  We present an algorithm for calculation of the Gaussian classical capacity of
a quantum bosonic memory channel with additive Gaussian noise. The algorithm,
restricted to Gaussian input states, is applicable to all channels with noise
correlations obeying certain conditions and works in the full input energy
domain, beyond previous treatments of this problem. As an illustration, we
study the optimal input states and capacity of a quantum memory channel with
Gauss-Markov noise [J. Sch\"afer, Phys. Rev. A 80, 062313 (2009)]. We evaluate
the enhancement of the transmission rate when using these optimal entangled
input states by comparison with a product coherent-state encoding and find out
that such a simple coherent-state encoding achieves not less than 90% of the
capacity.
