Convergence-Optimal Quantizer Design of Distributed Contraction-based Iterative Algorithms with Quantized Message Passing

In this paper, we study the convergence behavior of distributed iterative algorithms with quantized message passing. We first introduce general iterative function evaluation algorithms for solving fixed point problems distributively. We then analyze the convergence of the distributed algorithms, e.g. Jacobi scheme and Gauss-Seidel scheme, under the quantized message passing. Based on the closed-form convergence performance derived, we propose two quantizer designs, namely the time invariant convergence-optimal quantizer (TICOQ) and the time varying convergence-optimal quantizer (TVCOQ), to minimize the effect of the quantization error on the convergence. We also study the tradeoff between the convergence error and message passing overhead for both TICOQ and TVCOQ. As an example, we apply the TICOQ and TVCOQ designs to the iterative waterfilling algorithm of MIMO interference game.Comment: 17 pages, 9 figures, Transaction on Signal Processing, accepte

Distributive Stochastic Learning for Delay-Optimal OFDMA Power and Subband Allocation

In this paper, we consider the distributive queue-aware power and subband allocation design for a delay-optimal OFDMA uplink system with one base station, $K$ users and $N_F$ independent subbands. Each mobile has an uplink queue with heterogeneous packet arrivals and delay requirements. We model the problem as an infinite horizon average reward Markov Decision Problem (MDP) where the control actions are functions of the instantaneous Channel State Information (CSI) as well as the joint Queue State Information (QSI). To address the distributive requirement and the issue of exponential memory requirement and computational complexity, we approximate the subband allocation Q-factor by the sum of the per-user subband allocation Q-factor and derive a distributive online stochastic learning algorithm to estimate the per-user Q-factor and the Lagrange multipliers (LM) simultaneously and determine the control actions using an auction mechanism. We show that under the proposed auction mechanism, the distributive online learning converges almost surely (with probability 1). For illustration, we apply the proposed distributive stochastic learning framework to an application example with exponential packet size distribution. We show that the delay-optimal power control has the {\em multi-level water-filling} structure where the CSI determines the instantaneous power allocation and the QSI determines the water-level. The proposed algorithm has linear signaling overhead and computational complexity $\mathcal O(KN)$, which is desirable from an implementation perspective.Comment: To appear in Transactions on Signal Processin

Low Complexity Delay-Constrained Beamforming for Multi-User MIMO Systems with Imperfect CSIT

In this paper, we consider the delay-constrained beamforming control for downlink multi-user MIMO (MU- MIMO) systems with imperfect channel state information at the transmitter (CSIT). The delay-constrained control problem is formulated as an infinite horizon average cost partially observed Markov decision process. To deal with the curse of dimensionality, we introduce a virtual continuous time system and derive a closed-form approximate value function using perturbation analysis w.r.t. the CSIT errors. To deal with the challenge of the conditional packet error rate (PER), we build a tractable closed- form approximation using a Bernstein-type inequality. Based on the closed-form approximations of the relative value function and the conditional PER, we propose a conservative formulation of the original beamforming control problem. The conservative problem is non-convex and we transform it into a convex problem using the semidefinite relaxation (SDR) technique. We then propose an alternating iterative algorithm to solve the SDR problem. Finally, the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved.Comment: 14 pages, 7 figures, 1 table. This paper has been accepted by the IEEE Transactions on Signal Processin

Neutrinos in Large Extra Dimensions and Short-Baseline νe\nu_e Appearance

We show that, in the presence of bulk masses, sterile neutrinos propagating in large extra dimensions (LED) can induce electron-neutrino appearance effects. This is in contrast to what happens in the standard LED scenario and hence LED models with explicit bulk masses have the potential to address the MiniBooNE and LSND appearance results, as well as the reactor and Gallium anomalies. A special feature in our scenario is that the mixing of the first KK modes to active neutrinos can be suppressed, making the contribution of heavier sterile neutrinos to oscillations relatively more important. We study the implications of this neutrino mass generation mechanism for current and future neutrino oscillation experiments, and show that the Short-Baseline Neutrino Program at Fermilab will be able to efficiently probe such a scenario. In addition, this framework leads to massive Dirac neutrinos and thus precludes any signal in neutrinoless double beta decay experiments.Comment: 15 pages, 11 figure

Quantum phase diagram of an exactly solved mixed spin ladder

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4) and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic field increases. For weak rung coupling, the fractional magnetization plateau vanishs and exhibits new quantum phase transitions. However, in the ferromagnetic coupling regime, the system does not have a third saturation magnetization plat eau. The critical behaviour in the vicinity of the critical points is also derived systematically using the TBA.Comment: 20 pages, 2 figure

A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201

ExoMol line lists - XXXII. The rovibronic spectrum of MgO

Line lists for magnesium oxide are computed and extensive comparisons are made with existing experimental spectra. The LiTY line lists cover all ro-vibration transitions within the five lowest-lying electronic states ($X\,{}^1\Sigma^+$, $a\,{}^3\Pi$, $A\,{}^1\Pi$, $B\,{}^1\Sigma^+$ and $b\,{}^3\Sigma^{+}$) and five isotopologues: $^{24}$Mg$^{16}$O, $^{25}$Mg$^{16}$O, $^{26}$Mg$^{16}$O, $^{24}$Mg$^{17}$O, $^{24}$Mg$^{18}$O, $^{24}$Mg$^{17}$O and $^{24}$Mg$^{18}$O. The calculation use potential energy cures, spin-orbit and electronic angular momentum couplings curves determined by fitting to empirical energy levels; these levels are reproduced to within 0.01 \cm\ in most cases. Computed nuclear-motion wavefunctions are combined with {\it ab initio} dipole moment curves to give transition intensities and excited state radiative lifetimes which are compared with laboraroty measurements. The $^{24}$Mg$^{16}$O line list comprises 186 842 ($J\le 320$) ro-vibronic states and 72 833 173 transitions with angular momenta, $J$, up to 300 and covering wavenumbers up to 33 000 cm$^{-1}$ ($\lambda > 0.3$ $\mu$m). The line lists are suitable for temperatures up to about 5000 K. They are relevant to astrophysical studies of exoplanet atmospheres, cool stars and brown dwarfs, and are made available in electronic form at the CDS and ExoMol databases