### An analysis of the Burrows—Wheeler transformAn analysis of the Burrows—Wheeler transform

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 Author Manzini, Giovanni Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2001 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Burrows—Wheeler transform ♦ Block sorting ♦ Move-to-front encoding ♦ Worst-case analysis of compression Abstract The Burrows—Wheeler Transform (also known as Block-Sorting) is at the base of compression algorithms that are the state of the art in lossless data compression. In this paper, we analyze two algorithms that use this technique. The first one is the original algorithm described by Burrows and Wheeler, which, despite its simplicity outperforms the Gzip compressor. The second one uses an additional run-length encoding step to improve compression. We prove that the compression ratio of both algorithms can be bounded in terms of the $\textit{k}th$ order empirical entropy of the input string for any $\textit{k}$ ≥ 0. We make no assumptions on the input and we obtain bounds which hold in the worst case that is for every possible input string. All previous results for Block-Sorting algorithms were concerned with the average compression ratio and have been established assuming that the input comes from a finite-order Markov source. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2001-05-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 48 Issue Number 3 Page Count 24 Starting Page 407 Ending Page 430

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Source: ACM Digital Library