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What is the relationship between information theory and Coding theory? - Quora
basically:
- finite vs. asymptotic
- combinatorial vs. probabilistic (lotsa overlap their)
- worst-case (Hamming) vs. distributional (Shannon)

Information and coding theory most often appear together in the subject of error correction over noisy channels. Historically, they were born at almost exactly the same time - both Richard Hamming and Claude Shannon were working at Bell Labs when this happened. Information theory tends to heavily use tools from probability theory (together with an "asymptotic" way of thinking about the world), while traditional "algebraic" coding theory tends to employ mathematics that are much more finite sequence length/combinatorial in nature, including linear algebra over Galois Fields. The emergence in the late 90s and first decade of 2000 of codes over graphs blurred this distinction though, as code classes such as low density parity check codes employ both asymptotic analysis and random code selection techniques which have counterparts in information theory.

They do not subsume each other. Information theory touches on many other aspects that coding theory does not, and vice-versa. Information theory also touches on compression (lossy & lossless), statistics (e.g. large deviations), modeling (e.g. Minimum Description Length). Coding theory pays a lot of attention to sphere packing and coverings for finite length sequences - information theory addresses these problems (channel & lossy source coding) only in an asymptotic/approximate sense.
q-n-a  qra  math  acm  tcs  information-theory  coding-theory  big-picture  comparison  confusion  explanation  linear-algebra  polynomials  limits  finiteness  math.CO  hi-order-bits  synthesis  probability  bits  hamming  shannon  intricacy  nibble  s:null  signal-noise 
february 2017 by nhaliday
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