Lexical Permutation Sorting Algorithm

Arnavut, Ziya

doi:10.1093/comjnl/40.5.292

Cited by 23 publications

(14 citation statements)

References 3 publications

(3 reference statements)

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“…Unfortunately, for general strings and sequence lengths, the last column is the only column that yields a reversible transformation. These observations together motivate a variety of alternatives to the BWT, such as the algorithms described in [3], [6], where modifications in the table generation techniques allow for use of earlier table columns.…”

Section: Background and Definitionsmentioning

confidence: 99%

“…The BWT-based codes described in works like [1]- [3] present a logical starting point in the analysis of BWT-based codes. Since all of these algorithms use variations on move-to-front coding in describing the BWT output, a description of move-to-front coding follows.…”

Section: B a Move-to-front Code: The Baseline Bwt Algorithmmentioning

confidence: 99%

“…The use of an integer code after the BWT and the move-tofront algorithm differs significantly from the approaches used in algorithms like [1]- [3], which follow the BWT and move-tofront algorithm with a first-order entropy code. Since this work contains no direct analysis of this (extremely popular) entropy coding approach, a brief digression to compare these alternatives follows.…”

Section: B a Move-to-front Code: The Baseline Bwt Algorithmmentioning

confidence: 99%

“…The encoder begins by describing the index value and the lengths of the subsequences. 3 Rather than describing index by its natural binary description, the encoder includes the description of with the description of the subsequence lengths using the following two-stage code. In the first stage, the encoder passes through in order, sending a for each subsequence of that has length one, a for each subsequence of that has length greater than one, and a for the (length-one) subsequence of .…”

Section: Known State Space or Memory Constraintmentioning

confidence: 99%

“…To date, the majority of research devoted to BWT-based compression algorithms has focused on experimental comparisons of BWT-based algorithms with competing codes. Experimental results on algorithms using this transformation (e.g., [2], [3], [5]) indicate lossless coding rates better than those achieved by Ziv-Lempel-style codes (LZ'77 [8], LZ'78 [9], and their descendants) but typically not quite as good as those achieved by the prediction by partial mapping (PPM) schemes described in works like [10], [11], [2]. BWT code implementation yields complexity comparable to that of the Ziv-Lempel codes, which are significantly faster than algorithms like PPM [1], [2].…”

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confidence: 99%

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Universal lossless source coding with the Burrows Wheeler transform

Effros

Visweswariah

Kulkarni

et al. 2002

IEEE Trans. Inform. Theory

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Abstract-The Burrows Wheeler Transform (BWT) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: 1) statistical characterizations of the BWT output on both finite strings and sequences of length , 2) a variety of very simple new techniques for BWT-based lossless source coding, and 3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory sources.Index Terms-Burrows Wheeler Transform (BWT), rate of convergence, redundancy, text compression, universal noiseless source coding.

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Section: Background and Definitionsmentioning

confidence: 99%

Section: B a Move-to-front Code: The Baseline Bwt Algorithmmentioning

confidence: 99%

Section: B a Move-to-front Code: The Baseline Bwt Algorithmmentioning

confidence: 99%

Section: Known State Space or Memory Constraintmentioning

confidence: 99%