Models of the formation of CRC values and monitoring sums under the conditions of multiple distortions

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.