Retransmission schemes for communication systems with applications to group codes

Communication systems are considered in which there exists an auxiliary channel over which the receiver can make requests for retransmission. In general, it is assumed that the auxiliary channel is noiseless and the main channel is discrete and memoryless. It is also assumed that the a priori probabilities of the message symbols are known. A sequential receiver strategy is introduced which at each step minimizes the probability of retransmission subject to the condition that the probability of incorrect decoding does not exceed a given limit. The strategy is easy to implement in the case where group codes are used as error correctors and detectors. Moreover, in this case, conditions are given for which the strategy terminates with probability I, regardless of whether it is truncated. Examples are given for illustration.