Mathematical Study on Information Transform for Data Compression and Information Security

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The theme of this research project is on a study of novel transform of information for the efficient data compression and the secure data transmission.With respect to the information transform for data compression, we have first provided some interesting properties of the fix-free cock. Next, we need an efficient expression of the ordered tree for the date compression .and storage/ Therefore, we analyzed the performance of coding of ordered trees, and established the optimal codeword length function. Furthermore, we had studied the Bernoulli splitting process with biased probabilities, and gave asymptotically the expected branch number and depth of the trie by using the Mellin transform. Here, we encounter the entropy function in the residue of the related generating function. This phenomenon could be found in a case where the generalized amplitudes and frequencies are in the relation of multinomial coefficients and products of probabilities, respectively, in the generalized harmonic s … More eries. Furthermore, we proposed the Catalan code for integers by a combination of the pre-order coding and the enumerative coding of binary trees, and compared the performance of the code with that of Elias omega code.The transform for secure data transmission is studied from two aspects, that is, from the error-correcting coding and the data security points of views. Specifically, by introducing the theoretical framework of protection of data suffered from the compound errors, that is, the mixture of random errors and burst errors, we gave a new efficient decoding method of iterated codes for the compound error correction.On the other hand, for the study of data security we concentrated on synthesizing a new method which can protect against the attack of removing the watermarks. Here, we considered the relation to the error control code, and investigated the various kind of attacks. We have realized a method having both of the convenience for the user and of the strength against the collision and repeat attack. Less