An algorithm for recognition of a vector alphabet generating a sequence with a quasi-periodic structure

The problem of noise-proof a posteriori (off-line) recognition is considered for a vector alphabet generating sequences that include quasi-periodically alternating vector-fragments coinciding with elements of this alphabet. One variant of this problem is reduced to the discrete optimization problem under investigation. The exact polynomial solving the algorithm for the reduced problem is proved. This algorithm guarantees the maximum likelihood problem-solving in the case when the noise is additive and it is a Gaussian sequence of independent random values having identical distribution, whereas the number of alternating vector-fragments is unknown. The algorithm suggested has essentially smaller computational complexity in comparison with known one. © 2010 Pleiades Publishing, Ltd.