3 Pulse Code Modulation............................................................................................................... 3 Regenerative repeater.............................................................................................................. 3 Pulse Width Modulation......................................................................................................... 4 Pulse Position Modulation...................................................................................................... 4 e.g. 2) ...................................................................................................................................... 4 RR Cont .................................................................................................................................. 4 Sampling..................................................................................................................................... 4 e.g. 4) ...................................................................................................................................... 5 Huffman Coding Encipher: encoding → transmission decipher:  decoding → receiving  Prefix Property: any code should be uniquely decipherable. Complete code-word should become property of the new code? No complete code word can be a prefix at another code word enciphering m 1 0 → m 1 m 2 0 1 → m 2 Page 1 of 5 m → 0 11 → m 3 3 Highest probably messages will be given least number of bits and vice versa Algorithm 1. Arrange the messages according to order of decreasing probability 2. Consider the last 2 messages in the ensemble. Assign a 0 & 1 to those 2 messages 3. Add the probabilities of the last 2 messages 4. Arrange the messages in the order of decreasing probability. Keep the newest calculated probabilities on top if tie. 5. Go to step 2 until you only have 2 messages 6. Calculate efficiency e.g. 1) Calculate a Huffman code for the following message ensemble with probabilities: 0.1, 0.3, 0.16, 0.14, 0.13, 0.17 Ensure total probability = 1 n 1 P k1 k  0.10.30.160.140.130.17 Messages Probability II III IV V M 1 0.3 0.3 0.3 0.4 0.6 ← 0 M 2 0.17 0.23 0.3 0.3 ← 0 0.4 ← 1 M 3 0.16 0.17 0.23 ← 0 0.3 ← 1 M 4 0.14 0.
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