Improvements to the Burrows-Wheeler Compression Algorithm: After BWT Stages

The lossless Burrows-Wheeler Compression Algorithm has received considerable attention over recent years for both its simplicity and effectiveness. It is based on a permutation of the input sequence − the Burrows-Wheeler Transform − which groups symbols with a similar context close together. In the original version, this permutation was followed by a Move-To-Front transformation and a final entropy coding stage. Later versions used different algorithms which come after the Burrows-Wheeler Transform, since the stages after the BurrowsWheeler Transform have a significant influence on the compression rate. This article describes improved algorithms for the run length encoding, inversion frequencies and weighted frequency count stages that follow the Burrows-Wheeler Transform. Results for compression rates are presented for different variations of the algorithm together with compression and decompression times. Finally, an implementation with a compression rate of 2.238 bps on the Calgary Corpus is introduced, which is the best result published in this field to date.