On capacity of optical channels with coherent detection

Optical channel with direct detections, also known as Poisson channel, is well studied. With direction detections, only the intensity of the optical signal is measured and used as the carrier of information. In coherent detection, the phase of optical signal is also utilized. Constrained by optical devices, it is hard to directly measure this phase. However, it is possible to mix the input signal with a local reference signal to create output that is phase dependent. Generating such local signals can be based on the instantaneous receiver knowledge, and updated from time to time. We study the channel capacity of such channel, and make connection to the recent development in feedback channels. We are particularly interested in the low SNR regime, and present a capacity result based on a new scaling law.