Determination of the quality of error detection in communication by CRC concatenated with parity bits

This paper presents a method to determine the residual error probability and the Hamming-Distance of a coding technique that applies CRC in combination with parity bits. Such a combination can be found in industrial communication where an application specific CRC is embedded in regular fieldbus communication with a parity mechanism. In a typical error detection analysis, usually only the CRC is considered for the determination of the residual error probability or the Hamming-Distance. The effect of the parity bits has not been exploited yet, since no methods for the calculation of the concatenation were at hand. The inclusion of the parity mechanism allows more realistic information about the quality of the error detection.