Interpolation on a fixed interval discrete-valued sequence with random structure

Abstract

Discrete-valued sequences with random structure are widely used to describe electronic systems that operate under a priori uncertainty. An optimal interpolation algorithm on a fixed interval discrete-valued sequence with random structure have been obtained considering the Markov property of an extended process, which includes the value of a discrete-type sequence and its structure. This algorithm is recursive, and describes the evolution of the joint interpolation probability of the extended process in reverse time. Analysis of the optimal interpolation algorithm on a fixed interval was implemented by the example of decoding of a convolutional code by means of statistical computer modeling. For this example interpolation algorithm reduces the bit error probability to 3-4 times compared with the algorithm of filtering due to the fact that it takes into account all the received observations. The increase of statistical dependence between input symbols leads to a decrease in bit error rate in filtration and interpolation algorithms.