Optimizing completion delay in network coded systems over TDD erasure channels with memory

In this paper, we consider a network comprising a sender and a receiver in a time division duplex (TDD) erasure channel with memory, where transmission of network coded packets by the sender and listening to feedback from the receiver (about how many more coded packets are required) occur in rounds. The main objective is to decide the number of transmissions in the next round based on the received feedback such that the expected transmission time of M packets is minimized. Compared to previous studies where only memoryless erasures were considered, we incorporate memory into the optimization framework through a Gilbert-Elliot channel (GEC) model with Good and Bad states at the bit level and packet level. We then utilize infrequent feedbacks about the last channel state to make a more informed decision about the optimum number of coded packets for the next transmission round. Our numerical results show that when the memory content of the channel is relatively high, our scheme can make significant improvement in the mean completion delay (as high as 74%) compared to the scheme which is oblivious to the erasure temporal correlations. We also study the effect of packet length on the delay/throughput optimization in our framework and discuss its implications for the design of practical transmission networks.