Variable-to-fixed length codes for predictable sources

A number of papers have investigated the compression obtained by some well-known lossless data compression algorithms in the limit as the dictionary size approaches infinity. Using a very detailed analysis of the Tunstall (1967) code as an example, we demonstrate that asymptotic analyses can fail to provide the performance of an algorithm in the important case of a predictable source with a small to moderate dictionary size.

[1]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[2]  Marcelo J. Weinberger,et al.  Upper bounds on the probability of sequences emitted by finite-state sources and on the redundancy of the Lempel-Ziv algorithm , 1992, IEEE Trans. Inf. Theory.

[3]  Aaron D. Wyner,et al.  Improved redundancy of a version of the Lempel-Ziv algorithm , 1995, IEEE Trans. Inf. Theory.

[4]  Frans M. J. Willems,et al.  Variable to fixed-length codes for Markov sources , 1987, IEEE Trans. Inf. Theory.

[5]  Serap A. Savari,et al.  Redundancy of the Lempel-Ziv incremental parsing rule , 1997, IEEE Trans. Inf. Theory.

[6]  Marcelo Weinberger,et al.  Upper Bounds On The Probability Of Sequences Emitted By Finite-state Sources And On The Redundancy Of The Lempel-Ziv Algorithm , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[7]  Peter Elias,et al.  Predictive coding-I , 1955, IRE Trans. Inf. Theory.

[8]  Wojciech Szpankowski,et al.  A Generalized Suffix Tree and its (Un)expected Asymptotic Behaviors , 1993, SIAM J. Comput..

[9]  Abraham Lempel,et al.  Compression of individual sequences via variable-rate coding , 1978, IEEE Trans. Inf. Theory.

[10]  Peter Elias,et al.  Predictive coding-II , 1955, IRE Trans. Inf. Theory.

[11]  Brian Parker Tunstall,et al.  Synthesis of noiseless compression codes , 1967 .

[12]  Wojciech Szpankowski,et al.  Asymptotic properties of data compression and suffix trees , 1993, IEEE Trans. Inf. Theory.

[13]  Frederick Jelinek,et al.  Algorithms for Source Coding , 1975 .

[14]  Serap A. Savari,et al.  Generalized Tunstall codes for sources with memory , 1997, IEEE Trans. Inf. Theory.

[15]  Abraham J. Wyner.  The redundancy and distribution of the phrase lengths of the fixed-database Lempel-Ziv algorithm , 1997, IEEE Trans. Inf. Theory.

[16]  Serap A. Savari,et al.  Redundancy of the Lempel-Ziv String Matching Code , 1998, IEEE Trans. Inf. Theory.

[17]  Guy Louchard,et al.  Average redundancy rate of the Lempel-Ziv code , 1996, Proceedings of Data Compression Conference - DCC '96.

[18]  S. Savari,et al.  Variable-to-fixed length codes and the conservation of entropy , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.