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Arithmetic coding for data compression

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Published:01 June 1987Publication History
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Abstract

The state of the art in data compression is arithmetic coding, not the better-known Huffman method. Arithmetic coding gives greater compression, is faster for adaptive models, and clearly separates the model from the channel encoding.

References

  1. 1 Abramson, N. Information Theory and Coding. McGraw-Hill, New York, 1963. This textbook contains the first reference to what was to become the method of arithmetic coding (pp. 61-62).Google ScholarGoogle Scholar
  2. 2 Bentley. J.L., Sleator, D.D., Tarjan, R.E., and Wei, V.K. A locally adaptive data compression scheme. Commun. ACM 29, 4 (Apr. 1986), 320-330. Shows how recency effects can be incorporated explicitly into a text compression system. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3 Cleary, J.C., and Witten, I.H. A comparison of enumerative and adaptive codes. IEEE Trans. Inf. Theory IT-30,2 (Mar. 1984). 306-315. Demonstrates under quite general conditions that adaptive coding outperforms the method of calculating and transmitting an exact model of the message first.Google ScholarGoogle ScholarCross RefCross Ref
  4. 4 Clearv. I.G. and Witten. I.H. Data comoression using adaptive coding and'partial string matching. IEEE T>ans. Commu~ C&-32,4 (Apr. 1984). 396-402. Presents an adaptive modeling method that reduces a large sample of mixed-case English text to around 2.2 bits/character when arithmetically coded.Google ScholarGoogle Scholar
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  7. 7 Gallager, R.G. Variations on a theme by Huffman. IEEE Trans. tnf Theory IT-24, 6 (Nov. 19781, 668-674. Presents an adaptive Huffman coding algorithm, and derives new bounds on the redundancy of Huffman codes.Google ScholarGoogle Scholar
  8. 8 Held, G. Data Compression: Techniques and Applications. Wiley, New York, 1984. Explains a number of ad hoc techniques for compressing text. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9 Hester, J.H., and Hirschberg, D.S. Self-organizing linear search. ACM Comput. SKI-V. 17, 3 (Sept. 1985), 295-311. A general analysis of the technique used in the present article to expedite access to an array of dynamically changing frequency counts. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10 Huffman, D.A. A method for the construction of minimumredundancy codes. Proc. Inst. Electr. Radio Eng. 40, 9 (Sept. 1952), 1098-1101. The classic paper in which Huffman introduced his famous coding method.Google ScholarGoogle Scholar
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  12. 12 Kucera, H., and Francis, W.N. Compufational Analysis of Present-Day American English. Brown University Press, Providence, R.I. 1967. This large corpus of English is often used for computer experiments with text, including some of the evaluation reported in the present article.Google ScholarGoogle Scholar
  13. 13 Langdon, G.G. An introduction to arithmetic coding. IBMI. Res. Dev. 28, 2 (Mar. 1984), 135-149. Introduction to arithmetic coding from the point of view of hardware implementation.Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14 Langdon, G.G., and Rissanen, J. Compression of black-white images with arithmetic coding. 1EEE Trans. Commun. COM 29,6 (June 1981), 858.-867. Uses a modeling method specially tailored to black/white pictures, in conjunction with arithmetic coding, to achieve excellent compression results.Google ScholarGoogle Scholar
  15. 15 Pasco, R. Source coding algorithms for fast data compression. Ph.D. thesis, Dept. of Electrical Engineering, Stanford Univ., Stanford, Calif., 1976. An early exposition of the idea of arithmetic coding, but lacking the idea of incremental operation. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. 16 Rissanen, J.J. Generalized Kraft inequality and arithmmatic coding. IBM 1. Res. Dev. 20 (May 1976), 198-203. Another early exposition of the idea of arithmetic coding.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. 17 Rissanen. J.J. Arithmetic codings as number representations. Acta Polytech. Stand. Math. 31 (Dec. 1979), 44-51. Further develops arithmetic coding as a practical technique for data representation.Google ScholarGoogle Scholar
  18. 18 Rissanen, J., and Langdon, G.G. Arithmetic coding. IBM J. Res. Dev. 23, 2 (Mar. 1979). 149-162. Describes a broad class of arithmetic codes.Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. 19 Rissanen, J. and Langdon, G.G. Universal modeling and coding. IEEE Trans. Znf Theory IT-27, 1 (Jan. 1981), 12-23. Shows how data cornpression can be separated into modeling for prediction and coding with respect to a model.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. 20 Rubin, F. Arithmetic stream coding using fixed precision registers. IEEE Trans. If. Theory IT-25, 6 (Nov. 1979), 672-675. One of the first papers to present all the essential elements of practical arithmetic coding, including fixed-point computation and incremental operation.Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. 21 Shannon, C.E. and Weaver, W. The Mathematical Theory of Communication. University of Illinois Press, Urbana, Ill., 1949. A classic book that develops communication theory from the ground up. Google ScholarGoogle ScholarDigital LibraryDigital Library
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  23. 23 Ziv, J., and Lempel, A. Compression of individual sequences via variable-rate coding. IEEE Trans. InJ Theory IT-24, 5 (Sept. 1978), 530-536. Describes a method of text compression that works by replacing a substring with a pointer to an earlier occurrence of the same substring. Although it performs quite well, it does not provide a clear separation between modeling and coding.Google ScholarGoogle ScholarCross RefCross Ref

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      cover image Communications of the ACM
      Communications of the ACM  Volume 30, Issue 6
      June 1987
      92 pages
      ISSN:0001-0782
      EISSN:1557-7317
      DOI:10.1145/214762
      Issue’s Table of Contents

      Copyright © 1987 ACM

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      Publication History

      • Published: 1 June 1987

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