Geometrical Bounds on the Capacity of the Binary Bipolar Input AWGN Channel

We study power-effective communication systems over band-limited Additive White Gaussian Noise channels in which the transmitter's output is constrained to be symmetric binary (bipolar) or peak-limited. New geometrical analysis is introduced, and the admissible band-limited signals are shown to form a convex set. We improved the previous upper and lower bounds on capacity, the gap between the upper and lower bounds on capacity at high SNR is reduced to 1.7dB. New attributes of the optimal signals are derived, mainly the central role of binary signals with sign transition rate not exceeding the Nyquist rate of the channel. The results rely on an extensive numerical evaluation and would benefit from further analytical progress.