Zusammenfassung
In dieser Übersichtsarbeit werden die Grundgleichungen der iterativen Decodierung mittels elementarer Verfahren der Wahrscheinlichkeitsrechnung abgeleitet und zusammengestellt. Dabei zeigt sich, dass durch direkte Repräsentation einer Symbolzuverlässigkeit mittels der a-posteriori-Wahrscheinlichkeit diese Beziehungen einfach darzustellen sind, und die Prinzipien der iterativen Decodierung dadurch leicht fasslich formuliert werden können. Die Vorteile anderer gebräuchlicher Methoden zur Repräsentation von Symbolzuverlässigkeiten und deren Wechselbeziehungen werden diskutiert.
Abstract
In this tutorial paper the basic equations for iterative decoding are derived by elementary methods of probability calculus. It is shown that a representation of symbol reliabilities directly by means of a-posteriori probabilities simplifies derivations and makes it easy to understand the principles of iterative decoding. The advantages of other, commonly used descriptions and their interrelationships are discussed.
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Literatur
Bahl, L. R., Cocke, J., Jelinek, F., Raviv, J. (1974): Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory, vol. 20: 284–287.
Benedetto, S., Montorsi, G. (2002): The new frontier of channel coding: concatenated codes with interleaver and iterative decoding. In: 4th International ITG Conference on Source and Channel Coding, Berlin, Germany, January 2002: 35–45.
Berrou, C., Glavieux, A., Thitimajshima, P. (1993): Near Shannon limit error-correcting coding and decoding: turbo-codes. In: Proc. IEEE Int. Conf. Commun. (ICC). Geneva, Switzerland: 1064–1070.
Chung, S.-Y., Forney, G. D., Richardson, T. J., Urbanke, R. (2001): On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit. IEEE Communications Letters, 5: 58–60.
Costello, D. J., Banerjee, A., Fuja, T. E., Massey, P. C. (2002): Some reflections on the design of bandwidth efficient turbo codes. In: 4th International ITG Conference on Source and Channel Coding, Berlin, Germany, January 2002: 357–363.
Fischer, R. F. H. (2002): Precoding and signal shaping for digital transmission. New York: John Wiley & Sons.
Gallager, R. G. (1962): Low density parity check codes. IRE Trans. Info. Theory, IT-8: 21–28.
Haykin, S. (1996): Adaptive filter theory. 3rd edition. Englewood Cliffs, NJ: Prentice-Hall.
Hüttinger, S., Huber, J. (2002): „Multiple-Turbo-Codes” with transfer characteristics of component codes. In: Proceedings of the 36th Annual Conference on Information Sciences and Systems (CISS 2002), Princeton, NJ, March 2002.
Hüttinger, S., ten Brink, S., Huber, J. (2001): Turbo-Code representation of RA-Codes and DRS-Codes for reduced decoding complexity. In: Proceedings of the 35th Annual Conference onf Information Sciences and Systems (CISS 2001), Baltimore, Maryland: 118–123.
Massey, P. C., Costello Jr., D. J. (2001): New low-complexity turbo-like codes. In: IEEE Information Theory Workshop, Cairs, Australia, September 2001.
Peterson, W. W., Weldon Jr., E. J. (1972): Error-correcting codes. 2nd edition. Cambridge, Massachusetts: MIT Press.
Robertson, P., Höher, P., Villebrun, E. (1997): Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding. Europ. Trans. Telecommun. (ETT), 8(2): 119–125.
Shannon, C. E. (1948): A mathematical theory of communication. Bell System Technical Journal, vol. 27, part I: 379–427; part II: 623–656.
Tanner, R. M. (1981): A recursive approach to low complexity codes. IEEE Trans. Int. Theory, 27(5): 533–547.
ten Brink, S. (2000): A rate one-half code for approaching the Shannon limit by 0.1 db. IEE Electronics Letters, 36(15): 1293–1294.
Wachsmann, U., Fischer, R. F. H., Huber, J. B. (1999): Multilevel codes: theoretical concepts and practical design rules. IEEE Trans. Inf. Theory, IT-45(5): 1361–1391.
Wachsmann, U., Huber, J. B. (1995): Power and bandwidth efficient digital communication using turbo codes in multilevel codes. Europ. Trans. Telecommun. (ETT), Sept.–Oct. 1995, 6(5): 557–567.
Wiberg, N. (1996): Codes and decoding on general graphs. PhD thesis, Dept. of Electrical Engineering, Linköping, Sweden, 1996. Linköping studies in Science and Technology. Dissertation No. 440.
Worm, A., Höher, P., Wehn, N. (2000): Turbo-decoding without SNR estimation. IEEE Commun. Letter, 4(6): 193–195.
Wozencraft, J. M., Jacobs, I. M. (1965): Principles of communication engineering. New York: John Wiley & Sons.
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Huber, J. Grundlagen der Wahrscheinlichkeitsrechnung für iterative Decodierverfahren. Elektrotech. Inftech. 119, 386–394 (2002). https://doi.org/10.1007/BF03160509
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DOI: https://doi.org/10.1007/BF03160509