On Families of New Adaptive Compression Algorithms Suitable for Time-varying Source Data Luis Rueda 1⋆ and B. John Oommen 2⋆⋆ 1 School of Computer Science, University of Windsor 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canada. E-mail: lrueda@uwindsor.ca 2 School of Computer Science, Carleton University 1125 Colonel By Dr., Ottawa, ON, K1S 5B6, Canada. E-mail: oommen@scs.carleton.ca Abstract. In this paper, we introduce a new approach to adaptive coding which utilizes Stochastic Learning-based Weak Estimation (SLWE) techniques to adap- tively update the probabilities of the source symbols. We present the correspond- ing encoding and decoding algorithms, as well as the details of the probability updating mechanisms. Once these probabilities are estimated, they can be used in a variety of data encoding schemes, and we have demonstrated this, in particu- lar, for the adaptive Fano scheme and and an adaptive entropy-based scheme that resembles the well-known arithmetic coding. We include empirical results using the latter adaptive schemes on real-life files that possess a fair degree of non- stationarity. As opposed to higher-order statistical models, our schemes require linear space complexity, and compress with nearly 10% better efficiency than the traditional adaptive coding methods. 1 Introduction The problem that we address in this paper is the following. We are given an input sequence, X = x(1) ...x(M ), where each input symbol, x(i), is drawn from a source alphabet, S = {s i ,...,s m }, whose probabilities are P =[p 1 ,...,p m ] T . The encoding process is rendered by transforming X into an output sequence, Y = y(1) ...y(R), where each output symbol, y(i), is drawn from a code alphabet, A = {a 1 ,...,a r }. The intent of the exercise is to determine an encoding scheme that minimizes the size of Y , in such a way that X is completely recovered by the decompression process. The encoding process is rendered adaptive, and thus, the data is encoded by performing a single pass. This is carried out by assuming that P =[p 1 ,...,p m ] T is unknown, as opposed to the static coding algorithms which require two passes – the first to learn the probabilities, and the second to accomplish the encoding. Adaptive coding is the best choice in many applications that require on-line compression such as in communication networks, LANs, internet applications, e-mail, ftp, e-commerce, and digital television. ⋆ Member of the IEEE. Partially supported by NSERC, the Natural Science and Engineering Research Council of Canada. ⋆⋆ Fellow of the IEEE. Partially supported by NSERC, the Natural Science and Engineering Re- search Council of Canada.