Redundancy estimates for the Lempel-Ziv algorithm of data compression
Discrete Applied Mathematics
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Hi-index | 754.84 |
The fixed-database version of the Lempel-Ziv algorithm closely resembles many versions that appear in practice. We ascertain several key asymptotic properties of the algorithm as applied to sources with finite memory. First, we determine that for a dictionary of size n, the algorithm achieves a redundancy ρn=Hlog log n/log n+0(log log n/log n) where H is the entropy of the process. This is the first, nontrivial, lower bound on any Lempel-Ziv-type compression scheme. We then find the limiting distribution and all moments of the lengths of the phrases by comparing them to a random-walk-like variable with well-known behavior