A coding scheme for additive noise channels with feedback--II: Band-limited signals

In Part I of this paper, we presented a scheme for effectively exploiting a noiseless feedback link associated with an additive white Gaussian noise channel with {\em no} signal bandwidth constraints. We now extend the scheme for this channel, which we shall call the wideband (WB) scheme, to a band-limited (BL) channel with signal bandwidth restricted to
(- W, W)
. Our feedback scheme achieves the well-known channel capacity,
C = W \ln (1 +P_{u,v}/N_{0} W)
, for this system and, in fact, is apparently the first deterministic procedure for doing this. We evaluate the fairly simple exact error probability for our scheme and find that it provides considerable improvements over the best-known results (which are lower bounds on the performance of sphere-packed codes) for the one-way channel. We also study the degradation in performance of our scheme when there is noise in the feedback link.