Fuzzy tuned gossip algorithms in mobile ad hoc networks

“This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." “Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” DOI: 10.1109/MED.2009.5164552Mobile ad hoc networks (MANET) are modeled as agents that form communities without infrastructure, for a random period of time and with usually cooperative behavior. The nodes of MANET often carry information to disseminate. The dynamics of information delivery, mostly referred as average consensus, is a common problem in these networks. The gossip protocols are designed to implement this task. The standard algorithms that are used in these protocols exploit the network describing matrix, aka Laplacian, and exchange information to all node neighbors. In static networks the problem can be considered as an output feedback problem but in the case of MANET the problem is getting complicated due to the continuous change of network topology. In this paper the fuzzy reasoning approach is proposed to tune and leverage the gossip protocol. Illustrative simulations are included to demonstrate the application of the method and to present comparative results in various cases

Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks

In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.Comment: to appear in IEEE Transactions on Wireless Communication

A Chemistry-Inspired Framework for Achieving Consensus in Wireless Sensor Networks

The aim of this paper is to show how simple interaction mechanisms, inspired by chemical systems, can provide the basic tools to design and analyze a mathematical model for achieving consensus in wireless sensor networks, characterized by balanced directed graphs. The convergence and stability of the model are first proven by using new mathematical tools, which are borrowed directly from chemical theory, and then validated by means of simulation results, for different network topologies and number of sensors. The underlying chemical theory is also used to derive simple interaction rules that may account for practical issues, such as the estimation of the number of neighbors and the robustness against perturbations. Finally, the proposed chemical solution is validated under real-world conditions by means of a four-node hardware implementation where the exchange of information among nodes takes place in a distributed manner (with no need for any admission control and synchronism procedure), simply relying on the transmission of a pulse whose rate is proportional to the state of each sensor.Comment: 12 pages, 10 figures, submitted to IEEE Sensors Journa

Scalable Group Secret Key Generation over Wireless Channels

In this paper, we consider the problem of secret key generation for multiple parties. Multi-user networks usually require a trusted party to efficiently distribute keys to the legitimate users and this process is a weakness against eavesdroppers. With the help of the physical layer security techniques, users can securely decide on a secret key without a trusted party by exploiting the unique properties of the channel. In this context, we develop a physical layer group key generation scheme that is also based on the ideas of the analog function computation studies. We firstly consider the key generation as a function to be computed over the wireless channel and propose two novel methods depending on the users transmission capability (i.e. half-duplex and full-duplex transmissions). Secondly, we exploit the uniqueness of the prime integers in order to enable the simultaneous transmission of the users for key generation. As a result, our approach contributes to the scalability of the existing physical layer key generation algorithms since all users transmit simultaneously rather than using pairwise communications. We prove that our half-duplex network model reduces the required number of communications for group key generation down to a linear scale. Furthermore, the full-duplex network model reduces to a constant scale.Comment: 7 pages, 3 figure, transaction

Weighted Gossip: Distributed Averaging Using Non-Doubly Stochastic Matrices

This paper presents a general class of gossip-based averaging algorithms, which are inspired from Uniform Gossip [1]. While Uniform Gossip works synchronously on complete graphs, weighted gossip algorithms allow asynchronous rounds and converge on any connected, directed or undirected graph. Unlike most previous gossip algorithms [2]–[6], Weighted Gossip admits stochastic update matrices which need not be doubly stochastic. Double-stochasticity being very restrictive in a distributed setting [7], this novel degree of freedom is essential and it opens the perspective of designing a large number of new gossip-based algorithms. To give an example, we present one of these algorithms, which we call One-Way Averaging. It is based on random geographic routing, just like Path Averaging [5], except that routes are one way instead of round trip. Hence in this example, getting rid of double stochasticity allows us to add robustness to Path Averaging

Local Interference Can Accelerate Gossip Algorithms

In this paper, we show how interference can be exploited to perform gossip computations for average-based consensus over a larger local neighborhood, rather than only pairs of nodes. We use a new channel coding technique called computation coding to compute sums reliably over the wireless medium. Since many nodes can simultaneously average in a single round, our neighborhood gossip algorithm converges faster than the standard nearest neighbor gossip algorithm. For a network with n nodes and size m neighborhoods, neighborhood gossip requires O(n(2)/m(2)) rounds while standard gossip requires circle dot(n(2)) rounds. Furthermore, we show that if the power path loss coefficient is less than 4, the total transmit energy employed by neighborhood gossip is polynomially smaller than that employed by standard gossip