Generalized Kraft Inequality and Arithmetic Coding

Algorithms for encoding and decoding finite strings over a finite alphabet are described. The coding operations are arithmetic involving rational numbers li as parameters such that Zi2"i 5 2". This coding technique requires no blocking, and the per-symbol length of the encoded string approaches the associated entropy within E . The coding speed is comparable to that of conventional coding methods. Introduction The optimal conventional instantaneous Huffman code [ 11 for an independent information source with symbol probabilities ( p , , . . ., p , ) may be viewed as a solution to the integer programming problem: Find m natural numbers li as lengths of binary code words such that Cipil, is minimized under the constraining Kraft inequality