On the redundancy of the fixed-database Lempel-Ziv algorithm for /spl phi/-mixing sources

The redundancy problem of the fixed-database Lempel-Ziv (1977) algorithm is considered. It is demonstrated that for a class of /spl phi/-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.