Reliability-based Rate Allocation in Wireless Inter-session Network Coding Systems Keivan Ronasi, A. Hamed Mohsenian-Rad, Vincent W. S. Wong, Sathish Gopalakrishnan, and Robert Schober Department of Electrical and Computer Engineering The University of British Columbia, Vancouver, Canada e-mail: {keivanr, hamed, vincentw, sathish, rschober}@ece.ubc.ca Abstract— Network coding has recently received increasing attention to improve performance and increase capacity in both wired and wireless communication networks. In this paper, we focus on inter-session network coding, where multiple unicast sessions jointly participate in network coding. Wireless links are often unreliable because of varying channel conditions. We con- sider multi-hop unicast sessions over unreliable links and propose a distributed end-to-end transmission rate adjustment mecha- nism to maximize the aggregate network utility by taking into account the wireless link reliability information. This includes an elaborate modeling of end-to-end reliability. Simulation results show that by taking into account the reliability information, we can increase the network throughput by up to 100% for some network topologies. We can also increase the aggregate network utility significantly for various choices of utility functions. I. I NTRODUCTION Following the seminal paper by Ahlswede et al. [1], a rich body of work has focused on developing techniques to improve network performance using network coding. Network coding can be performed by jointly encoding multiple packets either from the same source or from different sources. The former is called intra-session network coding [1] while the latter is called inter-session network coding [2]. Network coding has been shown as a promising approach in commu- nication networking, particularly for maximizing capacity in wireless networks [3]. Other network coding design objectives include maximizing network lifetime [4], minimizing energy consumption [5], and maximizing the network throughput [6]. Wireless networks are usually unreliable (i.e., data flows may experience significant packet losses) due to channel imperfection, noise, and interference. It is crucial to de- velop strategies to improve reliability in wireless networks. Ghaderi et al. [7] determined the reliability gain of intra- session network coding for multicast flows. In their work, the expected number of retransmissions per packet is used as the performance metric for reliability. Reliability in intra-session network coding is also studied by Lun et al. in [8]. Lee et al. [9] proposed a method for rate allocation with reliability considerations but without network coding. In this paper, we focus on inter-session network coding for multiple unicast sessions in a wireless network. Our objective is to increase the network utility and the end-to-end reliability of data transmissions (e.g., HTTP, FTP, P2P traffic) by proper allocation of routing and inter-session network coding rates for each data source in the network. For this purpose, we use the failure probability of intermediate links to calculate the relia- bility (i.e., the probability that data is successfully received) of various routing and network coding paths. Given the calculated reliability information, we maximize the effective aggregate network throughput by choosing the optimal rate allocation for network coding paths. We use the network utility maximization framework developed by Kelly et al. in [10]. To the best of our knowledge, there has been no prior work on improving the end-to-end reliability in an inter-session network coding system among unicast sessions. The contributions of this paper are as follows: • We develop a recursive algorithm to calculate end-to- end reliability, i.e., the probability of correctly delivering a packet, over each routing and network coding path. This allows us to mathematically model the effective throughput for each unicast session in the network. • We formulate a network utility maximization problem for unreliable inter-session network coding systems. This problem formulation takes into account the network topology, mutual interference among wireless links, ses- sion utility functions, and link reliability information. • We propose a distributed algorithm to solve the formu- lated network utility maximization problem using the proximal method and gradient projection. • Simulation results show that by taking into account the reliability information, the aggregate network throughput can be increased by up to 100% while the aggregate network utility is also improved significantly. Unlike intra-session network coding, there is no dominant coding scheme for inter-session network coding. Our inter- session network coding scheme is similar to the scheme by Khreishah et al. in [6] for wired networks. However, we extend that model in [6] to the wireless networking case by representing wireless capacity using the contention graph. Fur- thermore, we take reliability information into consideration. In this regard, the system model in [6] can be considered as a special case of our inter-session network coding model. Our proposed approach is based on cooperation among all network users. Game theoretic analysis of inter-session network coding with non-cooperative users is also studied in [11]. The rest of this paper is organized as follows. The system model is described in Section II. Our algorithm to calculate end-to-end reliability is presented in Section III. We solve the considered network utility maximization problem in Section IV using a distributed algorithm. Simulation results are pre- sented in Section V. Conclusions are given in Section VI.