Optimum message transmission in a finite time

The basic problem of transmitting information through a noisy channel in a finite time with the least error is considered. The transmitted signals are either peak or average power limited, and the interference is presumed to be additive white gaussian noise. It is shown that the optimum signals are sequences of binary waveforms resembling a Slepian group code, the generators of which can be obtained from a modified Reed Code. An analysis is also made of near-optimum codes which allow some inequality in the distance between code words in signal space. The advantage of these near-optimum codes is that for a small sacrifice in error probability, either the information rate can be substantially increased, or the bandwidth of the system greatly reduced. The details of these sytems are given and the results show that a many-fold improvement is obtained. An instrumentation of the detector is also presented to show how the code groups at the receiver can be effectively stored as an arrangement of resistors.