Abstract
For several years, the completion time and the decoding delay problems in instantly decodable network coding (IDNC) were considered separately and were thought to act completely against each other. Recently, some works have aimed to balance the effects of these two important IDNC metrics, but none of them studied a further optimization of one by controlling the other. This paper investigates the effect of controlling the decoding delay to reduce the completion time below its currently best known solution in both perfect and imperfect feedback with persistent erasure channels. To solve the problem, the decoding-delay-dependent expressions of the users' and overall completion times are derived in the complete feedback scenario. Although using such expressions to find the optimal overall completion time is NP-hard, this paper proposes two novel heuristics that minimize the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Afterward, this paper extends the study to the imperfect feedback scenario, in which uncertainties at the sender affect its ability to anticipate accurately the decoding delay increase at each user. This paper formulates the problem in such an environment and derives the expression of the minimum increase in the completion time. Simulation results show the performance of the proposed solutions and suggest that both heuristics achieve a lower mean completion time, as compared with the best known heuristics for completion time reduction in perfect and imperfect feedback. The gap in performance becomes more significant as the erasure of the channel increases.