Inversion Coding

A Comparison of Methods for Redundancy Reduction in Recurrence Time Coding

“…As long as the treatment of initial occurrences of symbols is properly defined, the original string x n 1 is unambiguously recovered from the sequence of r(1), r (2), r(3), . .…”

“…According to (2), (3), and (4), we have three different representations of the recurrence time coding. These representations produce the same multiset of integers, but have different orders of elements.…”

“…1, after decoding all a's, we can use a list of quantities which are obtained by removing the contribution of symbol a from sm(b), instead of the original list {sm(b)} itself, to recover all the positions of symbol b. That quantity is called an inversion rank [2] (also inversion frequency), or ordered recurrence time (ort) [9], which is now defined formally.…”

“…If we encode the number of distinct symbols occurring in that interval, we obtain the MTF scheme [3], [7]. Another improvement of recurrence time coding, which counts the number of alphabetically bigger or smaller symbols in the interval, is also known [2], [9].…”

“…The three schemes have already been known, and actually applied to the block-sorting compression algorithm [4] as its second step component [2], [6]. However, they have not been analyzed and compared from the viewpoint that they can be thought of as different attempts to realize redundancy reduction in recurrence time coding.…”