A locally adaptive data compression scheme
Communications of the ACM
Elements of information theory
Elements of information theory
Arithmetic coding for data compression
Communications of the ACM
ACM Transactions on Information Systems (TOIS)
Compression of Low Entropy Strings with Lempel--Ziv Algorithms
SIAM Journal on Computing
An analysis of the Burrows—Wheeler transform
Journal of the ACM (JACM)
Second step algorithms in the Burrows-Wheeler compression algorithm
Software—Practice & Experience
Redundancy of the Lempel-Ziv-Welch Code
DCC '97 Proceedings of the Conference on Data Compression
Boosting textual compression in optimal linear time
Journal of the ACM (JACM)
The engineering of a compression boosting library: theory vs practice in BWT compression
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A simpler analysis of Burrows–Wheeler-based compression
Theoretical Computer Science
Universal lossless source coding with the Burrows Wheeler transform
IEEE Transactions on Information Theory
Variations on a theme by Huffman
IEEE Transactions on Information Theory
Move-to-Front, Distance Coding, and Inversion Frequencies revisited
Theoretical Computer Science
A new compression scheme for secure transmission
International Journal of Automation and Computing
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We present a technique for proving lower bounds on the compression ratio of algorithms which are based on the Burrows-Wheeler Transform (BWT). We study three well known BWT-based compressors: the original algorithm suggested by Burrows and Wheeler; BWT with distance coding; and BWT with run-length encoding. For each compressor, we show a Markov source such that for asymptotically-large text generated by the source, the compression ratio divided by the entropy of the source is a constant greater than 1. This constant is 2 - ε, 1.26, and 1.29, for each of the three compressors respectively. Our technique is robust, and can be used to prove similar claims for most BWT-based compressors (with a few notable exceptions). This stands in contrast to statistical compressors and Lempel-Ziv-style dictionary compressors, which are long known to be optimal, in the sense that for any Markov source, the compression ratio divided by the entropy of the source asymptotically tends to 1. We experimentally corroborate our theoretical bounds. Furthermore, we compare BWT-based compressors to other compressors and show that for "realistic" Markov sources they indeed perform bad and often worse than other compressors. This is in contrast with the well known fact that on English text, BWT-based compressors are superior to many other types of compressors.