Bounds on maximum throughput for digital communications with finite-precision and amplitude constraints

The following problem is discussed: given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t ₀ by at least some small positive constant d, then what is the maximum number of messages, N, that can be transmitted in a given time interval [0, T]? Upper bounds for arbitrary h(t) are computed by solving linear programs with bounded variables and one equality constraint. Solutions to linear programs in this class can be obtained very fast using, for example, a linear-time algorithm due to C. Witzgall (1980). Numerical results are shown for different impulse responses, including a simulated telephone subscriber loop impulse response. Assuming that the receiver resolution d is small, the upper bound is typically two to three times the lower bound for the cases examined