Packet error rates for DPSK and differentially encoded coherent BPSK

When a digital communication system transmits data in packet (block) form, straightforward techniques exist for computing the probability that at least one bit in the packet of N bits is in error. For differential phase-shift-keying (DPSK) or differentially encoded coherent biphase-shift-keying (DE-BPSK), the paired error tendency precludes the simpler computational approach used, for example for straight BPSK, if precise results are required. The exact expression for the probability of a packet error is derived for both DPSK and DE-BPSK. It is shown that ignoring the paired error tendency and using the simpler independent bit error assumption yields an upper bound which, for large packet sizes, is in error by no more than approximately 0.1 dB for DPSK and 0.2 dB for DE-BPSK. An excellent approximation is derived for both cases; that is useful for precise results