Performance limits of multilevel DPSK

Recently introduced differential phase-shift keying (DPSK) extensions, collectively referred to here as multilevel differential phase (MDP) formats, explore an increase in data throughput for a given bandwidth by effectively multiplexing differential phase encoding and amplitude modulation onto the same fiber link. In this letter, we derive and present analytic models for the quantum limits of bit-error rate for leading MDP modulation formats (binary phase differential phase amplitude-shift keying (DPASK), quaternary phase DPASK), comparing their performance to that of conventional systems.