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On the redundancy of the fixed-database Lempel-Ziv algorithm for φ-mixing sources

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2 Author(s)
En-hui Yang ; Dept. of Math., Nankai Univ., Tianjin, China ; J. C. Kieffer

The redundancy problem of the fixed-database Lempel-Ziv (1977) algorithm is considered. It is demonstrated that for a class of φ-mixing sources which includes Markov sources, unifilar sources, and finite-state sources as special cases, the redundancy of the fixed-database Lempel-Ziv algorithm with database size n is lower-bounded by H(loglogn)/logn+O((logloglogn)/logn) and upper-bounded by 2H(loglogn)/logn+O((logloglogn)/logn) where H is the entropy rate of the source. The method of proof is new and uses the concept of variable-length to variable-length codes

Published in:

IEEE Transactions on Information Theory  (Volume:43 ,  Issue: 4 )