Maximum a Posteriori Decoding of Arithmetic Codes in Joint Source-Channel Coding

  • Trevor Spiteri
  • Victor Buttigieg
Part of the Communications in Computer and Information Science book series (CCIS, volume 222)


Arithmetic codes are being increasingly used in the entropy coding stage in many multimedia transmission applications. Combining channel coding with arithmetic coding can give implementation and performance advantages compared to separate source and channel coding. In this work, novel improvements are introduced into a technique by Grangetto et al. that uses maximum a posteriori (MAP) estimation for decoding joint source-channel coding using arithmetic codes. The arithmetic decoder is modified for quicker symbol decoding and error detection by the introduction of a look-ahead technique, and the calculation of the MAP metric is modified for faster error detection. These modifications also result in improved performance compared to the original scheme. Experimental results show an improvement of up to 0.4 dB when using soft-decision decoding and 0.6 dB when using hard-decision decoding.


Arithmetic coding Joint source-channel coding Maximum a posteriori decoding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rissanen, J.J.: Generalized Kraft inequality and arithmetic coding. IBM Journal of Research and Development 20(3), 198–203 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Huffman, D.A.: A method for the construction of minimum-redundancy codes. Proceedings of the IRE 40(9), 1098–1101 (1952)CrossRefzbMATHGoogle Scholar
  3. 3.
    Shannon, C.E.: A mathematical theory of communication. Bell System Technical Journal 27, 379–423 (1948)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Vembu, S., Verdù, S., Steinberg, Y.: The source-channel separation theorem revisited. IEEE Transactions on Information Theory 41(1), 44–54 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Boyd, C., Cleary, J.G., Irvine, S.A., Rinsma-Melchert, I., Witten, I.H.: Integrating error detection into arithmetic coding. IEEE Transactions on Communications 45(1), 1–3 (1997)CrossRefGoogle Scholar
  6. 6.
    MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms, ch. 25, pp. 324–333. Cambridge University Press (2003)Google Scholar
  7. 7.
    Grangetto, M., Cosman, P., Olmo, G.: Joint source/channel coding and MAP decoding of arithmetic codes. IEEE Transactions on Communications 53(6), 1007–1016 (2005)CrossRefGoogle Scholar
  8. 8.
    Bi, D., Hoffman, M.W., Sayood, K.: Joint Source Channel Coding Using Arithmetic Codes. Synthesis Lectures on Communications. Morgan & Claypool Publishers (2010)Google Scholar
  9. 9.
    Witten, I.H., Neal, R.M., Cleary, J.G.: Arithmetic coding for data compression. Communications of the ACM 30(6), 520–540 (1987)CrossRefGoogle Scholar
  10. 10.
    Lelewer, D.A., Hirschberg, D.S.: Data compression. ACM Computing Surveys (3), 261–296 (September 1987)Google Scholar
  11. 11.
    Sayir, J.: Arithmetic coding for noisy channels. In: Proceedings of the 1999 IEEE Information Theory and Communications Workshop, pp. 69–71 (June 1999)Google Scholar
  12. 12.
    Guionnet, T., Guillemot, C.: Soft decoding and synchronization of arithmetic codes: Application to image transmission over noisy channels. IEEE Transactions on Image Processing 12(12), 1599–1609 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hagenauer, J.: Rate-compatible punctured convolutional codes (RCPC codes) and their applications. IEEE Transactions on Communications 36(4), 389–400 (1988)CrossRefGoogle Scholar
  14. 14.
    Grangetto, M., Scanavino, B., Olmo, G., Benedetto, S.: Iterative decoding of serially concatenated arithmetic and channel codes with JPEG 2000 applications. IEEE Transactions on Image Processing 16(6), 1557–1567 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Bahl, L.R., Cocke, J., Jelinek, F., Raviv, J.: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Transactions on Information Theory 20(2), 284–287 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Park, M., Miller, D.J.: Joint source-channel decoding for variable-length encoded data by exact and approximate MAP sequence estimation. IEEE Transactions on Communications 48(1), 1–6 (2000)CrossRefGoogle Scholar
  17. 17.
    Jelinek, F.: Fast sequential decoding algorithm using a stack. IBM Journal of Research and Development 13(6), 675–685 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Ben-Jamaa, S., Weidmann, C., Kieffer, M.: Analytical tools for optimizing the error correction performance of arithmetic codes. IEEE Transactions on Communications 56(9), 1458–1468 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Trevor Spiteri
    • 1
  • Victor Buttigieg
    • 1
  1. 1.University of MaltaMsidaMalta

Personalised recommendations