Fast and Compact Prefix Codes

It is well-known that, given a probability distribution over n characters, in the worst case it takes ?(n logn) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for any ? with 0 1, it takes O(n 1 / c logn) bits to store a prefix code with expected codeword length at most c times the minimum. In both cases, our data structures allow us to encode and decode any character in O(1) time.

[1]  Travis Gagie,et al.  Dynamic asymmetric communication , 2005, Data Compression Conference (DCC'06).

[2]  E. F. Moore,et al.  Variable-length binary encodings , 1959 .

[3]  Travis Gagie,et al.  Large alphabets and incompressibility , 2005, Inf. Process. Lett..

[4]  Faith Ellen,et al.  Optimal Bounds for the Predecessor Problem and Related Problems , 2002, J. Comput. Syst. Sci..

[5]  Dafna Sheinwald.  On binary alphabetical codes , 1992, Data Compression Conference, 1992..

[6]  Gonzalo Navarro,et al.  Compressed representations of sequences and full-text indexes , 2007, TALG.

[7]  Alistair Moffat,et al.  On the implementation of minimum redundancy prefix codes , 1997, IEEE Trans. Commun..

[8]  Michael L. Fredman,et al.  Surpassing the Information Theoretic Bound with Fusion Trees , 1993, J. Comput. Syst. Sci..

[9]  Bruce M. Maggs,et al.  Protocols for Asymmetric Communication Channels , 2001, J. Comput. Syst. Sci..

[10]  Roberto Grossi,et al.  High-order entropy-compressed text indexes , 2003, SODA '03.

[11]  Eugene S. Schwartz,et al.  Generating a canonical prefix encoding , 1964, CACM.

[12]  Shmuel Tomi Klein,et al.  Skeleton Trees for the Efficient Decoding of Huffman Encoded Texts , 2000, Information Retrieval.

[13]  János Komlós,et al.  Storing a sparse table with O(1) worst case access time , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[14]  Travis Gagie,et al.  Compressing probability distributions , 2005, Inf. Process. Lett..

[15]  Ruy Luiz Milidiú,et al.  Bounding the Inefficiency of Length-Restricted Prefix Codes , 2001, Algorithmica.

[16]  Travis Gagie,et al.  Worst-Case Optimal Adaptive Prefix Coding , 2008, WADS.

[17]  Gyula O. H. Katona,et al.  Huffman codes and self-information , 1976, IEEE Trans. Inf. Theory.

[18]  Marek Karpinski,et al.  A Fast Algorithm for Adaptive Prefix Coding , 2006, 2006 IEEE International Symposium on Information Theory.

[19]  Narao Nakatsu,et al.  Bounds on the redundancy of binary alphabetical codes , 1991, IEEE Trans. Inf. Theory.

[20]  J. Ian Munro,et al.  Succinct Representation of Balanced Parentheses and Static Trees , 2002, SIAM J. Comput..