Optimum frame synchronization for biorthogonally coded data

Many recent American unmanned planetary probes have used biorthogonally coded spacecraft-to-earth telemetry links. An examination of the frame-synchronization (sync) techniques employed on these missions revealed that they were not specifically designed for coded data. This led to a consideration of the optimum frame-sync problem for biorthogonally coded data received over the additive white Gaussian noise (AWGN) channel and decoded prior to sync acquisition. A frame-sync algorithm for biorthogonally coded data based on a super-symbol distance rule is proposed, along with a corresponding selection criterion for the sync sequence. It is argued heuristically that this approach is optimum with regard to minimizing the probability of false synchronization.