Constant-Delay and Constant-Feedback Moving Window Network Coding for Wireless Multicast: Design and Asymptotic Analysis

A major challenge of wireless multicast is being able to support a large number of users while simultaneously maintaining low delay and low feedback overhead. In this paper, we develop a joint coding and feedback scheme named moving window network coding with anonymous feedback (MWNC-AF) that simultaneously achieves constant decoding delay and constant feedback overhead, irrespective of the number of receivers n, without sacrificing either throughput or reliability. We explicitly characterize the asymptotic decay rate of the tail probability of the decoding delay and prove that injecting a fixed amount of information bits into the MWNC-AF encoder buffer in each time slot (called “constant data injection process”) achieves the fastest decay rate, thus showing how to obtain delay optimality in a large deviation sense. We then investigate the average decoding delay of MWNC-AF and show that, when the traffic load approaches capacity, the average decoding delay under the constant injection process is at most one half of that under a Bernoulli injection process. We prove that the per-packet encoding and decoding complexities of MWNC-AF both scale as O(logn) and are thus insensitive to the increase of the number of receivers n. Our simulations further underscore the performance of our scheme through comparisons with existing schemes and show that the delay, encoding, and decoding complexities are low even for a large number of receivers, demonstrating the efficiency, scalability, and ease of implementability of MWNC-AF.