Download presentation

Presentation is loading. Please wait.

1
**Entropy and Information Theory**

Aida Austin 4/24/2009

2
**Overview What is information theory? Random variables and entropy**

Entropy in information theory Applications Compression Data Transmission

3
**Information Theory Developed in 1948 by Claude**

E. Shannon at Bell Laboratories Introduced in “A Mathematical Theory of Communication'' Goal: Efficient transmission of information over a noisy network Defines fundamental limits on compression needed for reliable data communication Claude E. Shannon

4
**Random Variables A random variable is a function.**

Assigns numerical values to all possible outcomes (events) Example: A fair coin is tossed. Let X represent a random variable. Possible outcomes:

5
**Entropy in Information Theory**

Entropy is the measure of the average information content missing from a set of data when the value of the random variable is not known. Helps determine the average number of bits needed for storage or communication of a signal. As the number of possible outcomes for a random variable increases, entropy increases. As entropy increases, information decreases Example: MP3 sampled at 128 kbps has higher entropy rate than 320 kbps MP3

6
**Applications Data Compression MP3 (lossy) JPEG (lossy) ZIP (lossless)**

Cryptography Encryption Decryption Signal Transmission Across a Network Text Message Cell phone

7
**Data Compression “Shrinks” the size of a signal/file/etc. to**

reduce cost of storage and transmission Smaller data size reduces the possible outcomes of the associated random variables, thus decreasing the entropy of the data. Entropy - minimum number of bits needed to encode with a lossless compression. Lossless (no data lost) if the rate of compression = entropy rate

8
**Signal/Data Transmission**

Channel coding reduces bit error and bit loss due to noise in a network. As entropy increases, the likelihood of valuable information transmitted decreases. Example: Consider a signal composed of random variables. We may know the probability of certain values being transmitted, but we do not know the exact values will be received unless the transmission rate = entropy rate.

9
Questions?

10
**Resources http://www.gap-system.org/~history/PictDisplay/Shannon.html**

Similar presentations

OK

Coding Theory Efficient and Reliable Transfer of Information

Coding Theory Efficient and Reliable Transfer of Information

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on media research institute Free download ppt on data handling in maths for class 8 Ppt on weather and climate for grade 5 Ppt on plane table surveying Ppt on limits and derivatives tutorial Ppt on planets in the solar system Ppt on printed circuit board Ppt on bluetooth hacking downloads Ppt on mindset change Free ppt on layers of atmosphere