On variants of block-sorting compression using context from both the left and right

The block-sorting text compression algorithm can be viewed as associating a context with each character to be compressed, and then sorting the characters on their contexts. Normally, the context associated with each character is the string to the left of the character. Recently, Ratushnyak suggested that it might be possible instead to build a context by interleaving characters taken alternately from the left and right. We show that transformations of this type are not reversible in general unless additional information is supplied. Further, the amount of additional information needed to reverse the transformation is necessarily large, and so such transformations are unlikely to be of interest as part of a compression algorithm.