The capacity of fast fading channels using lattice codes: Is separability necessary?

This paper considers communication over the point-to-point Gaussian channel with stationary and ergodic channel gain and full channel state information. The capacity of this channel can be achieved in a straightforward manner via any capacity-achieving codebook for the non-fading Gaussian channel, in conjunction with separable coding, i.e., coding independently over each fading state. Despite its elegance, separable coding causes substantial delays in the communication process. In this paper, we propose a lattice coding scheme that achieves the fast fading channel capacity without separable coding. Interestingly, the decision regions used are universal for a given channel distribution, as long as the sequence of channel realizations is robustly typical. Some of the techniques used in the achievability proof are of independent interest and can be applied to a variety of channels as well as different classes of codebooks.