We consider joint optimization of data routing and resource allocation in multicast multihop wireless networks where interference between links is taken into account. The use of network coding in such scenarios leads to a nonconvex optimization problem. By applying the probability collectives (PCs) technique the original problem is turned into a new problem which is convex over probability distributions. The resulting problem is then further decomposed into a data routing subproblem at network layer and a power allocation subproblem at physical layer in order to achieve a cross-layer distributed solution for the whole range of SINR values. The proposed approach is also extended to minimum cost multicast problems and routing problems based on multicommodity flow and single Steiner tree, resulting in new distributed algorithms for such problems.

In this paper, we propose a new analytical model for stable throughput evaluation of wireless network coding. In this new approach we consider the arrival and departure rates in and from the wireless nodes, respectively, in steady state. Our analytical model is founded on a multi-class open queueing network. In this model, we include two basic processes of network coding, i.e., packets combination and packets multicasting, in a suitable manner considering the constraints of the queueing networks. In this respect, we consider the coded packets as new classes of customers. By solving the related traffic equations and applying the stability condition, we compute the maximum stable throughput, i.e., the maximum packet generation rate at which the packets reach their destinations with finite delays. We apply our approach to a symmetric WLAN with unicast flows and a slotted random access MAC scheme, and compute the maximum stable throughputs for the cases of simple routing and network coding, distinctly. Finally, we confirm our analytical results by simulation.

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Abstract-We investigate the problem of index coding, where a sender transmits distinct packets over a shared link to multiple users with side information. The aim is to find an encoding scheme (linear combinations) to minimize the number of transmitted packets, while providing each user with sufficient amount of data for the recovery of the desired parts. It has been shown that finding the optimal linear index code is equivalent to a matrix completion problem, where the observed elements of the matrix indicate the side information available for the users. This modeling results in an incomplete square matrix with all ones on the main diagonal (and some other parts), which needs to be completed with minimum rank. Unfortunately, this is a case in which conventional matrix completion techniques based on nuclear-norm minimization are proved to fail [Huang, Rouayheb 2015]. Instead, an alternating projection (the AP algorithm) method is proposed in [Huang, Rouayheb 2015]. In this paper, in addition to proving the convergence of the AP algorithm under certain conditions, we introduce a modification which considerably improves the run time of the method.

The authors investigate the content distribution among the vehicles of a cluster in a vehicular ad-hoc network, exploiting network coding. The vehicles collaborate to disseminate the coded data packets, received from a roadside infostation based on IEEE 802.11 medium access control (MAC) protocol. Two types of network coding are considered: random linear network coding (RLNC) over a large finite field and random XORed network coding (RXNC). An analytical model is proposed to address the effect of random access MAC as well as the correlation among received coded packets on the performance of content distribution. First, a p-persistent carrier sense multiple access approximation for IEEE 802.11 MAC is adopted, to derive the expected amount of time necessary to deliver the whole information (a data file) to the vehicles, that is, content distribution delay, based on RLNC. Second, the content distribution delay for RXNC is investigated. In this respect, the authors determine the probability of a newly received packet to be innovative for RXNC and characterise the probability that all nodes succeed to retrieve the data file, that is, content delivery ratio. Finally, the success of content distribution process for erasure channels is assessed.