In this paper, we study the problem of distributing a real-time video sequence to a group of partially connected cooperative wireless devices using instantly decodable network coding (IDNC). In such a scenario, the coding conflicts occur to service multiple devices with an immediately decodable packet and the transmission conflicts occur from simultaneous transmissions of multiple devices. To avoid these conflicts, we introduce a novel IDNC graph that represents all feasible coding and transmission conflict-free decisions in one unified framework. Moreover, a real-time video sequence has a hard deadline and unequal importance of video packets. Using these video characteristics and the new IDNC graph, we formulate the problem of minimizing the mean video distortion before the deadline as a finite horizon Markov decision process (MDP) problem. However, the backward induction algorithm that finds the optimal policy of the MDP formulation has high modelling and computational complexities. To reduce these complexities, we further design a two-stage maximal independent set selection algorithm, which can efficiently reduce the mean video distortion before the deadline. Simulation results over a real video sequence show that our proposed IDNC algorithms improve the received video quality compared to the existing IDNC algorithms.
In the context of partially connected networks, the related works to our work are @cite_7 @cite_1 @cite_37 @cite_22 . In particular, the authors in @cite_7 provided various necessary and sufficient conditions that characterize the number of transmissions required to recover all missing packets at all devices. The authors in @cite_1 continued the work in @cite_7 and showed that solving the minimum number of transmissions problem exactly or even approximately is computationally intractable. Moreover, the authors in @cite_7 @cite_1 adopted algebraic network coding in large finite fields. Unlike the works in @cite_7 @cite_1 , we consider erasure channels, XOR based network coding, explicit packet delivery deadline and unequal importance of video packets.
@cite_37 @cite_1 @cite_22 @cite_7
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Consider a scenario of broadcasting a common content to a group of cooperating wireless nodes that are within proximity of each other. Nodes in this group may receive partial content from the source due to packet losses over wireless broadcast links. We further consider that packet losses are different for different nodes. The remaining missing content at each node can then be recovered, thanks to cooperation among the nodes. In this context, the minimum amount of time that can guarantee a complete acquisition of the common content at every node is referred to as the completion time. It has been shown that instantly decodable network coding (IDNC) reduces the completion time as compared to no network coding in this scenario. Yet, for applications such as video streaming, not all packets have the same importance and not all users are interested in the same quality of content. This problem is even more interesting when additional, but realistic constraints, such as strict deadline, bandwidth, or limited energy are added to the problem formulation. We assert that direct application of IDNC in such a scenario yields poor performance in terms of content quality and completion time. In this paper, we propose a novel Content-Aware IDNC scheme that improves content quality and network coding opportunities jointly by taking into account significance of each packet towards the desired quality of service (QoS). Our proposed Content-Aware IDNC maximizes the quality under the completion time constraint, and minimizes the completion time under the quality constraint.We demonstrate the benefits of Content-Aware IDNC through simulations. Consider a connected network of n nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and exchanges coded packets with its neighbors. This paper provides necessary and sufficient conditions that characterize the set of all transmission strategies that permit every node to ultimately learn (recover) all k packets. When the network satisfies certain regularity conditions and packets are randomly distributed, this paper provides tight concentration results on the number of transmissions required to achieve universal recovery. For the case of a fully connected network, a polynomial-time algorithm for computing an optimal transmission strategy is derived. An application to secrecy generation is discussed. We consider the scenario of broadcasting for realtime applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested in finding a code that is instantly decodable by the maximum number of users. First, we prove that this problem is NP-Hard in the general case. Then we consider the practical probabilistic scenario, where users have i.i.d. loss probability, and the number of packets is linear or polynomial in the number of users. In this case, we provide a polynomial-time (in the number of users) algorithm that finds the optimal coded packet. Simulation results show that the proposed coding scheme significantly outperforms an optimal repetition code and a COPE-like greedy scheme. We consider scenarios where wireless clients are missing some packets, but they collectively know every packet. The clients collaborate to exchange missing packets over an error-free broadcast channel with capacity of one packet per channel use. First, we present an algorithm that allows each client to obtain missing packets, with minimum number of transmissions. The algorithm employs random linear coding over a sufficiently large field. Next, we show that the field size can be reduced while maintaining the same number of transmissions. Finally, we establish lower and upper bounds on the minimum number of transmissions that are easily computable and often tight as demonstrated by numerical simulations.