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

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.