Universal lossless source coding with the Burrows Wheeler Transform

Michelle Effros, Karthik Visweswariah, Sanjeev R. Kulkarni, Sergio Verdú

Research output: Contribution to journalArticle

58 Scopus citations

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 n → ∞, 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.

Original languageEnglish (US)
Pages (from-to)1061-1081
Number of pages21
JournalIEEE Transactions on Information Theory
Volume48
Issue number5
DOIs
StatePublished - May 2002

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Burrows Wheeler Transform (BWT)
  • Rate of convergence
  • Redundancy
  • Text compression
  • Universal noiseless source coding

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