Researchers have proposed a novel squeezed-state pulse-position modulation (S-PPM) format and an associated inverse-squeezing conditional pulse-nulling (IS-CPN) receiver, which promise to enhance efficiency in optical communication. This scheme utilizes squeezed vacuum states for empty slots and displaced squeezed states for pulse slots. The key insight is that the IS-CPN receiver can map the S-PPM signal into an equivalent coherent-state PPM signal with significantly larger pulse energy, allowing for a closed-form expression for the receiver error probability under ideal conditions.

The analysis of the IS-CPN receiver was extended to more realistic scenarios, including common phase diffusion, a prevalent phenomenon in optical communication systems. A finite-path MAP (Maximum A Posteriori) formulation with phase-averaged likelihoods was employed for this purpose. Numerical results demonstrate that IS-CPN outperforms conventional CPN (conditional pulse-nulling) under the same energy constraint. This advantage persists even in the presence of phase noise and with finite photon-number resolution.

The combination of squeezed-state modulation with inverse-squeezing conditional nulling represents a significant advancement in optical communication. This approach not only improves robustness against channel imperfections like phase noise but also optimizes photon utilization, which is crucial for high-speed, low-power communication systems. The findings suggest a promising path for the development of more efficient and reliable optical communication technologies in the future.