Universal filtering and prediction of individual sequences corrupted by noise

We address the problem of filtering and prediction of an individual binary sequence based on its noisy past, as an extension to [l]. The performance criterion investigated is the expected fraction of errors. We propose algorithms and compare their performance to that of the best finite state machine (FSM). We improve on previous results [l] by showing that optimum performance can be achieved by Lempel-Ziv-based estimation algorithms.