  We propose a simple architecture based on multimode quantum memories for
collective readout of classical information keyed using a pair coherent states,
exemplified by the well-known binary phase shift keying format. Such a
configuration enables demonstration of the superadditivity effect in classical
communication over quantum channels, where the transmission rate becomes
enhanced through joint detection applied to multiple channel uses. The proposed
scheme relies on the recently introduced idea to prepare Hadamard sequences of
input symbols that are mapped by a linear optical transformation onto the pulse
position modulation format [Guha, S. {\em Phys. Rev. Lett.}\ {\bf 2011}, {\em
106}, 240502]. We analyze two versions of readout based on direct detection and
an optional Dolinar receiver which implements the minimum-error measurement for
individual detection of a binary coherent state alphabet.
