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Information & Coding Theory

Channel (errors). Information & Coding Theory. Information. Information. . Symbols s 1 ,…,s q. Encoding Source/Channel. signal. Decoding Channel/Source. Source. signal + noise. Symbols s 1 ,…,s q. Destin- ation. Noise. Example : Morse Code. telegraph wire. transmitter.

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Information & Coding Theory

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  1. Channel (errors) Information & Coding Theory Information Information  Symbols s1,…,sq Encoding Source/Channel signal Decoding Channel/Source Source signal + noise Symbols s1,…,sq Destin- ation Noise Example: Morse Code telegraph wire transmitter receiver Encoding Decoding dots, dashes spaces ∙ ─ _ A, …, Z A, …, Z keyer recognizer shortwave radio Example: ASCII Code seven-bit blocks Telephone wire seven-bit blocks keyboard modem modem terminal screen Character character

  2. Information Source – the symbols are undefined, and the “meaning” of the information being sent is not dealt with – only an abstract measure of the “amount” or “quantity. • Examples • text of various forms – reports, papers, memos, books, scientific data (numbers) • pictures of various forms – diagrams, art, photographic images, scientific data (e.g. from satellites) • sound of various forms – music, speech, noises, recorded sound, radio • animation of various forms – moving pictures, film, video tape, video camera, television • equations representing mathematical ideas or algorithms – two textual representation systems with graphical output: Tex & Mathematica

  3. Analog vs. Digital sound (amplitude versus time) picture (amplitude versus space) Examples of (apparently) analog sources of information: pressure: + →  granularity – molecular intensity: [0, 1]  [0, 1] → + granularity – crystalline microphone → tape recorder → speaker lenses → film (negative) → print (positive) Examples of (apparently) digital sources of information: Text a′ ? B sequences of characters different languages have different characters (often the typeface or writing style conveys additional meaning or information)

  4. Examples of composites (some digital and analog) • color printing (as opposed to photography) • television intensity unquantized, temporally discrete • color spatially discrete spatially discrete (dots) spectrum discrete (color separation) intensity discrete (dot or no dot) random signal contains largest amount of information

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