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

Abstract

Abstract-A major challenge of wireless multicast is to be 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 successfully addresses this challenge. In particular, we show that our scheme simultaneously achieves both a constant decoding delay and a 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 of the delay distribution, and prove that transmitting 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 the capacity, the average decoding delay under the constant injection process is at most one half of that under a Bernoulli injection process. In addition, we prove that the per-packet encoding and decoding complexity of MWNC-AF both scale as O(log n), with the number of receivers n. Our simulations further underscore the performance of our scheme through comparisons with other schemes and show that the delay, encoding and decoding complexity are low even for a large number of receivers, demonstrating the efficiency, scalability, and ease of implementability of MWNC-AF.Index Terms-Wireless multicast, low delay, low feedback, scaling law analysis.

High Throughput Low Delay Wireless Multicast via Multi-Channel Moving Window Codes

“…The data packets participate in the coding procedure progressively, and hence the receivers are able to decode packets progressively, leading to a lower decoding delay. However, when the traffic load ρ is high (close to 1), the average delay increases dramatically on the order of Θ 1 (1−ρ) 2 [6,8]. Feedback challenge: To achieve reliable multicast or to improve the delay performance (e.g., [2][3][4][6][7][8][9][10]), the transmitter needs to collect channel state information or reception status reports (such as ACKs/NAKs) from the receivers through feedback.…”

“…However, when the traffic load ρ is high (close to 1), the average delay increases dramatically on the order of Θ 1 (1−ρ) 2 [6,8]. Feedback challenge: To achieve reliable multicast or to improve the delay performance (e.g., [2][3][4][6][7][8][9][10]), the transmitter needs to collect channel state information or reception status reports (such as ACKs/NAKs) from the receivers through feedback. Conventionally, the feedback overhead increases linearly with the number of receivers, e.g., [2][3][4][7][8][9][10], which becomes a system bottleneck when the multicast sessions have a large number of receivers.…”

“…To the best of our knowledge, MC-MWC is the first wireless multicast scheme in which the delay decreases linearly as the number of channels grows, with no loss in the per-channel-throughput. • Low Feedback Overhead: By combining MC-MWC with the recently proposed anonymous feedback technique [6,12], the total feedback overhead of MC-MWC is a constant, independent of not only the number of receivers in each session but also the number of sessions in the network. • Trace-driven and numerical results are provided to validate the analytical results and show that 1) MC-MWC achieves significant throughput and delay improvements in the practical scenarios even when the number of users (channels) is not large, 2) the implementation complexity of MC-MWC is low in practice.…”

“…The key idea behind MC-MWC is a simple Merging strategy, through which multiple multicast sessions can be jointly served by the shared multi-channel 1 We use the standard order notation: for two real-valued sequences {xn} and {yn}, xn = o(yn) if limn→∞ xn/yn = 0; and xn = ω(yn) if limn→∞ xn/yn = ∞; and xn = Ω(yn) if limn→∞ xn/yn ≥ z for some constant z > 0; and xn = Θ(yn) if z 1 ≤ limn→∞ xn/yn ≤ z 2 for some constants z 1 > 0 and z 2 > 0.2 In this paper, we consider the end-to-end delay (including queueing delay and transmission delay), which is measured from the time a packet arrives at the transmitter to the time that the packet is decoded at the receiver. In comparison, the delay metric considered in e.g., [5,6,9,10] only accounts for the transmission delay. arXiv:1801.01613v1 [cs.IT] 5 Jan 2018(55)Consider 1 {I d >k} I d and 1 {Ij >k} as the rewards earned in interval I d .…”

“…2 In this paper, we consider the end-to-end delay (including queueing delay and transmission delay), which is measured from the time a packet arrives at the transmitter to the time that the packet is decoded at the receiver. In comparison, the delay metric considered in e.g., [5,6,9,10] only accounts for the transmission delay. arXiv:1801.01613v1 [cs.IT] 5 Jan 2018…”