On Optimality of Variants of the Block Sorting Compression

the permuted string into many parts and encodes symbols using different arithmetic codes by the parts. Each part has symbols whose contexts are the same. If the permutation is random, the scheme is asymptotically optimal for any finite-order Markov source. The permutation in the BWT is not completely random. For example, if three or more contexts are the same and they overlap each other, symbols following them appear in the permuted string in original order or its reversal. However, we conjecture that the permuted string is memoryless and our schemes work. Reference