Repetitive signaling using a noisy feedback channel

Abstract

Several feedback coding schemes considered recently are repetitive signaling schemes. The sender retransmits the message, if necessary, on the basis of information received over the feedback channel. This paper considers a repetitive signaling scheme in which the user's estimate of the transmitted message is sent over the feedback channel to the sender with high energy if the user is uncertain of the estimate and with lower energy if otherwise. The sender retransmits the message with high energy if it decides the user's estimate is incorrect. This scheme is applied to a wide-band, additive-white-Gaussian-noise, average-power-constrained feedback communication system. Orthogonal signals are used for transmission over both forward and feedback channels. A lower bound is obtained for the probability of error when arbitrary decision rules are used. This lower bound is achieved asymptotically for long block duration by using decision rules implemented with correlation receivers. The resulting asymptotic error performance is superior to that of any feedback coding scheme previously considered for use in a wide-band additive-white-Gaussian-noise system for any values of the forward and feedback channel capacities.