  A scheme for transferring classical information over a lossy bosonic channel
is proposed by generalizing the proposal presented in Phys. Rev. Lett. 106,
240502 (2011) by Guha. It employs codewords formed by products of coherent
states of fixed mean photon number with multiple phases which, through a
passive unitary transformation, reduce to a Pulse-Position Modulation code with
multiple pulse phases. The maximum information rate achievable with optimal,
yet difficult to implement, detection schemes is computed and shown to saturate
the classical capacity of the channel in the low energy regime. An easy to
implement receiver based on a conditional Dolinar detection scheme is also
proposed finding that, while suboptimal, it allows for improvements in an
intermediate photon-number regime with respect to previous proposals.
