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Control sum mechanism efficiency research aimed at distortion revealing in a message being transmitted is a relevant task that is solved using different possible information transfer operation condition models.
In the paper distortions are modelled as an overlay of noise component with low signal/noise ratio , which poses most practical interest. Considered class of control sums is related to message consistency control mechanisms which are implemented, in particular, in TCP protocol. Functional dependency of control sum error probability from value is acquired for latter’s low value.
The paper considers error probability in every of four message block integrity checking methods: digital signature, cyclical redundant code, control sums in vector space over a field of two elements and control sums in a ring of integers. Comparison of asymptotic representations of transmitted binary signal and for large transmitted block’s volume is presented in the paper.
Values of main members for asymptotic decomposition are obtained for the integrity checking methods noted. These values are calculated as an example for parameters of TCP protocol segments.
We consider error probabilities in protocols using CRC to detect distortions in transmitted batches. A probability-theory model of an additive long-term noise is constructed as a sequence of independent noise blocks of a prescribed length. We show that there are conditions to be imposed on the form of the k-order polynomial forming the CRC and on block size s such that the error probability α is close to 2−k and does not depend on s provided that distortion probability P1 is high.
The paper examines probability-theoretic models of information distortion at message level. We research control sum distribution segments that are typical for network protocols like TCP.
As an addition operation we use both bitwise coordinate addition and addition of numbers in binary code with carry. Control sum error probability for asymptotic assessments provided distortion probability is low are deduced for described distortion models. These assessments could be relevant for large lengths of message segments.