The CRC for the CPS Header of an ATM AAL2 cell is generated by a CRC generator which uses the 8 bits of the CID field to generate partial 5 bits CRCs which are loaded in a first table. The 6 bits LI field and 5 bits UUI field are added to the partial 5 bits CRC to form 16 bits. The CRC generator uses the 2.sup.16 bits to generate a second CRC table. The CRC for a particular CPS header is generated by correlating bits in the CID field, LI field and UUI field with the two tables.