A two-way communication problem with application to information retrieval

A special case of two-way communication is considered. Two memoryless channels are used. The forward channel carries questions, generated by a memoryless source. Each question specifies a component of a vector, generated by a memoryless vector source. The value of that component is transmitted to the requesting party via the backward channel. The goal is to minimize the capacity required in the backward channel when the information rate in the forward channel is given. The result is formulated as a coding theorem stating the necessary and sufficient capacity of the backward channel when all possible questions are equally likely and the components of the above mentioned vector are independent stochastic variables with equal entropy. Some explicit codes are also derived. The rates of these codes are close to the necessary minimum. The nonsymmetric case where the questions have unequal probability and the vector components have unequal entropy is reformulated as a source coding problem.