Improved redundancy of a version of the Lempel-Ziv algorithm

Abstract

The fixed-database Lempel-Ziv algorithm (FDLZ) closely resembles practical versions of the LZ algorithm that are widely in use. Bender and Wolf (1991) suggested a variant of LZ which empirically appears to perform well. We suggest a finite memory version of their scheme, and show that it has redundancy /spl rho//sub n/=O(1/log n) where n is the memory size. We are concerned with a data source which is a stationary, finite-memory random sequence that takes values in an alphabet of finite size A. The data source can be losslessly encoded using (H+/spl rho//sub n/) bits per source symbol, where n is a measure of the complexity of the code, and /spl rho//sub n//spl rarr/0, as n/spl rarr//spl infin/. The LZ algorithm is a universal procedure (which does not depend on the source statistics) for encoding the source at a rate close to the entropy.<>