Achievable rates for a constrained Gaussian channel.

We consider a continuous-time channel where the input waveform x(t) is constrained to take on but two values, i.e. x(t) = +-square root P, where P is the signal power. The signal is passed through a linear filter and added to white Gaussian noise. With a suitable choice of filter, this channel is a model of the channel corresponding to a magnetic storage medium. We are interested in the channel capacity, C(0), of this channel, and in particular the relation of C(0) to C(p) and C(AV), where C(p) is the capacity of the same channel with the two- level constraint on x(t) replaced by the "peak-power" constraint /x(t)/ = square root P, and C(AV) the capacity of the channel with the (classical) "average-power" constraint 1 over T integral (T)(0) x(2)(t)dt = P, for Large T. It has been known for some time how to compute C(AV). Of course C(0) = C(p) = C(AV), and one of our main results is the surprising fact that C(0) = C(p). We cannot find C(0) = C(p) exactly, but in this paper we obtain, for certain filters, lower bounds which are fairly close to C(AV).