The Imaginary Sliding Window As a New Data Structure for Adaptive Algorithms

Abstract.1 The scheme of the sliding window is known in Information Theory, Computer Science, the problem of predicting and in stastistics. Let a source with unknown statistics generate some word . . . x-1x0x1x2 . . . in some alphabet A. For every moment t, t = . . . -1, 0, 1, . . ., one stores the word ("window") xt-wxt-w+1 . . . xt-1 where w,w 1, is called "window length". In the theory of universal coding, the code of the xt depends on source ststistics estimated by the window, in the problem of predicting, each letter xt is predicted using information of the window, etc. After that the letter xt is included in the window on the right, while xt-w is removed from the window. It is the sliding window scheme. This scheme has two merits: it allows one i) to estimate the source statistics quite precisely and ii) to adapt the code in case of a change in the source' statistics. However this scheme has a defect, namely, the necessity to store the window (i.e. the w...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Boris Ryabko
• Keywords: Computer Science, CORR 2008, Education, Sliding Window, Window