Abstract
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.
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A preliminary version of this paper appeared in the Proceedings of the 2006 IEEE International Symposium on Information Theory (ISIT 2006).
M. Karpinski’s work partially supported by a DFG grant, Max-Planck Research Prize, and IST grant 14036 (RAND-APX).
Y. Nekrich’s work partially supported by IST grant 14036 (RAND-APX).
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Karpinski, M., Nekrich, Y. A Fast Algorithm for Adaptive Prefix Coding. Algorithmica 55, 29–41 (2009). https://doi.org/10.1007/s00453-007-9140-4
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DOI: https://doi.org/10.1007/s00453-007-9140-4