Delay-Optimal Hybrid ARQ Protocol Design for Channels and Receivers with Memory as a Stochastic Control Problem

Automatic repeat request (ARQ) protocols are utilized as a flexible way to adapt data transmission to channel variations whenever a feedback channel is available. The transmitter encodes the information into a packet and the receiver attempts to decode it. If decoding is not successful, the receiver signals the transmitter to either resend the same information or send additional information about the data. In this paper we consider ARQ protocols where the transmitter controls the amount of error correction capability introduced in the information sequence to minimize the expected delay. We formulate this problem as a stochastic control problem and study two cases of interest depending on whether or not the receiver feeds back information about the channel state. Some of the benefits of this formulation are an expression for the optimal packet size and delay as a solution of a fixed point equation and a unified treatment for channels with Markov statistics and for receivers with memory.