Matrix Probabilities

  • William Turin
Part of the Information Technology: Transmission, Processing and Storage book series (PSTE)


A communication system performance analysis includes the calculation of performance characteristics such as received symbol-error probability, the average interval between errors, the average length of an error burst, error number distribution in a message, etc. The convenience of calculating these and similar characteristics often determines the choice of an error source model. In this chapter, we develop methods of calculation based on the HMM.


Markov Chain Discrete Fourier Transform Recursive Equation Convolution Theorem Matrix Distribution 
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  1. 1.
    M. S. BartlettIntroduction to Stochastic Processes with Special Reference to Methods and Applications(Cambridge Univ. Press, Cambridge, 1978).Google Scholar
  2. 2.
    E. L. Bloch, O. V. Popov, and W. Ya. Turin, “Error number distribution for the stationary symmetric channel with memory,”Second International Symposium on Information TheoryAcademiai Kiado, Budapest, 1972.Google Scholar
  3. 3.
    K. L. ChungMarkov Chains with Stationary Transition Probabilities(Springer-Verlag, Berlin, 1960).zbMATHCrossRefGoogle Scholar
  4. 4.
    W. FellerAn Introduction to Probability Theory and Its Applications 1(John Wiley & Sons, New York, 1962).Google Scholar
  5. 5.
    I. I. Gichman and A. V. Scorochod, The Theory of Stochastic Processes(in Russian), 1, (Science Publishers, Moscow, 1971).Google Scholar
  6. 6.
    J. G. Kemeny and J. L. SnellFinite Markov ChainsVan Nostrand, (Princeton, New Jersey, 1960).Google Scholar
  7. 7.
    B. A. Fuchs and B. V. ShabatFunctions of a Complex Variable 1(Addison-Wesley Publishing Co., Reading, Massachusetts, 1964).zbMATHGoogle Scholar
  8. 8.
    W. Huggins, “Signal flow graphs and random signals,”Proc. IRE 4574–86, 1957.CrossRefGoogle Scholar
  9. 9.
    S. KullbackInformation Theory and Statistics(John Wiley & Sons, New York, 1959).zbMATHGoogle Scholar
  10. 10.
    S. J. Mason and H. J. ZimmermannElectronic Circuits Signals and Systems(John Wiley & Sons, New York, 1965).Google Scholar
  11. 11.
    G. A. Medvedev and V. P. TarasenkoProbabilistic Methods in Extremal Systems Investigation(in Russian), (Science Publishers, Moscow, 1967).Google Scholar
  12. 12.
    O. V. Popov and W. Ya. Turin, “The probability distribution law of different numbers of errors in a combination,”Telecommunications and Radioengineering(5), 1967.Google Scholar
  13. 13.
    L. Rabiner and B.-H. JuangFundamentals of Speech Recognition(Prentice Hall, Englewood Cliffs, New Jersey, 1993).Google Scholar
  14. 14.
    L. R. Rabiner and C. M. RaderDigital Signal Processing(IEEE Press, New York, 1972).Google Scholar
  15. 15.
    W. Ya. Turin, “Probability distribution laws for the number of errors in several combinations,” Telecommunications and Radioengineering 27 (12), 1973.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • William Turin
    • 1
  1. 1.AT&T Labs—ResearchFlorham ParkNew JerseyUSA

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