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

N. Mogilevskaya
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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.
离散q元信道误差流源模型组
数字数据传输信道中的错误是指报文接收者获得的数据与原始数据不匹配的事件。为了描述通信通道中的错误结构,使用了错误流的概念,即符号序列,其元素在没有错误时等于零,如果存在错误则为非零,并且错误源被理解为某些条件错误流发生器。二进制信道的误差源有许多数学模型,每一个模型都能很好地描述特定类型的数据传输信道的干扰环境。错误流模型的使用对研究纠错编解码器的质量具有重要意义。但是通信系统不仅使用二进制信号,而且还使用数字多位置信号(q-ary信号)。对于q元数据传输信道,误差的数学建模方法研究较少。本工作的目的是构建二进制fin模型的q元版本。该模型是基于使用随机变量的模糊区间序列的一组模型中最通用的模型。二元fin模型的一个特点是,它概括了许多众所周知的模型,并允许通过仅改变模型的内部参数来模拟根本不同的干扰环境。本文给出了这样一些模型参数设置的例子,它们的误差流的性质与其他知名模型所建立的流的性质一致。本文将一组基于模糊区间随机变量序列的二元模型转移到基数大于2的伽罗瓦域的情况下。非二进制错误流的生成分两个阶段。第一阶段形成误差位置,第二阶段生成误差值。数学上的q-ary fin模型,作为特例,包括许多著名的二元误差源模型的自然q-ary类似物,如Turin模型、Smith-Bowen-Joyce模型、Fritschmann-Svoboda模型等。它允许复杂结构的建模误差,也允许具有时变特性的通信信道的误差流。
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