On One Statistical Model of Error Rate in the Stream of Packet Data Transmission through Communication Channels
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ON ONE STATISTICAL MODEL OF ERROR RATE IN THE STREAM OF PACKET DATA TRANSMISSION THROUGH COMMUNICATION CHANNELS S. O. Dovgyi,1 O. I. Yurikov,2† and M. O. Zozyuk2‡
UDC 519.246
Abstract. A statistical model of the frequency of errors in the packet data transmission through communication channels is proposed. This is a stochastic sequence defined as the averaged proportion of erroneous data packets. A diffusion approximation of such a sequence is used: discrete Markov diffusion, which is defined by a difference stochastic equation. The parameters of such a model are estimated using covariance statistics on the trajectories of the stochastic sequence of signal transmission errors. Keywords: statistical model, difference stochastic equation, stationary process, equilibrium, covariance statistics, parameters estimation along trajectories. BASIC DEFINITIONS Our goal is to generate a model of error inclusions in packet data transmission over communication channels. In the data transmission protocols, a packet integrity check (CRC code, parity etc.) is built-in, which restores the original data at the reception point due to the redundancy of the transmission code [1, 2]. This redundancy, however, reduces the data rate and requires additional digital signal processing. The task of determining the statistical parameters and their estimates of the fraction of the “corrupted” data packets with respect to their total volume is determined by equilibrium state of the frequency of erroneous packets. This equilibrium state is an invariant point of the regression function or, equivalently, zero point of the regression function of increments of evolutionary process [3]. Consider a string for receiving N data packets {1, 2, K , N } , containing both holistic and corrupted blocks arranged in random order, as illustrated in Fig. 1. Define the following binary random variables as packet integrity indicators
ì0 if the package n is holistic, k ³ 0, 1 £ n £ N . d n (k ) = í î1 if the package n is corrupted, Then the normalized sum of random indicators
S N (k ) =
1 N
N
å d r (k ),
k ³ 0,
(1)
n =1
determines the proportion of packet errors in the process of receiving and transmitting a signal over communication channels. The discrete-time random process S N ( k ) , k ³ 0 , is called statistical experiment [3] and takes values from 1
Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine, [email protected]. 2National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine, †[email protected]; ‡[email protected]. Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2020, pp. 63–69. Original article submitted May 6, 2019. 1060-0396/20/5605-0739 ©2020 Springer Science+Business Media, LLC
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Pack 1
Pack 2
Pack 3 Corrupted
…
…
Pack t
Pack t + 1
…
Corrupted
Fig. 1. Typical packet flow of data transmission with errors. the interval [0,1]. The extreme value 0 corresponds to the situation where all
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