FIR parity check codes

This paper describes a method for packet synchronization and error detection for use in a synchronous digital communications system. The method relies upon a class of linear block codes that have parity checks that are expressed in terms of a finite-impulse response (FIR) filter. This system is incorporated in the newly established ITU standard of digital cable television standard, J.83 appendix B, which is based on an MPEG 2 transport packet data stream. This technique is also the basis for cable modem downstream transmission defined in the IEEE 802.14 and MCNS standards. The parity check structure is based on a pseudonoise sequence generated by a (binary) primitive polynomial. This structure allows for a computationally efficient implementation of the parity check FIR filter, in a recursive manner, that is none the less self-synchronizing. The FIR parity check codes that are described are characterized as the dual of a CRC-type, shortened cyclic code. The theory and computational structure of these codes are presented here; the J.83B code is used as an example of the general theory.