Summary: The Burrows-Wheeler Compression (BWC) described by Burrows and Wheeler has received considerable attention. An essential part of BWC schemes is the Move-to-Front coder (recency ranking). In this paper we introduce a different coding (ranking) scheme, the inversion coder. We prove the information theoretic relationship between interval ranks and canonical sorting permutations. We also introduce a faster and more memory efficient-algorithm for inversion ranks. Finally, we explore the relationship between inversion ranks and recency ranks and show that inversion coding is superior to interval ranking as well as recency ranking.