Decoding of LDPC-Based 2D-Barcodes Using a 2D-Hidden-Markov-Model
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.
KeywordsData matrix code LDPC code Estimation-Decoding 2D-Hidden-Markov-Model
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- 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
- 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.ISO/IEC: Information technology — international symbology specification — data matrix (2000)Google Scholar
- 11.Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous univariate distributions. A Wiley-Interscience Publication, 2nd edn. Wiley, New York (1994)Google Scholar
- 12.MacKay, D., Neal, R.: Good codes based on very sparse matrices. In: Cryptography and Coding, pp. 100–111 (1995)Google Scholar
- 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.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
- 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.Woodland, J.N., Silver, B.: Classifying apparatus and method (1949)Google Scholar