Arithmetic Coding

• Huffman coding works well for larger alphabets and gets to within one bit of the entropy lower bound. Can we do better. Yes

• Basic idea in arithmetic coding:

  • represent each string x of length n by an interval [l,r) in [0,1).
  • The width r-l of the interval [l,r) represents the probability of x occurring.
  • The interval [l,r) can itself be represented by any number, called a tag, within the half open interval.
  • The k significant bits of the tag .t1t2t3... is the code of x. That is, . .t1t2t3...tk000... is in the interval [l,r).

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