Error Detection in the Presence of Synchronization Loss

Cyclic codes are very attractive for error detection because of their low cost encoding and decoding circuits, and because of their high guaranteed minimum distance, but they suffer from very poor protection when word frame synchronization is lost. This note suggests starting the encoder and decoder circuits in an essentially random state, instead of the usual all-zero state. Under this condition of operation it is shown that the undetected error rate against synchronization loss is
2^{-p}
where
p
is the number of parity check bits.