A Simpler Analysis of Burrows-Wheeler Based Compression.

In this paper we present a new technique for worst-case analysis of compression algorithms which are based on the Burrows-Wheeler Transform. We deal mainly with the algorithm purposed by Burrows and Wheeler in their first paper on the subject [6], called bw0. This algorithm consists of the following three steps: 1) Compute the Burrows-Wheeler transform of the text, 2) Convert the transform into a sequence of integers using the move-to-front algorithm, 3) Encode the integers using Arithmetic code or any order-0 encoding (possibly with run-length encoding). We prove a strong upper bound on the worst-case compression ratio of this algorithm. This bound is significantly better than bounds known to date and is obtained via simple analytical techniques. Specifically, we show that for any input string s, and μ> 1, the length of the compressed string is bounded by μ·s Hk(s) + log(ζ(μ)) ·s + gk where Hk is the k-th order empirical entropy, gk is a consta