1. A communications system, comprising: a transmitter for transmitting a signal includes a sequence of symbols; a receiver for the sequence of symbols; and a channel coupling the transmitter to the receiver; the sequence of symbols including at least two different symbols which can be transmitted in one-unit interval and each symbol associated with its own signal level; the sequence of symbols defining an eye diagram for graphically representing in one or more eyes all possible unit-interval sized waveforms of a signal overlain in a graph one-unit interval wide; the eye diagram having a horizontal axis representing a time axis and a vertical axis representing the signal level; each eye forming a polygon having a horizontal axis representing a time axis and a vertical axis representing the signal level; a bounding box defining a region of each eye in the eye diagram bounded in time to a middle half of the unit interval and bounded in signal level by specific signal levels just below and just above the eye; a sampling point in the unit interval within each eye to determine which signal the waveform in any unit interval represents; means for determining a maximal convex subset within each eye; and means for determining a largest orthogonal rectangle that fits in the convex subset of each eye; the sampling point for each eye being positioned at a signal level equal to the center of the rectangle.