A digital interface for Gaussian relay networks: lifting codes from the discrete superposition model to Gaussian relay networks

For every Gaussian relay network with a single source-destination pair, it is known that there exists a corresponding deterministic network called the discrete superposition network that approximates its capacity uniformly over all SNR's to within a bounded number of bits. The next step in this program of rigorous approximation is to determine whether coding schemes for discrete superposition models can be lifted to Gaussian relay networks with a bounded rate loss independent of SNR. We establish precisely this property and show that the superposition model can thus serve as a strong surrogate for designing codes for Gaussian relay networks. We show that a code for a Gaussian relay network, with a single source-destination pair and multiple relay nodes, can be designed from any code for the corresponding discrete superposition network simply by pruning it. In comparison to the rate of the discrete superposition network's code, the rate of the Gaussian network's code only reduces at most by a constant that is a function only of the number of nodes in the network and independent of channel gains. This result is also applicable for coding schemes for MIMO Gaussian relay networks, with the reduction depending additionally on the number of antennas. Hence, the discrete superposition model can serve as a digital interface for operating Gaussian relay networks.Comment: 5 pages, 2010 IEEE Information Theory Workshop, Cair

A digital interface for Gaussian relay and interference networks: Lifting codes from the discrete superposition model

For every Gaussian network, there exists a corresponding deterministic network called the discrete superposition network. We show that this discrete superposition network provides a near-optimal digital interface for operating a class consisting of many Gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the Gaussian network, while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network. This constant depends only on the number of nodes in the network and not on the channel gains or SNR. Moreover the capacities of the two networks are within a constant of each other, again independent of channel gains and SNR. We show that the class of Gaussian networks for which this interface property holds includes relay networks with a single source-destination pair, interference networks, multicast networks, and the counterparts of these networks with multiple transmit and receive antennas. The code for the Gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it. This lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for Gaussian relay networks. We present similar results for the K x K Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks.Comment: Final versio

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks

We are given a set of sensors at given locations, a set of potential locations for placing base stations (BSs, or sinks), and another set of potential locations for placing wireless relay nodes. There is a cost for placing a BS and a cost for placing a relay. The problem we consider is to select a set of BS locations, a set of relay locations, and an association of sensor nodes with the selected BS locations, so that number of hops in the path from each sensor to its BS is bounded by hmax, and among all such feasible networks, the cost of the selected network is the minimum. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard, and is hard to even approximate within a constant factor. For this problem, we propose a polynomial time approximation algorithm (SmartSelect) based on a relay placement algorithm proposed in our earlier work, along with a modification of the greedy algorithm for weighted set cover. We have analyzed the worst case approximation guarantee for this algorithm. We have also proposed a polynomial time heuristic to improve upon the solution provided by SmartSelect. Our numerical results demonstrate that the algorithms provide good quality solutions using very little computation time in various randomly generated network scenarios

Electrical and Magnetic behaviour of PrFeAsO0.8F0.2 superconductor

The superconducting and ground state samples of PrFeAsO0.8F0.2 and PrFeAsO have been synthesised via easy and versatile single step solid state reaction route. X-ray & Reitveld refine parameters of the synthesised samples are in good agreement to the earlier reported value of the structure. The ground state of the pristine compound (PrFeAsO) exhibited a metallic like step in resistivity below 150K followed by another step at 12K. The former is associated with the spin density wave (SDW) like ordering of Fe spins and later to the anomalous magnetic ordering for Pr moments. Both the resistivity anomalies are absent in case of superconducting PrFeAsO0.8F0.2 sample. Detailed high field (up to 12Tesla) electrical and magnetization measurements are carried out for superconducting PrFeAsO0.8F0.2 sample. The PrFeAsO0.8F0.2 exhibited superconducting onset (Tconset) at around 47K with Tc({\rho} =0) at 38K. Though the Tconset remains nearly invariant, the Tc({\rho} =0) is decreased with applied field, and the same is around 23K under applied field of 12Tesla. The upper critical field (Hc2) is estimated from the Ginzburg Landau equation (GL) fitting, which is found to be ~ 182Tesla. Critical current density (Jc) being calculated from high field isothermal magnetization (MH) loops with the help of Beans critical state model, is found to be of the order of 103 A/cm2. Summarily, the superconductivity characterization of single step synthesised PrFeAsO0.8F0.2 superconductor is presented.Comment: 15 Pages Text + Fig