Group of models of error flow sources for discrete q-ary channels

Abstract

An error in a digital data transmission channel is an event consisting in the fact that the data obtained by the message receiver does not match the original data. To describe the structure of errors in a communication channel, the concept of error flow is used, that is, sequences of symbols, the elements of which are equal to zero in the absence of an error and are non-zero if error presences, and the source of errors is understood as some conditional error flow generator. There are many mathematical models of error sources for binary channels, each of which adequately describes the interference environment of a particular type of data transmission channel. The use of error flow models is relevant for studying the quality of error-correcting codecs. But communication systems use not only binary, but also digital multi-position signals (q-ary signals). For q-ary data transmission channels, methods of mathematical modeling of errors have been studied little. The purpose of this work is to construct a q-ary version of the binary FIn-model. This model is the most general model from the group of models based on the use of fuzzy-interval sequences of random variables. A feature of the binary FIn-model is that it generalizes many well-known models and allows modeling fundamentally different cases of interference environment by changing only the internal parameters of the model. This paper presents such examples of model parameter settings that the properties of their error flows coincide with the properties of flows that are built by other well-known models. In this paper, a group of binary models built on the basis of the use of fuzzy-interval sequences of random variables is transferred to the case of Galois fields of cardinality greater than two. The generation of a non-binary error flow occurs in two stages. At the first stage, error positions are formed, and at the second stage, error values are generated. The mathematical q-ary FIn-model includes, as special cases, natural q-ary analogs of many well-known models of binary error sources, such as the models of Turin, Smith-Bowen-Joyce, Fritschmann-Svoboda, etc. It allows modeling errors of a complex structure, and also error flows of communication channels with time-varying characteristics.