Residual Error Probability of Embedded CRC by Stochastic Automata

Abstract

Cyclic Redundancy Check (CRC) is an approved coding technique to detect errors in industrial communication. Using a checksum calculated with the help of a generator polynomial, CRC guarantees a low probability of undetected errors (residual error probability, Pre). The choice of an appropriate polynomial has significant impact on the quality of error detection. Since CRC itself is very efficient, it is obvious to embed safety-critical data protected by an additional CRC into the net data protected by the original CRC in order to increase the error detection of the safety-critical data. The paper introduces a method to determine the corresponding Pre by means of stochastic automata. Using the example of the fieldbus PROFIBUS-PA as embedding communication protocol, polynomials for the additional CRC were analyzed. As result, the impact of generator polynomials in the additional CRC on the Pre as well as the improvement of the error detection capabilities is shown.