Bit Error Rates for Ultrafast APD Based Optical Receivers: Exact and Large Deviation Based Asymptotic Approaches

Exact analysis as well as asymptotic analysis, based on large-deviation theory (LDT), are developed to compute the bit-error rate (BER) for ultrafast avalanche-photodiode (APD) based optical receivers assuming on-off keying and direct detection. The effects of intersymbol interference (ISI), resulting from the APD\u27s stochastic avalanche buildup time, as well as the APD\u27s dead space are both included in the analysis. ISI becomes a limiting factor as the transmission rate approaches the detector\u27s bandwidth, in which case the bit duration becomes comparable to APD\u27s avalanche buildup time. Further, the effect of dead space becomes significant in high-speed APDs that employ thin avalanche multiplication regions. While the exact BER analysis at the generality considered here has not been reported heretofore, the asymptotic analysis is a major generalization of that developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, 1992], in which the LDT was used to estimate the BER assuming APDs with an instantaneous response (negligible avalanche buildup time) and no dead space. These results are compared with those obtained using the common Gaussian approximation approach showing the inadequacy of the Guassian approximation when ISI noise has strong presence

Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We review recent progress in understanding the full phase diagram of a one-dimensional, driven, two-species lattice model [Lahiri and Ramaswamy, PRL 79 (1997) 1150] in which the mobility of each species depends on the density of the other. The model shows three phases. The first is characterised by phase separation of an exceptionally robust sort, termed Strong Phase Separation, which survives at all temperature. The second phase has trivial static correlations, but density fluctuations are transported by a pair of kinematic waves involving both species. In the most interesting case, the two linearised eigenmodes, although nonlinearly coupled, have different dynamic exponents. The third ``phase'' arises at the phase boundary between the first two. Here, the first species evolves autonomously, but its fluctuations influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, with density fluctuations persisting even in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law.Comment: 9 pages, 1 postscript figure, added new reference

Epidemic Spreading with External Agents

We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network topology. For networks which are `spatially constrained', we show that the spread of infection can be significantly speeded up even by a few such external agents infecting randomly. Moreover, for general networks, we derive upper-bounds on the order of the spreading time achieved by certain simple (random/greedy) external-spreading policies. Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external-spreading policies; these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with a random spreading policy. This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for spreading in such spatially constrained networks

Precoding-Based Network Alignment For Three Unicast Sessions

We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network only performs random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear scheme, which we refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A primary difference between this setting and the wireless interference channel is that the network topology can introduce dependencies between elements of the transfer matrix, which we refer to as coupling relations, and can potentially affect the achievable rate of PBNA. We identify all possible such coupling relations, and interpret these coupling relations in terms of network topology and present polynomial-time algorithms to check the presence of these coupling relations. Finally, we show that, depending on the coupling relations present in the network, the optimal symmetric rate achieved by precoding-based linear scheme can take only three possible values, all of which can be achieved by PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340

Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves

We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by Lahiri and Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these results to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations, and self-consistent mode-coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context

Advantages of Bayesian monitoring methods in deciding whether and when to stop a clinical trial: an example of a neonatal cooling trial.

BackgroundDecisions to stop randomized trials are often based on traditional P value thresholds and are often unconvincing to clinicians. To familiarize clinical investigators with the application and advantages of Bayesian monitoring methods, we illustrate the steps of Bayesian interim analysis using a recent major trial that was stopped based on frequentist analysis of safety and futility.MethodsWe conducted Bayesian reanalysis of a factorial trial in newborn infants with hypoxic-ischemic encephalopathy that was designed to investigate whether outcomes would be improved by deeper (32 °C) or longer cooling (120 h), as compared with those achieved by standard whole body cooling (33.5 °C for 72 h). Using prior trial data, we developed neutral and enthusiastic prior probabilities for the effect on predischarge mortality, defined stopping guidelines for a clinically meaningful effect, and derived posterior probabilities for predischarge mortality.ResultsBayesian relative risk estimates for predischarge mortality were closer to 1.0 than were frequentist estimates. Posterior probabilities suggested increased predischarge mortality (relative risk > 1.0) for the three intervention groups; two crossed the Bayesian futility threshold.ConclusionsBayesian analysis incorporating previous trial results and different pre-existing opinions can help interpret accruing data and facilitate informed stopping decisions that are likely to be meaningful and convincing to clinicians, meta-analysts, and guideline developers.Trial registrationClinicalTrials.gov NCT01192776 . Registered on 31 August 2010