Compressed sensing aims to retrieve sparse signals from very few samples. It relies on dedicated reconstruction algorithms and well-chosen measurement matrices. In combination with network coding, which operates traditionally over finite fields, it leverages the benefits of both techniques. However, compressed sensing has been primarily investigated over the real field. F2OMP is one of the few recovery algorithms to reconstruct signals over finite fields. However, its use in practical cases is limited since its performance depends mainly on binary matrices for signal recovery. This paper reports results of extensive simulations enhancing the features of well-performing measurement matrices for F2OMP as well as methods to build them. Moreover, a modified version of the algorithm, F2OMP-loop, is proposed. It offers a compromise between performance, stability, and processing time. This allows to design a joint compressed sensing and network coding framework over finite fields.

We consider the problem of secure communications in a Gaussian two-way relay channel applying the compute-and-forward scheme using nested lattice codes. Two nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We provide an achievable secrecy rate region under a weak secrecy criterion and provide the proof. We show that the achievable sum secrecy rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that both the nodes must encode their messages such that the common computation rate pair falls outside the MAC capacity region of the relay.

Can linear time-invariant dynamics be used to model the epidemics on the networks? This paper shows that this is indeed possible. Given the topology of a network in terms of an undirected graph we form a state space representation of a linear system to study the behavior of this network and to compare calculations against simulations of epidemics. In particular, an epidemic modeling approach based on systems theory usable even for lager networks is introduced and its potential is demonstrated. Also, methods to form the state variables of a corresponding LTI system are proposed. Presented results show that this approach is highly effective to evaluate epidemic dynamics analytically in every discrete time step omitting agent-based simulations. Moreover, it is shown that it can be used for network analysis and network optimization against virus spreading. This opens the door for using systems theory tools in network analysis.

We investigate the problem of secure communications in a Gaussian multiway relay channel applying the compute-and-forward scheme under usage of nested lattice codes. All nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We start with the general case of the single-input multiple-output L-user multiway relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. In particular, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the single-input single-output and the multiple-input single-input L-user multiway relay channel as well as the two-way relay channel. We discuss these results and show the dependence between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the compute-and-forward rate without secrecy.

Compute-and-forward is a framework for reliable physical layer network coding introduced by Nazer and Gastpar. Instead of decoding single messages, it decodes linear combinations of messages with the help of nested lattice codes. Nazer and Gastpar derived an achievable rate for each node depending on the channel coefficients and the desired equation coefficients. However, it is open how to choose the coefficient vector with the equation coefficients. We provide a branch-and-bound algorithm that calculates the coefficient vector, which results in the highest computation rate at a single node. We implemented the algorithm in Matlab and compared the number of iterations to the number of needed iterations if we use a complete search over all possible vectors.

Secrecy on the physical layer is a promising technique to simplify the overall cross-layer secrecy concept. In many recent works on the multiple antenna wiretap channel, perfect channel state information to the intended receiver as well as the passive eavesdropper are assumed. In this paper, the transmitter has only partial information about the channel to the eavesdropper, but full information on the main channel to the intended receiver. The applied channel model is the flat-fading multiple-input single-output wiretap channel. We minimize the outage probability of secure transmission under single-stream beamforming and the use of artificial noise in the null space of the main channel. Furthermore, we derive a suboptimal beamforming scheme based on a Markov bound, which performs reasonably well. The results generalize the cases with perfect as well as without channel state information of the eavesdropper channel. Numerical simulations illustrate the secrecy outage probability over the degree of channel knowledge and confirm the theoretical results.

We consider a discrete-time frequency- selective block-fading channel with Rayleigh fading and correlated scattering. This is relevant in the area of UWB and if transceiver filters are included in the capacity analysis. Under an average power constraint, we assume a single-user, single-antenna transmission with full CSI at the receiver and no CSI at the transmitter. For the employed model, we analyze the variance of the random capacity and the outage capacity. The variance together with the ergodic capacity are adequate means to estimate and basically characterize the behavior of the outage capacity via Chebyshev's inequality. Furthermore, expressions for high SNR are derived and the impact of correlated scattering compared to uncorrelated scattering is systematically studied on both, the ergodic and the outage capacity.

We study the ergodic capacity of a frequency-selective Rayleigh fading channel with correlated scattering, which finds application in the area of UWB. Under an average power constraint, we consider a single-user, single-antenna transmission. Coherent reception is assumed with full CSI at the receiver and no CSI at the transmitter. We distinguish between a continuous- and a discrete-time channel, modeled either as random process or random vector with generic covariance. As a practically relevant example, we examine an exponentially attenuated Ornstein-Uhlenbeck process in detail. Finally, we give numerical results, discuss the relation between the continuous- and the discrete-time channel model and show the significant impact of correlated scattering.

The performance of an ultra-wideband (UWB) communication system applying pulse position modulation (PPM) is investigated. The optimum impulse shift position in the case of binary overlapping PPM (2OPPM) is analytically derived for the AWGN channel. It is shown that the information throughput of a UWB system in the AWGN channel can be optimized by adjusting the time overlap of the pulse shape used according to the actual signal-to-noise ratio (SNR).