Generalization of the BWT transformation and inversion ranks

Summary form only given. We expand the theoretical foundations of LPSA (lexical permutation sorting algorithm) (see Arnavut, Z., and Magliveras, S.S., The Computer Journal, vol.40, no.5, pp.292-5, 1997) from permutations to multiset permutations (data strings) and give the general theory behind the BWT combinatorially. We then show the information theoretic relationship between interval ranks and canonical sorting permutations. Finally, we explore the relationship between inversion ranks and recency ranks and present improved compression results over other BSC (binary symmetric channel) coders, such as Bzip and Szip.