Synchronization of isolated words of SMD codes in noise (Q1070992)

The article considers synchronization of code words (n,k) of separable maximum-distance codes (SMD codes) in the case of which each code arrives from the channel in noise. The author introduces the concept of the index of nonintersection at n-s positions \((m_{n-s})\) as the minimum of the paired distances between n-s symbol prefixes and n-s symbol suffixes of code words under shift s. A method of constructing SMD codes with maximum \(m_{n-s}\) values is given, as well as relations that make it possible to determine \(P_{syn}(s)\) (the probability of false synchronization) for them and to estimate \(P_ e(s)\) (the probability of error associated with false synchronization). Results of numerical computer calculations are presented.