A Fast Algorithm for Adaptive Prefix Coding

In this paper we present a new algorithm for adaptive prefix coding. Our algorithm encodes a text S of m symbols in O(m) time, i.e., in O(1) amortized time per symbol. The length of the encoded string is bounded above by (H+1)m+O(nlog 2 m) bits where n is the alphabet size and H is the entropy. This is the first algorithm that adaptively encodes a text in O(m) time and achieves an almost optimal bound on the encoding length in the worst case. Besides that, our algorithm does not depend on an explicit code tree traversal.