The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In ISIT'12 Brahma, \"{O}zg\"{u}r and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with $N$ non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most $N+1$ active states (only $N+1$ out of the $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an optimal schedule exists with at most $N+1$ active states. The key step of our proof is to write the minimum of a submodular function by means of its Lov\'{a}sz extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.Comment: Submitted to IEEE Information Theory Workshop (ITW) 201

Switched Local Schedules for Diamond Networks

We consider a Gaussian diamond network where a source communicates with the destination through $n$ non-interfering half-duplex relays. We focus on half-duplex schedules that utilize only local channel state information, i.e., each relay has access to its incoming and outgoing channel realizations. We demonstrate that random independent switching, resulting in multiple listen-transmit sub cycles at each relay, while still respecting the overall locally optimal listen-transmit fractions, enables to approximately achieve at least $3/4$ of the capacity of the $2$-relay diamond network. With a single listen-transmit cycle, this fraction drops from $3/4$ to $1/2$. We also provide simulation results that point to the same fractions of capacity being retained over networks with more than $2$ relays

Low Complexity Scheduling and Coding for Wireless Networks

The advent of wireless communication technologies has created a paradigm shift in the accessibility of communication. With it has come an increased demand for throughput, a trend that is likely to increase further in the future. A key aspect of these challenges is to develop low complexity algorithms and architectures that can take advantage of the nature of the wireless medium like broadcasting and physical layer cooperation. In this thesis, we consider several problems in the domain of low complexity coding, relaying and scheduling for wireless networks. We formulate the Pliable Index Coding problem that models a server trying to send one or more new messages over a noiseless broadcast channel to a set of clients that already have a subset of messages as side information. We show through theoretical bounds and algorithms, that it is possible to design short length codes, poly-logarithmic in the number of clients, to solve this problem. The length of the codes are exponentially better than those possible in a traditional index coding setup. Next, we consider several aspects of low complexity relaying in half-duplex diamond networks. In such networks, the source transmits information to the destination through $n$ half-duplex intermediate relays arranged in a single layer. The half-duplex nature of the relays implies that they can either be in a listening or transmitting state at any point of time. To achieve high rates, there is an additional complexity of optimizing the schedule (i.e. the relative time fractions) of the relaying states, which can be $2^n$ in number. Using approximate capacity expressions derived from the quantize-map-forward scheme for physical layer cooperation, we show that for networks with $n\leq 6$ relays, the optimal schedule has atmost $n+1$ active states. This is an exponential improvement over the possible $2^n$ active states in a schedule. We also show that it is possible to achieve at least half the capacity of such networks (approximately) by employing simple routing strategies that use only two relays and two scheduling states. These results imply that the complexity of relaying in half-duplex diamond networks can be significantly reduced by using fewer scheduling states or fewer relays without adversely affecting throughput. Both these results assume centralized processing of the channel state information of all the relays. We take the first steps in analyzing the performance of relaying schemes where each relay switches between listening and transmitting states randomly and optimizes their relative fractions using only local channel state information. We show that even with such simple scheduling, we can achieve a significant fraction of the capacity of the network. Next, we look at the dual problem of selecting the subset of relays of a given size that has the highest capacity for a general layered full-duplex relay network. We formulate this as an optimization problem and derive efficient approximation algorithms to solve them. We end the thesis with the design and implementation of a practical relaying scheme called QUILT. In it the relay opportunistically decodes or quantizes its received signal and transmits the resulting sequence in cooperation with the source. To keep the complexity of the system low, we use LDPC codes at the source, interleaving at the relays and belief propagation decoding at the destination. We evaluate our system through testbed experiments over WiFi

Techniques de coopération appliquées aux futurs réseaux cellulaires

A uniform mobile user quality of service and a distributed use of the spectrum represent the key-ingredients for next generation cellular networks. Toward this end, physical layer cooperation among the network infrastructure and the wireless nodes has emerged as a potential technique. Cooperation leverages the broadcast nature of the wireless medium, that is, the same transmission can be heard by multiple nodes, thus opening up the possibility that nodes help one another to convey the messages to their intended destination. Cooperation also promises to offer novel and smart ways to manage interference, instead of just simply disregarding it and treating it as noise. Understanding how to properly design such cooperative wireless systems so that the available resources are fully utilized is of fundamental importance.The objective of this thesis is to conduct an information theoretic study on practically relevant wireless systems where the network infrastructure nodes cooperate among themselves in an attempt to enhance the network performance in many critical aspects, such as throughput, robustness and coverage. Wireless systems with half-duplex relay stations as well as scenarios where a base station overhears another base station and consequently helps serving this other base station's associated mobile users, represent the wireless cooperative networks under investigation in this thesis. The prior focus is to make progress towards characterizing the capacity of such wireless systems by means of derivation of novel outer bounds and design of new provably optimal transmission strategies.Une qualité de service uniforme pour les utilisateurs mobiles et une utilisation distribuée du spectre représentent les ingrédients clés des réseaux cellulaires de prochaine génération. Dans ce but, la coopération au niveau de la couche physique entre les nœuds de l’infrastructure et les nœuds du réseau sans fil a émergé comme une technique à fort potentiel. La coopération s’appuie sur les propriétés de diffusion du canal sans fil, c’est-à-dire que la même transmission peut être entendue par plusieurs nœuds, ouvrant ainsi la possibilité pour les nœuds de s’aider à transmettre les messages à leur destination finale. La coopération promet aussi d’offrir une façon nouvelle et intelligente de gérer les interférences, au lieu de simplement les ignorer et les traiter comme du bruit. Comprendre comment concevoir ces systèmes radio coopératifs, afin que les ressources disponibles soient pleinement utilisées, est d’une importance fondamentale. L’objectif de cette thèse est de mener une étude du point de vue de la théorie de l’information, pour des systèmes sans fil pertinents dans la pratique, où les nœuds de l’infrastructure coopèrent en essayant d’améliorer les performances du réseau. Les systèmes radio avec des relais semi-duplex ainsi que les scénarios où une station de base aide à servir les utilisateurs mobiles associés à une autre station de base, sont les réseaux sans fil coopératifs étudiés dans cette thèse. Le but principal est la progression vers la caractérisation de la capacité de ces systèmes sans fil au moyen de dérivation de nouvelles bornes supérieures pour les performances et la conception de nouvelles stratégies de transmission permettant de les atteindre