A Practical Perspective of Wireless Network Coding Marium Jalal Chaudhry 1,2 , Timo H¨ am¨ al¨ ainen 1 , Jyrki Joutsensalo 1 , Farhat Saleemi 2 , Kari Luostarinen 3 1 Department of Information Technology, University of Jyv¨ askyl¨ a, Finland 2 Department of Electronic Engineering, Lahore College For Women University, Lahore, Pakistan 3 Metso Paper Inc. Jyv¨ askyl¨ a, Finland Abstract—Wireless networks are one of the most essential components of the communication networks. In contrast to the wired networks, the inherent broadcast nature of wireless networks provides a breeding ground for both opportunities and challenges ranging from security to reliability. Moreover, energy is a fundamental design constraint in wireless networks. The boom of wireless network is closely coupled with the schemes that can reduce energy consumption. Network coding for the wireless networks is seen as a potential candidate scheme that can help overcome the energy and security challenges while providing significant benefits. This paper presents a basic model for formulating network coding problem in wireless setting. Since the optimal solution to wireless network coding is NP (non- deterministic polynomial-time)-hard, we intend to explore the impact of different parameters with random and non-random solutions. We present extensive simulation to show the strength of random network coding scheme in general wireless network scenarios. This study provide a comprehensive insight into the limits of wireless network coding. I. I NTRODUCTION Wireless networks are one of the most essential components of the communication networks. In contrast to the wired networks, the inherent broadcast nature of wireless networks provides a breeding ground for both opportunities and chal- lenges ranging from security to reliability. Moreover, energy is a fundamental design constraint in wireless networks. The boom of wireless network is closely coupled with the schemes that can reduce energy consumption. Network coding for the wireless networks is seen as a potential candidate scheme that can help overcome the energy and security challenges while providing significant benefits. In reference to its applications in wireless network, the typical setting of the network coding problem of consist of a server and a set of clients. Server has set of all packets needed by clients. Each client needs a packet( or packets) called required packets and might have overheard packets due to broadcast nature of wireless networks during some previous transmission. Server can make use of the overheard packets at the clients to reduce the overall number of transmissions. The goal of the wireless network coding problem is to reduce the number of transmissions as explained in the following example. Consider an example of a simple wireless network shown in Fig 1 consisting of a server and four clients. In this example a server(wireless tower) needs to satisfy 4 wireless clients by transmitting 4 packets p 1 ,p 2 ,p 3 ,p 4 if it does not use network coding but using network coding the transmissions is reduced to half i.e. p 1 + p 2 and p 3 + p 4 . Unfortunately optimal solution to network coding problem for wireless network is NP-Complete i.e. a polynomial time so- lution does not exist. Therefore finding the minimum number Required: P Overheared: P Required: P Overheared: P Required: P Overheared: P Required: P Overheared: P Fig. 1. An example of network coding in wireless networks of transmissions and the coded packet combinations that can help in reducing the number of transmissions is not possible in a realistic time for any general input. Due to hardness of finding exact solution to the problem, a set of algorithms is developed to address the issue which, in most of the practical situations, guarantees a lesser number of transmissions as compared to traditional schemes although not the least one. This paper presents a basic model for formulating network coding problem in wireless setting. Since the optimal solution to wireless network coding is NP-hard [1], we intend to ex- plore the impact of different parameters with random and non- random solutions. We present extensive simulation to show the strength of random network coding scheme in general wireless network scenarios. This study provide a comprehensive insight into the limits of wireless network coding. II. PREVIOUS WORK The network coding was firstly introduced by Ahlswede et al. [2] in 2000. Figure 2 represents the famous example given by Ahlswede et al. showing the necessity of using network coding i.e., coding at the intermediate nodes of the network in order to achieve multicast capacity. The main result by Ahlswede et al. [2] was to show that network coding can help to send the data traffic at the same rate as the min-cut between the sender and the receiver. The work on network coding was further explored by Koetter and Medard [3] giving Corresponding author Marium Jalal Chaudhry mariumjalal@yahoo.com