Coded unicast downstream traffic in a wireless network: analysis and WiFi implementation

Asaf Cohen 0 Erez Biton 0 Joseph Kampeas 0 Omer Gurewitz 0 0 Department of Communication Systems Engineering, Ben-Gurion University of the Negev , Beer-Sheva, 84105, Israel In this article, we design, analyze and implement a network coding based scheme for the problem of transmitting multiple unicast streams from a single access point to multiple receivers. In particular, we consider the scenario in which an access point has access to infinite streams of data to be distributed to their intended receivers. After each time slot, the access point receives acknowledgments on previous transmissions. Based on the acknowledgements, it decides on the structure of a coded or uncoded packet to be broadcast to all receivers in the next slot. The goal of the access point is to maximize the cumulative throughput or discounted cumulative throughput in the system. We first rigorously model the relevant coding problem and the information available to the access point and the receivers. We then formulate the problem using a Markov decision process with an infinite horizon, analyze the value function under the uncoded and coded policies and, despite the exponential number of states, devise greedy and semi-greedy policies with a running time which is polynomial with high probability. We then analyze the two users case in more detail and show the optimality of the semi-greedy policy in that case. Finally, we describe a simple implementation of the suggested concepts within a WiFi open-source driver. The implementation performs the network coding such that the enhanced WiFi architecture is transparent above the MAC layer. 1 Introduction The inherent broadcast nature of the wireless medium, which allows each transmission to be heard by all users simultaneously, makes network coding techniques pertinent. In such techniques, nodes do not necessarily forward incoming packets. Rather, they can transmit a manipulation (usually a linear combination [1]) of their incoming data. However, in order for such a combination to be valuable to multiple users, each such user needs to possess different piece of the information encoded into the combined packet. Accordingly, one of the key challenges in network coding techniques is to decide which packets to manipulate in each transmission. While efficient algorithms answer this challenge in the multicast setting [2], the problem of multiple unicast remains open [3]. On the down side, the wireless medium characteristics make wireless transmissions susceptible to losses due to noise and interference (i.e., low SNR and SINR). In order to cope with packet loss in MAC layer, conventional wireless protocols rely on retransmissions (e.g., WiFi, [4]). In such protocols, each packet has to be acknowledged by the intended receiver. Packets which are not acknowledged are retransmitted over and over again until they are received successfully by the receiver, or until dropped by the sender. Typical last mile wireless Internet access architecture comprises a gateway, e.g., an access point (AP) or a Base Station (BS), to which all clients are wirelessly connected (e.g., WiFi, WiMAX, LTE). In such architecture, all traffic to and from the wired Internet must pass through the gateway via the wireless medium. Accordingly, all transmissions by the gateway are potentially heard by all clients associated with this gateway. In this article, we utilize these aforementioned wireless properties of channel, protocol and last mile architecture and suggest coded wireless retransmissions for downstream traffic. In particular, we suggest a novel scheme which is based on Markov decision process (MDP [5-7]), that combines multiple MAC layer retransmissions which are intended to different receivers, into a single packet transmission. 1.1 Main contributions Our contributions are thus as follows. First, we suggest an ongoing process in which the AP (or gateway) alternates between transmitting uncoded and coded packets. Receivers acknowledge packets they have received successfully and in addition provide feedbacks to the AP regarding packets they overheard which were not meant for them. Based on these feedbacks the AP chooses which retransmitted packets (if any) should be coded in each retransmission. Our model is inherently not multicast each receiver has a different stream as its demand. Moreover, we assume an infinite horizon model, where there is no point in time in which all demands are met and the system reaches a terminating step. Packets arrive at the AP continuously, and only the current packets for each user are available for coding. Based on this model, we are able to analytically solve throughput problems. We believe that these two aspects of our model are of key importance, since this is the typical use of most wireless Internet access networks. Second, we show that the aforementioned continuous transmission process can be modeled as a discrete time stochastic process, in which at each state the next state is determined solely based on the AP decision which packet to transmit next (i.e., which coded or un-coded packets should comprise the next transmission) and based on the channel state of each and every receiver which determines which nodes receive the next transmission. We suggest an AP policy which is based on MDP theory, in which the reward attained in each iteration corresponds to the number of successful packets received in each transmission. Third, we leverage this continuous, infinite time stochastic model, to compute stationary behavior, which in turn allows us to define convergence, calculate the resulting asymptotic performance efficiently (using only a set of linear equations), and assess the benefit in coding directly and analytically. Specifically, we give the matrix equation that computes the cumulative expected reward (equivalent to the system throughput when a unit reward is given to decoding of one packet) for any state in the system given the transition probabilities and the reward vector. This enables us to directly compute the performance of any coded or un-coded strategy. For the two user case, we indeed give a few possible strategies and compute the resulting performance. Fourth, we show that in order to reach an optimal decision, the AP needs to consider all possible future states of the system, channel states of all users and all possible actions and outcomes. This procedure certainly cannot scale to large number of users. Accordingly, we suggest a greedy approach in which at each transmission the AP tries to maximize the instantaneous reward received for each transmission (as opposed to maximizing an expected or discounted reward, which takes into account the expected rewards at future states). We further suggest an enhancement to the greedy approach, termed semi-greedy approach, which takes some concern into the future, without adding significant complexity to the greedy approach. In the semi-greedy approach, we also suggest a direct analysi (...truncated)