On The Probability of Error Using a Repeat-Request Strategy on the Additive White Gaussian Noise Channel

In a recent paper, Forney studied a repeat-request strategy for communication of digital information over a discrete memoryless channel when a fedback channel is available. 3 In this system the receiver decodes a received message only when it is relatively "sure" that one particular message was actually transmitted. If the receiver is not confident that one particular message was actually transmitted, then it requests (via the feedback channel) that the transmitter repeat the message. Forney showed that considerable improvement in the resulting error probability (over the best one-way scheme) was obtainable with a negligible degradation in the effective rate of transmission. In this paper we apply Forney's ideas to the additive white Gaussian noise channel (with no bandwidth constraint) and obtain analogous results. Furthermore, our coding scheme is constructive-- the codes being orthogonal codes. 71 72 T H E BELL SYSTEM TECHNICAL JOURNAL. JANUARY 1969 We will consider the following channel. The channel input signal is a real-valued function s(t), defined on the interval [0, T], which satisfies the "energy" constraint T