Semidefinite Relaxation Based Blind Equalization using Constant Modulus Criterion

Blind equalization is a classic yet open problem. Statistic-based algorithms, such as constant modulus (CM), were widely investigated. One inherent issue with blind algorithms is the phase ambiguity of equalized signals. In this letter, we propose a novel scheme based on CM criterion and take advantage of the asymmetric property in a class of LDPC codes to resolve the phase ambiguity. Specifically, a new formulation with modified CM objective function and relaxed code constraints is presented.Comment: 8 pages, lette

On passage to over-groups of finite indices of the Farrell-Jones conjecture

We use the controlled algebra approach to study the problem that whether the Farrell-Jones conjecture is closed under passage to over-groups of finite indices. Our study shows that this problem is closely related to a general problem in algebraic $K$- and $L$-theories. We use induction theory to study this general problem. This requires an extension of the classical induction theorem for $K$- and $L$- theories of finite groups with coefficients in rings to with twisted coefficients in additive categories. This extension is well-known to experts, but a detailed proof does not exist in the literature. We carry out a detailed proof. This extended induction theorem enables us to make some reductions for the general problem, and therefore for the finite index problem of the Farrell-Jones conjecture.Comment: 17 page

Topological Rigidity for FJ by the Infinite Cyclic Group

We call a group FJ if it satisfies the $K$- and $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. We show that if $G$ is FJ, then the simple Borel conjecture (in dimensions $\ge 5$) holds for every group of the form $G\rtimes\mathbb Z$. If in addition $Wh(G\times \mathbb Z)=0$, which is true for all known torsion free FJ groups, then the bordism Borel conjecture (in dimensions $n\ge 5$) holds for $G\rtimes\mathbb Z$. One of the key ingredients in proving these rigidity results is another main result, which says that if a torsion free group $G$ satisfies the $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$, then any semi-direct product $G\rtimes\mathbb Z$ also satisfies the $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. Our result is indeed more general and implies the $L$-theoretic Farrell-Jones conjecture with coefficients in additive categories is closed under extensions of torsion free groups. This enables us to extend the class of groups which satisfy the Novikov conjecture.Comment: 26 pages. Comments are welcom

Joint Receiver Design for Internet of Things

Internet of things (IoT) is an ever-growing network of objects that connect, collect and exchange data. To achieve the mission of connecting everything, physical layer communication is of indispensable importance. In this work, we propose a new receiver tailored for the characteristics of IoT communications. Specifically, our design is suitable for sporadic transmissions of small-to-medium sized packets in IoT applications. With joint design in the new receiver, strong reliability is guaranteed and power saving is expected.Comment: 9 pages, scholarly articl

On Invariants of C∗\text{C}^*-algebras with the ideal property

In this paper, we consider $\text{C}^*$-algebras with the ideal property (the ideal property unifies the simple and real rank zero cases). We define two categories related the invariants of the $\text{C}^*$-algebras with the ideal property. And we showed that these two categories are in fact isomorphic. As a consequence, the Elliott's Invariant and the Stevens' Invariant are isomorphic for $\text{C}^*$-algebras with the ideal property

One-way deficit and quantum phase transitions in XXXX Model

Quantum correlations including entanglement and quantum discord has drawn much attention in characterizing quantum phase transitions. Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath [Phys. Rev. Lett. 89, 180402 (2002)]. It links quantum thermodynamics with quantum correlations and provides a new standpoint for understanding quantum non-locality. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the XX model. In the thermodynamic limit, the XX model undergoes a first order transition from fully polarized to a critical phase with quasi-long-range order with decrease of quantum parameter. We find that the one-way deficit becomes nonzero after the critical point. Therefore, the one-way deficit characterizes the quantum phase transition in the XX model.Comment: 5 pages, 1 figur

Non-iterative Joint Detection-Decoding Receiver for LDPC-Coded MIMO Systems Based on SDR

Semi-definite relaxation (SDR) detector has been demonstrated to be successful in approaching maximum likelihood (ML) performance while the time complexity is only polynomial. We propose a new receiver jointly utilizing the forward error correction (FEC) code information in the SDR detection process. Strengthened by the code constraints, the joint SDR detector provides soft information of much improved reliability to downstream decoder and therefore outperforms existing receivers with substantial gain.Comment: 5 pages, 3 figures, conference. arXiv admin note: substantial text overlap with arXiv:1806.04295, arXiv:1803.0584

Optimal Verification of Two-Qubit Pure States

In a recent work [Phys. Rev. Lett. 120, 170502 (2018)], Pallister et al. proposed an optimal strategy to verify non-maximally entangled two-qubit pure states under the constraint that the accessible measurements being locally projective and non-adaptive. Their nice result leads naturally to the question: What is the optimal strategy among general LOCC measurements? In this Letter, we answer this problem completely for two-qubit pure states. To be specific, we give the optimal strategy for each of the following available classes of measurements: (i) local operations and one-way classical communication (one-way LOCC) measurements; (ii) local operations and two-way classical communication (two-way LOCC) measurements; and (iii) separable measurements. Surprisingly, our results reveal that for the two-qubit pure state verification problem, two-way LOCC measurements remarkably outperforms one-way LOCC measurements and has the same power as the separable measurements

High order fast algorithm for the Caputo fractional derivative

In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of $u'(t)$ with the kernel $(t_n-t)^{-\alpha}$. In the fast algorithm, the interval $[0,t_{n-1}]$ is split into nonuniform subintervals. The number of the subintervals is in the order of $\log n$ at the $n$-th time step. The fractional kernel function is approximated by a polynomial function of $K$-th degree with a uniform absolute error on each subinterval. We save $K+1$ integrals on each subinterval, which can be written as a convolution of $u'(t)$ with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from $O(n)$ to $O((K+1)\log n)$ at the $n$-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples

Entanglement versus Bell nonlocality of quantum nonequilibrium steady state

We study the entanglement and the Bell nonlocality of a coupled two-qubit system, in which each qubit is coupled with one individual environment. We study how the nonequilibrium environments (with different temperatures or chemical potentials) influence the entanglement and the Bell nonlocality. Dependent on the inter-qubit coupling strength (relatively weak or strong compared to local qubits' frequencies) or the environmental nature (bosonic or fermionic), the two-qubit steady state can have strong correlations and violate the Bell inequalities with two or three measurements per party. Equilibrium environments compared to the nonequilibrium environments (with fixed mean temperatures or chemical potentials) do not give the maximal entanglement or the maximal violation of Bell inequalities if the two qubits are not identical, such as the two qubits having an energy detuning or coupling to the environment with unbalanced weights. The nonequilibrium conditions (characterized by the temperature differences) which give the maximal violation of Bell inequalities are different from the nonequilibrium conditions which give the maximal entanglement. The entanglement and the Bell nonlocality have different responses to the nonequilibrium environments. The spatial asymmetric two-qubit system coupled with nonequilibrium bosonic environments shows the thermal rectification effect, which can be witnessed by the Bell nonlocality. Our study demonstrates that the nonequilibrium environments are both valuable for the entanglement and Bell nonlocality resources, based on different optimal nonequilibrium conditions though.Comment: 13 pages, 11 figure