Scheduling for Network Coded Multicast: A Conflict Graph Formulation

Abstract

Abstract-Consider network coded multicast traffic over a wireless network in the bandwidth limited regime. We formulate the joint medium access and subgraph optimization problem by means of a graphical conflict model. The nature of network coded flows is not captured by classical link-based scheduling and therefore requires a novel approach based on conflicting hyperarcs. By means of simulations, we evaluate the performance of our algorithm and conclude that it significantly outperforms existing scheduling techniques. I. INTRODUCTIONIn a multi-hop wireless network an optimal strategy to multicast to a group of receivers is to use random linear network coding over an optimized subgraph. Random linear codes are capacity achieving for a given subgraph [1] and this subgraph can be computed by means of solving a linear or convex program [2]. The subgraph optimization is a fairly tractable problem and furthermore solvable in a distributed fashion making it relevant in practice. An essential assumption of [2] is that all nodes in the network transmit on orthogonal channels and thus conflicts due to interfering transmissions do not arise. This is a reasonable assumption in a power limited regime, where bandwidth is not scarce and one might simply avoid interference by orthogonalizing the entire network. However, in many if not most scenarios wireless networks are interference limited. To that end a high frequency reuse within the network is necessary which has to be achieved by carefully scheduling simultaneous transmissions.The prevalent approach to this problem is to construct an interference-free transmission schedule by means of some heuristic and then to compute an optimal subgraph over this, now essentially orthogonal, network. As an example, in [3] the authors propose a suboptimal collision-free strategy where two nodes cannot transmit simultaneously if they are within two hops. While this is a practical solution, it is not clear how it affects the overall performance of the network. Furthermore, from a systems perspective it is unsatisfying to have one component (the network coding subgraph) carefully optimized, while the other essential part (the medium access) is done in a more or less ad-hoc fashion.To that end, we suggest a framework, where subgraph optimization and channel access are treated jointly. We construct

Hide and code: Session anonymity in wireless line networks with coded packets

“…For that, we make use of an auxiliary undirected graph C = (V, A), called conflict graph, similar to what was used in [18] or [19]. In our formulation, the vertices in the conflict graph correspond to nodes in the network, that is V = N .…”

NCAPQ: Network Coding-Aware Priority Queueing for UDP Flows over COPE

“…A linear optimization framework for packing butterflies is proposed in [6]. Scheduling over coded wireless networks is considered, and the computational complexity of scheduling and network coding is discussed in [20], [21], [22] This paper combines the NCAQM and NCAPP mechanisms proposed independently in [2] and [3], respectively. We first show that these mechanisms are complementary: NCAQM creates coding opportunities (which is necessary in high load regimes) while NCAPP drains coded faster than uncoded packets (which is important in low load regimes).…”

Coding and control for communication networks

“…A conservative approach for managing interference is to assign to each node an orthogonal channel and therefore avoid interference at the price of reduced bandwidth efficiency. The approach taken in [41], on the other hand, is a scheduling technique designed for network coded multicast traffic. Its basic idea is, in short, to activate subsets of neighbors in a manner that takes advantage of packets overheard by neighbors (the so-called broadcast Fig.…”

“…7 Shown on the left-hand side is a wireless network with 12 nodes, one source, and two multicast groups, each consisting of two nodes. Shown on the right-hand side are two possible rate regions: the smaller region R * is obtained using orthogonal scheduling, and the larger region is obtained using a more efficient coding scheme [41] advantage) as well as of frequency reuse in the network due to efficient scheduling of non-conflicting transmissions. Moreover, if we have two different multicast connections then, while there is no competition for capacity among receivers within a multicast connection, there may be competition for resources among different multicast connections.…”

“…7. The rate region R * is obtained using orthogonal coding, and the region R is obtained using the coding approach of [41]. Observe that the rate regions are almost rectangular.…”