Approximate Decoding Approaches for Network Coded Correlated Data

This paper considers a framework where data from correlated sources are transmitted with help of network coding in ad-hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth bottlenecks. We first show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples about the possible of our algorithms that can be deployed in sensor networks and distributed imaging applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our low complexity solution for delivery of correlated data sources

Fundamental Limits of Low-Density Spreading NOMA with Fading

Spectral efficiency of low-density spreading non-orthogonal multiple access channels in the presence of fading is derived for linear detection with independent decoding as well as optimum decoding. The large system limit, where both the number of users and number of signal dimensions grow with fixed ratio, called load, is considered. In the case of optimum decoding, it is found that low-density spreading underperforms dense spreading for all loads. Conversely, linear detection is characterized by different behaviors in the underloaded vs. overloaded regimes. In particular, it is shown that spectral efficiency changes smoothly as load increases. However, in the overloaded regime, the spectral efficiency of low- density spreading is higher than that of dense spreading

Clustered wireless sensor networks

The study of topology in randomly deployed wireless sensor networks (WSNs) is important in addressing the fundamental issue of stochastic coverage resulting from randomness in the deployment procedure and power management algorithms. This dissertation defines and studies clustered WSNs, WSNs whose topology due to the deployment procedure and the application requirements results in the phenomenon of clustering or clumping of nodes. The first part of this dissertation analyzes a range of topologies of clustered WSNs and their impact on the primary sensing objectives of coverage and connectivity. By exploiting the inherent advantages of clustered topologies of nodes, this dissertation presents techniques for optimizing the primary performance metrics of power consumption and network capacity. It analyzes clustering in the presence of obstacles, and studies varying levels of redundancy to determine the probability of coverage in the network. The proposed models for clustered WSNs embrace the domain of a wide range of topologies that are prevalent in actual real-world deployment scenarios, and call for clustering-specific protocols to enhance network performance. It has been shown that power management algorithms tailored to various clustering scenarios optimize the level of active coverage and maximize the network lifetime. The second part of this dissertation addresses the problem of edge effects and heavy traffic on queuing in clustered WSNs. In particular, an admission control model called directed ignoring model has been developed that aims to minimize the impact of edge effects in queuing by improving queuing metrics such as packet loss and wait time

A Markov chain model for the decoding probability of sparse network coding

Random linear network coding has been shown to offer an efficient communication scheme, leveraging a remarkable robustness against packet losses. However, it suffers from a high-computational complexity, and some novel approaches, which follow the same idea, have been recently proposed. One of such solutions is sparse network coding (SNC), where only few packets are combined with each transmission. The amount of data packets to be combined can be set from a density parameter/distribution, which could be eventually adapted. In this paper, we present a semi-analytical model that captures the performance of SNC on an accurate way. We exploit an absorbing Markov process, where the states are defined by the number of useful packets received by the decoder, i.e., the decoding matrix rank, and the number of non-zero columns at such matrix. The model is validated by the means of a thorough simulation campaign, and the difference between model and simulation is negligible. We also include in the comparison of some more general bounds that have been recently used, showing that their accuracy is rather poor. The proposed model would enable a more precise assessment of the behavior of SNC techniques.This work has been supported by the Spanish Government (Ministerio de Economía y Competitividad, Fondo Europeo de Desarrollo Regional, FEDER) by means of the projects COSAIF, “Connectivity as a Service: Access for the Internet of the Future” (TEC2012-38754-C02-01), and ADVICE (TEC2015-71329-C2-1-R). This work was also financed in part by the TuneSCode project (No. DFF 1335-00125) granted by the Danish Council for Independent Research

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure