CRC in Coded Schemes with Bounded-Distance Decoding

The undetected error probability of CRC combined with an error-correcting code with bounded-distance decoding is considered. It is shown that to minimize this probability, the CRC polynomial should be matched to the code. In particular, good CRC polynomials reported in the literature for pure CRC schemes may not be good when combined with coding. Guidelines to choose a good CRC polynomial to be combined with a given code are provided.