Incoherent on-off keying with classical and non-classical light

We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the $g^{(2)}$ second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.