Decoding of LDPC-Based 2D-Barcodes Using a 2D-Hidden-Markov-Model

  • Wolfgang Proß
  • Franz Quint
  • Marius Otesteanu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 314)


This paper deals with the decoding of a new 2D-barcode that is based on Low-Density Parity-Check (LDPC) codes and Data Matrix Codes (DMC). To include typical damages that occur in industrial environment we chose a Markov-modulated Gaussian-channel (MMGC) model to represent everything in between the embossing and the camera-based acquisition of a LDPC-based DMC. For the decoding of LDPC codes with a MMGC the performance of Estimation-Decoding (ED), that adds a Hidden-Markov-Model (HMM) to the standard Belief-Propagate (BP)-decoder, is analyzed. We prove the advantage of ED in combination with a reestimation of the HMM’s transition probabilities. With respect to our application a decoding algorithm called ED2D-algorithm is developed that includes ED, a 2-dimensional HMM (2D-HMM) and a reestimation of the 2D-HMM’s transition probabilities. In a following evaluation the results of the ED-performance analysis are confirmed and a superior decoding behavior of our LDPC-based DMC decoded with the ED2D-decoder compared to the original Reed-Solomon-based version is shown.


Data matrix code LDPC code Estimation-Decoding 2D-Hidden-Markov-Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bahl, L.R., Cocke, J., Jelinek, F., Raviv, J.: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inform. Theory 20(2), 284–287 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Baum, L.E., Petrie, T., Soules, G., Weiss, N.: A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains. The Annals of Mathematical Statistics 41(1), 164–171 (1970)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Eckford, A.W.: Low-density parity-check codes for Gilbert-Elliott and Markov-modulated channels. Ph.D. thesis, University of Toronto (2004)Google Scholar
  4. 4.
    Eleftheriou, E., Mittelholzer, T., Dholakia, A.: Reduced-complexity decoding algorithm for low-density parity-check codes. Electronics Letters 37(2), 102–104 (2001)CrossRefGoogle Scholar
  5. 5.
    Gallager, R.G.: Low density parity check codes. IRE Trans. on Information Theory 1, 21–28 (1962)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Garcia-Frias, J.: Decoding of low-density parity-check codes over finite-state binary markov channels. IEEE Transactions on Communications 52(11), 1841 (2004)CrossRefGoogle Scholar
  7. 7.
    Hu, X.Y., Eleftheriou, E., Arnold, D.M.: Regular and irregular progressive edge-growth tanner graphs. IEEE Transactions on Information Theory 51(1), 386–398 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hu, X.Y., Eleftheriou, E., Arnold, D.M., Dholakia, A. (eds.): Efficient implementations of the sum-product algorithm for decoding LDPC codes, vol. 2 (2002)Google Scholar
  9. 9.
    ISO/IEC: Information technology — international symbology specification — data matrix (2000)Google Scholar
  10. 10.
    Johnson, N.L.: Systems of frequency curves generated by methods of translation. Biometrika 36(1-2), 149 (1949)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous univariate distributions. A Wiley-Interscience Publication, 2nd edn. Wiley, New York (1994)Google Scholar
  12. 12.
    MacKay, D., Neal, R.: Good codes based on very sparse matrices. In: Cryptography and Coding, pp. 100–111 (1995)Google Scholar
  13. 13.
    Proß, W., Quint, F., Otesteanu, M.: Using peg-ldpc codes for object identification. In: 2010 9th Electronics and Telecommunications (ISETC), pp. 361–364 (2010)Google Scholar
  14. 14.
    Ratzer, E.A. (ed.): Low-density parity-check codes on Markov channels. In: Proceedings of 2nd IMA Conference on Mathematics and Communications, Lancaster, UK (2002)Google Scholar
  15. 15.
    Tanner, R.M.: A recursive approach to low complexity codes. IEEE Transactions on Information Theory 27, 533–547 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Wadayama, T. (ed.): An iterative decoding algorithm of low density parity check codes for hidden Markov noise channels. In: Proceedings of International Symposium on Information Theory and Its Applications, Honolulu, Hawaii, USA (2000)Google Scholar
  17. 17.
    Woodland, J.N., Silver, B.: Classifying apparatus and method (1949)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wolfgang Proß
    • 1
    • 2
  • Franz Quint
    • 1
  • Marius Otesteanu
    • 2
  1. 1.Faculty of Electrical Engineering and Information TechnologyUniversity of Applied Sciences KarlsruheKarlsruheGermany
  2. 2.Faculty of Electronics and TelecommunicationsPolitehnica University of TimişoaraTimişoaraRomania

Personalised recommendations