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Following are some of the major results obtained in the area of Data Compression. Have optimized Fano encoding by storing the probabilities in a Binary Search Tree, and updating them using adaptive Conditional Rotations (Proc. ISCIS 2007, Int. J. Comm. Sys. 2008). Have used a stochastic learning-based weak estimation strategy to enhance data compression when the distribution of the data in the files is non-stationary (Proc. ADVIS 2004, IEEE T:SMC 2006). Have devised a greedy adaptive version of Fano's method, which is very important in communications and networking applications. This scheme is adaptive and simultaneously uses less space than other methods that require complex tree structures. The compression efficiency of the scheme is nearly optimal, and it requires about one-sixth of the space used by the adaptive Huffman coding scheme (Proc. IEEE-Aerospace 2002, Inf. Sci. 2006). Have proposed an enhanced static encoding algorithm that implements Fano coding. The importance of this scheme is that it allows the user to obtain canonical codes, which are desirable since they allow extremely fast decoding and use less space in a straightforward manner (Proc. IEEE-SMC 2001 and IP & M 2004).