Convergence of a Bayesian iterative error-correction procedure on a noisy shift register sequence

Authors:
Miodrag J. Mihaljevic;Jovan Dj. Golic
Affiliations:
Institute of Applied Mathematics and Electronics, Belgrade School of Electrical Engineering, University of Belgrade, Beograd, Yugoslavia;Institute of Applied Mathematics and Electronics, Belgrade School of Electrical Engineering, University of Belgrade, Beograd, Yugoslavia
Venue:
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Year:
1992

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Abstract

Convergence of an algorithm for a linear feedback shift register initial state reconstruction using the noisy output sequence, based on a bitwise Bayesian iterative error-correction procedure and different weight parity-checks, is analyzed. It is proved that the self-composition of the Bayes error probability converges to zero if and only if the noise probability is less than a critical value expressed in terms of the numbers of parity-checks. An alternative approach to the critical noise estimation based on the residual error-rate after each iterative revision is also discussed.