Development of novel transform-based lossless compression schemes

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We have developed and analyzed two transformations for lossless compression: generalized radix permutation (GRP) and compression by substring enumeration (CSE). The GRP transform was proposed as a parametric generalization of the BWT of the block-sorting data compression algorithm. Our proposed extension can be applied to arbitrary parameter values and can transform a string in time linear in the string length. We then analyze the CSE algorithm, and propose encoding models that achieve asymptotic optimality for stationary ergodic sources and Markov sources of any order. We also establish a concrete way for efficient implementation of CSE. CSE often produces more codewords than necessary. In order to reduce such redundancy, we propose a method for computing the maximum length of the substrings that should be enumerated in CSE to uniquely identify the input string. As for an application of these transformations, we propose a practical secret sharing scheme for string data.