On the Performance of a Feedback Communication System Utilizing a Cumulative Decision Scheme

A cumulative decision scheme that can be employed in a feedback communication system is treated. Any decision to decode depends upon all messages that have been received prior to the decision. The average error over all transmissions as well as the forward error may be controlled. Performance is compared to an error-detection repeat-request noncumulative scheme utilizing group codes. Optimal performance of the cumulative scheme with respect to the noncumulative scheme is given for short-length best group codes. It is also demonstrated that the use of feedback does not necessarily increase appreciably the amount of hardware necessary to effect error control.