  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.
