On asymptotic optimality of a sliding window variation of Lempel-Ziv codes

The authors modify the algorithm of Z. Ziv and A. Lempel (1977), LZ77, restricting pointers to start only at the boundary of a previously parsed phrase in a window. Although the number of parsed phrases should increase more than those in LZ77, the number of bits needed to encoded pointers is considerably reduced since the number of possible positions to be encoded is much smaller. It is shown that, for any stationary finite state source, the modified LZ77 code is asymptotically optimal with the convergence rate O(log log M/log M), where M is the size of a sliding window