This thesis considers the communication situation where repetitions of a message sequence are used to improve the reliability of correct reception. This problem arises in systems where the transmitted power is inherently insufficient.

A general model for the above problem is formulated, from which the optimum receiver is derived and its probability of error calculated. Then we examine a case of PAM transmission of repeated signals in which the optimum receiver is greatly simplified. For this case we derive a suboptimum receiver which is easier to implement and whose performance compares favourably with the optimum one.

Finally, we discuss applications of the above schemes to the "SARSAT" satellite program.