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

Multi-Phase Hadamard receivers for classical communication on lossy bosonic channels