Asymptotic assessments of CRC error probabilities in some telecommunication protocols

We study the value distributions for the control cyclic redundancy check (CRC) of length k , drawn at the data section of volume n . The behavior of CRC value distribution is examined at large n and fixed values of k ( k = const, n → ∞). With the application of the character theory, we find the conditions of asymptomatic uniformity of the CRC distribution. The asymptomatic results can be applied during the assessment of errors of a series of protocols such as USB, X.25, HDLC, Bluetooth, Ethernet, etc.