On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

SUSY Dark Matter In Light Of CDMS/XENON Limits

In this talk we briefly review the current CDMS/XENON constraints on the neutralino dark matter in three popular supersymmetric models: the minimal (MSSM), the next-to-minimal (NMSSM) and the nearly minimal (nMSSM). The constraints from the dark matter relic density and various collider experiments are also taken into account. The conclusion is that for each model the current CDMS/XENON limits can readily exclude a large part of the parameter space allowed by other constraints and the future SuperCDMS or XENON100 can cover most of the allowed parameter space. The implication for the Higgs search at the LHC is also discussed. It is found that in the currently allowed parameter space the MSSM charged Higgs boson is quite unlikely to be discovered at the LHC while the neutral Higgs bosons $H$ and $A$ may be accessible at the LHC in the parameter space with a large $\mu$ parameter.Comment: talk given at 2nd International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Asymmetry, Nov 5-6, 2010, Hsinchu, Taiwan (to appear in Int. J. Mod. Phys. D

Estimating the central charge from the R\'enyi entanglement entropy

We calculate the von Neumann and R\'enyi bipartite entanglement entropy of the $O(2)$ model with a chemical potential on a 1+1 dimensional Euclidean lattice with open and periodic boundary conditions. We show that the Calabrese-Cardy conformal field theory predictions for the leading logarithmic scaling with the spatial size of these entropies are consistent with a central charge $c=1$. This scaling survives the time continuum limit and truncations of the microscopic degrees of freedom, modifications which allow us to connect the Lagrangian formulation to quantum Hamiltonians. At half-filling, the forms of the subleading corrections imposed by conformal field theory allow the determination of the central charge with an accuracy better than two percent for moderately sized lattices. We briefly discuss the possibility of estimating the central charge using quantum simulators.Comment: 10 pages, 8 figures, 3 table

Top quark forward-backward asymmetry and charge asymmetry in left-right twin Higgs model

In order to explain the Tevatron anomaly of the top quark forward-backward asymmetry $A_{FB}^t$ in the left-right twin Higgs model, we choose to give up the lightest neutral particle of $\hat{h}$ field as a stable dark matter candidate. Then a new Yukawa interaction for $\hat{h}$ is allowed, which can be free from the constraint of same-sign top pair production and contribute sizably to $A_{FB}^t$. Considering the constraints from the production rates of the top pair ($t\bar t$), the top decay rates and $t\bar{t}$ invariant mass distribution, we find that this model with such new Yukawa interaction can explain $A_{FB}^t$ measured at the Tevatron while satisfying the charge asymmetry $A_{C}^t$ measured at the LHC.Moreover, this model predicts a strongly correlation between $A_{C}^t$ at the LHC and $A_{FB}^t$ at the Tevatron, i.e., $A_{C}^t$ increases as $A_{FB}^t$ increases.Comment: 17 pages, 9 figures; matches the published versio