On Minimizing the Maximum Broadcast Decoding Delay for Instantly Decodable Network Coding

In this paper, we consider the problem of minimizing the maximum broadcast decoding delay experienced by all the receivers of generalized instantly decodable network coding (IDNC). Unlike the sum decoding delay, the maximum decoding delay as a definition of delay for IDNC allows a more equitable distribution of the delays between the different receivers and thus a better Quality of Service (QoS). In order to solve this problem, we first derive the expressions for the probability distributions of maximum decoding delay increments. Given these expressions, we formulate the problem as a maximum weight clique problem in the IDNC graph. Although this problem is known to be NP-hard, we design a greedy algorithm to perform effective packet selection. Through extensive simulations, we compare the sum decoding delay and the max decoding delay experienced when applying the policies to minimize the sum decoding delay [1] and our policy to reduce the max decoding delay. Simulations results show that our policy gives a good agreement among all the delay aspects in all situations and outperforms the sum decoding delay policy to effectively minimize the sum decoding delay when the channel conditions become harsher. They also show that our definition of delay significantly improve the number of served receivers when they are subject to strict delay constraints

Delay Minimization for Instantly Decodable Network Coding in Persistent Channels with Feedback Intermittence

In this paper, we consider the problem of minimizing 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 persisten

Completion Time Reduction in Instantly Decodable Network Coding Through Decoding Delay Control

For several years, the completion time and decoding delay problems in Instantly Decodable Network Coding (IDNC) were considered separately and were thought to completely act against each other. Recently, some works aimed to balance the effects of these two important IDNC metrics but none of them studied a further optimization of one by controlling the other. In this paper, we study the effect of controlling the decoding delay to reduce the completion time below its currently best known solution. We first derive the decoding-delay-dependent expressions of the users' and overall completion times. Although using such expressions to find the optimal overall completion time is NP-hard, we design a novel heuristic that minimizes the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Simulation results show that this new algorithm achieves both a lower mean completion time and mean decoding delay compared to the best known heuristic for completion time reduction. The gap in performance becomes significant for harsh erasure scenarios

On Throughput and Decoding Delay Performance of Instantly Decodable Network Coding

In this paper, a comprehensive study of packet-based instantly decodable network coding (IDNC) for single-hop wireless broadcast is presented. The optimal IDNC solution in terms of throughput is proposed and its packet decoding delay performance is investigated. Lower and upper bounds on the achievable throughput and decoding delay performance of IDNC are derived and assessed through extensive simulations. Furthermore, the impact of receivers' feedback frequency on the performance of IDNC is studied and optimal IDNC solutions are proposed for scenarios where receivers' feedback is only available after and IDNC round, composed of several coded transmissions. However, since finding these IDNC optimal solutions is computational complex, we further propose simple yet efficient heuristic IDNC algorithms. The impact of system settings and parameters such as channel erasure probability, feedback frequency, and the number of receivers is also investigated and simple guidelines for practical implementations of IDNC are proposed.Comment: This is a 14-page paper submitted to IEEE/ACM Transaction on Networking. arXiv admin note: text overlap with arXiv:1208.238

Rate Aware Instantly Decodable Network Codes

This paper addresses the problem of reducing the delivery time of data messages to cellular users using instantly decodable network coding (IDNC) with physical-layer rate awareness. While most of the existing literature on IDNC does not consider any physical layer complications and abstract the model as equally slotted time for all users, this paper proposes a cross-layer scheme that incorporates the different channel rates of the various users in the decision process of both the transmitted message combinations and the rates with which they are transmitted. The consideration of asymmetric rates for receivers reflects more practical application scenarios and introduces a new trade-off between the choice of coding combinations for various receivers and the broadcasting rate for achieving shorter completion time. The completion time minimization problem in such scenario is first shown to be intractable. The problem is, thus, approximated by reducing, at each transmission, the increase of an anticipated version of the completion time. The paper solves the problem by formulating it as a maximum weight clique problem over a newly designed rate aware IDNC (RA-IDNC) graph. The highest weight clique in the created graph being potentially not unique, the paper further suggests a multi-layer version of the proposed solution to improve the obtained results from the employed completion time approximation. Simulation results indicate that the cross-layer design largely outperforms the uncoded transmissions strategies and the classical IDNC scheme

A Graph Model for Opportunistic Network Coding

Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase in complexity. In this paper, we design a simple IDNC-like graph model for a specific subclass of ONC, by introducing a more generalized definition of its vertices and the notion of vertex aggregation in order to represent the storage of non-instantly-decodable packets in ONC. Based on this representation, we determine the set of pairwise vertex adjacency conditions that can populate this graph with edges so as to guarantee decodability or aggregation for the vertices of each clique in this graph. We then develop the algorithmic procedures that can be applied on the designed graph model to optimize any performance metric for this ONC subclass. A case study on reducing the completion time shows that the proposed framework improves on the performance of IDNC and gets very close to the optimal performance

Generalized Instantly Decodable Network Coding for Relay-Assisted Networks

In this paper, we investigate the problem of minimizing the frame completion delay for Instantly Decodable Network Coding (IDNC) in relay-assisted wireless multicast networks. We first propose a packet recovery algorithm in the single relay topology which employs generalized IDNC instead of strict IDNC previously proposed in the literature for the same relay-assisted topology. This use of generalized IDNC is supported by showing that it is a super-set of the strict IDNC scheme, and thus can generate coding combinations that are at least as efficient as strict IDNC in reducing the average completion delay. We then extend our study to the multiple relay topology and propose a joint generalized IDNC and relay selection algorithm. This proposed algorithm benefits from the reception diversity of the multiple relays to further reduce the average completion delay in the network. Simulation results show that our proposed solutions achieve much better performance compared to previous solutions in the literature.Comment: 5 pages, IEEE PIMRC 201