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, P _re ). 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 P _re 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 P _re as well as the improvement of the error detection capabilities is shown.