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 A in [0,1).
  • The width of the interval A represents the probability of x occurring.
  • The interval A can itself be represented by any number, called a tag, within the half open interval.
  • The significant bits of the tag is the code of x.

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