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by Istituto Di, Matematica Computazionale, Giovanni Manzini
http://matcomp1.imc.pi.cnr.it/~manzini/tr-99-13/tr9913.us.ps.gz
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Abstract:
The Burrows-Wheeler Transform (also known as Block-Sorting) is at the base of compression algorithms which are the state of the art in lossless data compression. In this paper we analyze two algorithms which 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 k-th order empirical entropy of the input string for any 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.
Citations
|
523
|
Arithmetic coding for data compression
– Witten, Neal, et al.
- 1987
|
|
293
|
A block-sorting lossless data compression algorithm
– Burrows, Wheeler
- 1994
|
|
107
|
Arithmetic coding revisited
– Moffat, Neal, et al.
- 1995
|
|
106
|
A locally adaptive data compression scheme
– Bentley, Sleator, et al.
- 1986
|
|
100
|
Implementing the ppm data compression scheme,” in
– Moffat
- 1990
|
|
85
|
Unbounded length contexts for PPM
– Cleary, Teahan, et al.
- 1995
|
|
68
|
Data Compression using Dynamic Markov Modelling
– Cormack, Horspool
- 1987
|
|
67
|
Design and analysis of dynamic Huffman codes
– Vitter
- 1987
|
|
30
|
Analysis of arithmetic coding for data compression
– Howard, Vitter
- 1992
|
|
25
|
The burrows-wheeler transform for block sorting text compression: Principles and improvements
– Fenwick
- 1996
|
|
22
|
Practical implementations of arithmetic coding
– Howard, Vitter
- 1992
|
|
21
|
Universal lossless source coding with the Burrows Wheeler transform
– Effros, Visweswariah, et al.
- 2002
|
|
20
|
Compression of low entropy strings with Lempel-Ziv algorithms
– Kosaraju, Manzini
- 1999
|
|
19
|
Block sorting text compression — final report
– Fenwick
- 1996
|
|
16
|
Data Compression with the Burrows-Wheeler Transform
– Nelson
- 1996
|
|
14
|
The context trees of block sorting compression
– Larsson
|
|
10
|
The bzip2 home page
– Seward
- 1997
|
|
8
|
Data Compression by Means of a Book Stack
– Ryabko
- 1980
|
|
7
|
Text compression using recency rank with context and relation to context sorting, block sorting and PPM
– Sadakane
- 1997
|
|
6
|
An implementation of block coding
– Wheeler
- 1995
|
|
5
|
The Canterbury corpus home
– Arnold, Bell
|
|
5
|
On optimality of variants of the block sorting compression
– Sadakane
- 1998
|
|
2
|
A method for the construction of minimim redundancy codes
– Huffman
- 1952
|
|
2
|
The szip home page
– Schindler
- 1997
|
|
2
|
Upgrading bred with multiples tables
– Wheeler
- 1997
|
