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Understanding Information Theory: Communication Systems and Encoding

Dive into the realm of information theory - analyzing flow of data, encoding symbols, noise interference, and error correction in communication systems. Learn about information entropy, efficient encoding, and quantifying information. Explore applications in telecommunications and compression.

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Understanding Information Theory: Communication Systems and Encoding

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  1. Information Theory Michael J. Watts http://mike.watts.net.nz

  2. Lecture Outline • What is information theory? • Communications Systems • Measuring Information and uncertainty • Information entropy and encoding

  3. What is Information Theory? • Area of applied mathematics • Concerned with the analysis of a “communications system”

  4. Components of Communications Systems • Source • Where the information is coming from • Encoder • Encodes the information and transmits it as a signal • Channel • Medium over which information is transmitted

  5. Components of Communications Systems • Noise • Random interference added to signal • Decoder • Receives the information and decodes it for the destination • Destination • What is receiving the information

  6. Information Theory • Information theory analyses the flow of information through these systems • How much information can go through it • How the information can be encoded • Must quantify information first

  7. Information Theory • Definitions of information • Data used to make a decision • Data that informs • Information tells you something you did not already know

  8. Quantity of Information • Assume we have a random variable X • X can have exactly N states • Each state has a probability P(n) • Probability of the state occurring determines its uncertainty • As P(n) approaches 0.5, uncertainty approaches 1

  9. Quantity of Information • High uncertainty == more information • The more uncertain an event is, the more information is conveyed when it occurs • Surprise! • Entropy is the total uncertainty over all variables • Total uncertainty of the system

  10. Encoding • Encoding is representing symbols as bits • Number of bits is proportional to number of symbols • Size of alphabet • Min. bits / symbol(N) = bits * uncertainty(N) • More certain == fewer bits • Efficient encoding == fewer average bits • Data compression

  11. Error Correction • Noise complicates things • Definition of noise • Error correcting codes account for noise • Correct a change in any one bit • Add bits to an encoding scheme • Additional bits represent the information • Hamming code • Used in CD's and elsewhere

  12. Summary • Information theory deals with the transmission and encoding of symbols (information) • Information is measured as how “surprising” a symbol is • Applications in telecommunications and compression • Noise can interfere with a signal • Error correction is needed

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