Abstract
Abstract. This article explores the a mathematical model of the a data transmission channel with errors grouping. We propose an estimating method for energy gain from coding and energy efficiency of binary codes in channels with grouped errors. The proposed method uses a simplified Bennet and Froelich’s model and allows leading the research of the energy gain from coding for a wide class of data channels without restricting the way of the length distributing the error bursts. The reliability of the obtained results is confirmed by the information of the known results in the theory of error-correcting coding in the simplified variant.
Highlights
The usage of redundant codes to increase the reliability of the transmitted information requires the designer to take into account various factors, including the nature of the error distribution in the communication channel [1,2,3,4,5,6,7,8,9]
One of the main criteria of the error-correcting code efficiency is the energy gain from coding (EGC), which refers to the reduction of the minimum required ratio of signal energy to spectral power density of noise
As the result of the research, we have developed a scientific and methodological apparatus description of the error behaviour in discrete channels
Summary
The usage of redundant codes to increase the reliability of the transmitted information requires the designer to take into account various factors, including the nature of the error distribution in the communication channel [1,2,3,4,5,6,7,8,9]. At any point of time, error condensations, so-called error bursts, can occur, inside of which the error probability is significantly higher than the average error probability calculated for a considerable transmission time In such conditions, protection methods that are optimal for the independent error hypothesis are absolutely ineffective in real communication channels [4,5,6,7,8,9]. One of the main criteria of the error-correcting code efficiency is the energy gain from coding (EGC), which refers to the reduction of the minimum required ratio of signal energy to spectral power density of noise It allows to apply a system of an error-correcting code while ensuring the given probability of the erroneous receiver of signs [10,11,12]. The current direction of research is to develop methods of estimating the energy gain from coding in channels with grouping errors
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