Abstract
Some probability-theoretical models of packet-mode-transmitted information distortions have been considered. The main attention has been paid to distortions, including the possible interferences that affect several transmission cycles. Distortions are simulated by a sequence of impacts determined by dependent random variables. Correspondingly, k-dimensional CRC values also allow them to be represented as the sum of k-dimensional, differently distributed, dependent random terms. In some cases, they can be reduced to the sums of independent terms in a k-dimensional vector space over a field of two elements; then, the known limit theorems on the convergence to uniform distributions become applicable to them. For impacts that stretch to m cycles, the prospects of obtaining convergence conditions for CRC distributions in the case of sums of m-dependent terms or terms that form a nonhomogeneous Markov chain have been discussed.
Similar content being viewed by others
References
Ignatov, V.A., Teoriya informatsii i peredachi signalov (Theory of Information and Signal Transmission), Moscow: Sovetskoe Radio, 1979.
Peterson, W.W. and Weldon, E.J., Error-Correcting Codes, MIT Press, 1976.
Baranov, P.A., The model for calculating the volume of error-free messages transmitted over telecommunications systems, Probl. Inf. Bezop., Komp’yut. Sist.,, 2015, no. 1, pp. 46–51.
Williams, R.N., A Painless Guide to CRC Error Detection Algorithms, 1993. http://www.info-system.ru/library/algo/crc1.pdf.
Dunsmore, B. and Skandier, T., Telecommunications Technologies Reference, Cisco, 2002.
Baranov, A.P. and Baranov, P.A., Estimation of the probability of a CRC error with a small distortion of transmitted information, Probl. Inf. Bezop., Komp’yut. Sist., 2016, no. 2, pp. 75–83.
Baranov, P.A., On the distribution of CRC values in the binary noise model, Probl. Inf. Bezop., Komp’yut. Sist., 2015, no. 2, pp. 47–51.
Baranov, A.P. and Baranov, P.A., Asymptotic estimates of the probabilities of CRC errors in some telecommunication protocols, Probl. Inf. Bezop., Komp’yut. Sist., 2016, no. 1, pp. 70–75.
Vainshtein, L.A. and Zubakov, V.D., Vydelenie signalov na fone sluchainykh pomekh (Separation of Signals from Random Noise), Moscow: Sovetskoe radio, 1960.
Ibragimov, I.A. and Linnik, Yu.V., Nezavisimye i statsionarno svyazannye velichiny (Independent and Stationarily Coupled Values), Moscow: Nauka, 1965.
Vorob’ev, N.N., Addition of independent random variables on finite Abelian groups, Mat. Sb., 1954, vol. 34, no. 1, pp. 89–126.
Karlin, S., A First Course in Stochastic Processes, 1975, 2nd ed.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.P. Baranov, P.A. Baranov, 2017, published in Problemy Informatsionnoi Bezopasnosti, Komp’yuternye Sistemy.
About this article
Cite this article
Baranov, A.P., Baranov, P.A. Models of the formation of CRC values and monitoring sums under the conditions of multiple distortions. Aut. Control Comp. Sci. 51, 959–964 (2017). https://doi.org/10.3103/S0146411617080065
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411617080065