On routing-optimal networks for multiple unicasts

In this paper, we consider the problem of multiple unicast sessions over a directed acyclic graph. It is well known that linear network coding is insufficient for achieving the capacity region, in the general case. However, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing-optimal networks. We identify a class of routing-optimal networks, which we refer to as information-distributive networks, defined by three topological features. Due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector, and the traffic transmitted through the network is exactly the information transmitted over the cut-sets between the sources and the sinks in the corresponding network coding scheme. We present examples of information-distributive networks, including some examples from (1) index coding and (2) from a single unicast session with hard deadline constraint. © 2014 IEEE

Precoding-Based Network Alignment For Three Unicast Sessions

We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network only performs random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear scheme, which we refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A primary difference between this setting and the wireless interference channel is that the network topology can introduce dependencies between elements of the transfer matrix, which we refer to as coupling relations, and can potentially affect the achievable rate of PBNA. We identify all possible such coupling relations, and interpret these coupling relations in terms of network topology and present polynomial-time algorithms to check the presence of these coupling relations. Finally, we show that, depending on the coupling relations present in the network, the optimal symmetric rate achieved by precoding-based linear scheme can take only three possible values, all of which can be achieved by PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340

Distributed design of network codes for wireless multiple unicasts

Previous results on network coding for low-power wireless transmissions of multiple unicasts rely on opportunistic coding or centralized optimization to reduce the power consumption. This paper proposes a distributed strategy for reducing the power consumption in a network coded wireless network with multiple unicasts. We apply a simple network coding strategy called “reverse carpooling,” which uses only XOR and forwarding operations. In this paper, we use the rectangular grid as a simple network model and attempt to increase network coding opportunities without the overhead required for centralized design or coordination. The proposed technique designates “reverse carpooling lines” analogous to a collection of bus routes in a crowded city. Each individual unicast then chooses a route from its source to its destination independently but in a manner that maximizes the fraction of its path spent on reverse carpooling lines. Intermediate nodes apply reverse carpooling opportunistically along these routes. Our network optimization attempts to choose the reverse carpooling lines in a manner that maximizes the expected power savings with respect to the random choice of sources and sinks

Multiple Unicast Capacity of 2-Source 2-Sink Networks

We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networks with arbitrary connectivity, the sum capacity is achieved simply by routing. For wireless networks, we explore the degrees of freedom (DoF) of multihop X networks with a layered structure, allowing arbitrary number of hops, and arbitrary connectivity within each hop. For the case when there are no more than two relay nodes in each layer, the DoF can only take values 1, 4/3, 3/2 or 2, based on the connectivity of the network, for almost all values of channel coefficients. When there are arbitrary number of relays in each layer, the DoF can also take the value 5/3 . Achievability schemes incorporate linear forwarding, interference alignment and aligned interference neutralization principles. Information theoretic converse arguments specialized for the connectivity of the network are constructed based on the intuition from linear dimension counting arguments.Comment: 6 pages, 7 figures, submitted to IEEE Globecom 201

A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem

The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for identifying solutions mainly rely on highly restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a path-based Constraint Satisfaction Problem (CSP) and an edge-based CSP. While CSPs are NP-complete in general, we present a path-based probabilistic distributed algorithm and an edge-based probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation. Numerical results illustrate the performance improvement of our approach over existing methods.Comment: submitted to TON (conference version published at IEEE GLOBECOM 2015

Performance improvement of an optical network providing services based on multicast

Operators of networks covering large areas are confronted with demands from some of their customers who are virtual service providers. These providers may call for the connectivity service which fulfils the specificity of their services, for instance a multicast transition with allocated bandwidth. On the other hand, network operators want to make profit by trading the connectivity service of requested quality to their customers and to limit their infrastructure investments (or do not invest anything at all). We focus on circuit switching optical networks and work on repetitive multicast demands whose source and destinations are {\em \`a priori} known by an operator. He may therefore have corresponding trees "ready to be allocated" and adapt his network infrastructure according to these recurrent transmissions. This adjustment consists in setting available branching routers in the selected nodes of a predefined tree. The branching nodes are opto-electronic nodes which are able to duplicate data and retransmit it in several directions. These nodes are, however, more expensive and more energy consuming than transparent ones. In this paper we are interested in the choice of nodes of a multicast tree where the limited number of branching routers should be located in order to minimize the amount of required bandwidth. After formally stating the problem we solve it by proposing a polynomial algorithm whose optimality we prove. We perform exhaustive computations to show an operator gain obtained by using our algorithm. These computations are made for different methods of the multicast tree construction. We conclude by giving dimensioning guidelines and outline our further work.Comment: 16 pages, 13 figures, extended version from Conference ISCIS 201

Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements

We consider the problem of maximizing aggregate user utilities over a multi-hop network, subject to link capacity constraints, maximum end-to-end delay constraints, and user throughput requirements. A user's utility is a concave function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia traffic, and is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. We first show that it is NP-complete either (i) to construct a feasible solution strictly meeting all constraints, or (ii) to obtain an optimal solution after we relax maximum delay constraints or throughput requirements up to constant ratios. We then develop a polynomial-time approximation algorithm named PASS. The design of PASS leverages a novel understanding between non-convex maximum-delay-aware problems and their convex average-delay-aware counterparts, which can be of independent interest and suggest a new avenue for solving maximum-delay-aware network optimization problems. Under realistic conditions, PASS achieves constant or problem-dependent approximation ratios, at the cost of violating maximum delay constraints or throughput requirements by up to constant or problem-dependent ratios. PASS is practically useful since the conditions for PASS are satisfied in many popular application scenarios. We empirically evaluate PASS using extensive simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Compared to existing algorithms and a conceivable baseline, PASS obtains up to $100\%$ improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints that are acceptable for practical video conferencing applications