In this paper, we introduce a game theoretic frame- work for studying the problem of minimizing the delay of instantly decodable network coding (IDNC) for cooperative data exchange (CDE) in decentralized wireless network. In this configuration, clients cooperate with each other to recover the erased packets without a central controller. Game theory is employed herein as a tool for improving the distributed solution by overcoming the need for a central controller or additional signaling in the system. We model the session by self- interested players in a non-cooperative potential game. The utility functions are designed such that increasing individual payoff results in a collective behavior achieving both a desirable system performance in a shared network environment and the Nash bargaining solution. Three games are developed: the first aims to reduce the completion time, the second to reduce the maximum decoding delay and the third the sum decoding delay. We improve these formulations to include punishment policy upon collision occurrence and achieve the Nash bargaining solution. Through extensive simulations, our framework is tested against the best performance that could be found in the conventional point- to-multipoint (PMP) recovery process in numerous cases: first we simulate the problem with complete information. We, then, simulate with incomplete information and finally we test it in lossy feedback scenario. Numerical results show that our formulation with complete information largely outperforms the conventional PMP scheme in most situations and achieves a lower delay. They also show that the completion time formulation with incomplete information also outperforms the conventional PMP. Index Terms—Cooperative data exchange, instantly decodable network coding, non-cooperative games, potential game, Nash equilibrium.
In this paper, we consider the problem of min- imizing the multicast decoding delay of generalized instantly decodable network coding (G-IDNC) over persistent forward and feedback erasure channels with feedback intermittence. In such an environment, the sender does not always receive acknowledgement from the receivers after each transmission. Moreover, both the forward and feedback channels are subject to persistent erasures, which can be modelled by a two state (good and bad states) Markov chain known as Gilbert-Elliott channel (GEC). Due to such feedback imperfections, the sender is unable to determine subsequent instantly decodable packets combination for all receivers. Given this harsh channel and feedback model, we first derive expressions for the probability distributions of decoding delay increments and then employ these expressions in formulating the minimum decoding problem in such environment as a maximum weight clique problem in the G-IDNC graph. We also show that the problem formulations in simpler channel and feedback models are special cases of our generalized formulation. Since this problem is NP-hard, we design a greedy algorithm to solve it and compare it to blind approaches proposed in literature. Through extensive simulations, our adaptive algorithm is shown to outperform the blind approaches in all situations and to achieve significant improvement in the decoding delay, especially when the channel is highly persistent. Index Terms—Multicast Channels, Persistent Erasure Chan- nels, G-IDNC, Decoding Delay, Lossy Intermittent Feedback, Maximum Weight Clique Problem.