  Optical communication channels are ultimately quantum-mechanical in nature,
and we must therefore look beyond classical information theory to determine
their communication capacity as well as to find efficient encoding and decoding
schemes of the highest rates. Thermal channels, which arise from linear
coupling of the field to a thermal environment, are of particular practical
relevance; their classical capacity has been recently established, but their
quantum capacity remains unknown. While the capacity sets the ultimate limit on
reliable communication rates, it does not promise that such rates are
achievable by practical means. Here we construct efficiently encodable codes
for thermal channels which achieve the classical capacity and the so-called
Gaussian coherent information for transmission of classical and quantum
information, respectively. Our codes are based on combining polar codes with a
discretization of the channel input into a finite "constellation" of coherent
states. Encoding of classical information can be done using linear optics.
