1,721,444 research outputs found
Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance
No full textLet X,Y denote two independent real Gaussian × and × matrices with ,≥, each constituted by zero mean i.i.d. columns with common covariance. The Roy's largest root criterion, used in multivariate analysis of variance (MANOVA), is based on the statistic of the largest eigenvalue, Θ1, of (A+B)−1B, where A=XXT and B=YYT are independent central Wishart matrices. We derive a new expression and efficient recursive formulas for the exact distribution of Θ1. The expression can be easily calculated even for large parameters, eliminating the need of pre-calculated tables for the application of the Roy's test
On the probability that all eigenvalues of Gaussian, Wishart, and double Wishart random matrices lie within an interval
Full text linkWe derive the probability that all eigenvalues of a random matrix M lie within an arbitrary interval [a, b], Ï(a, b) Î ́â Pra ⤠λmin(M), λmax(M) ⤠b, when M is a real or complex finite-dimensionalWishart, doubleWishart, or Gaussian symmetric/Hermitian matrix. We give efficient recursive formulas allowing the exact evaluation of Ï(a, b) for Wishart matrices, even with a large number of variates and degrees of freedom. We also prove that the probability that all eigenvalues are within the limiting spectral support (given by the MarÄenko-Pastur or the semicircle laws) tends for large dimensions to the universal values 0.6921 and 0.9397 for the real and complex cases, respectively. Applications include improved bounds for the probability that a Gaussian measurement matrix has a given restricted isometry constant in compressed sensing
Short Codes for Quantum Channels With One Prevalent Pauli Error Type
Full text linkOne of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic errors, i.e., errors represented by arbitrary combinations of Pauli X, Y and Z operators, in this paper we investigate the design of stabilizer QECC able to correct a given number eg of generic Pauli errors, plus eZ Pauli errors of a specified type, e.g., Z errors. These codes can be of interest when the quantum channel is asymmetric in that some types of error occur more frequently than others. We first derive a generalized quantum Hamming bound for such codes, then propose a design methodology based on syndrome assignments. For example, we found a [[9, 1]] quantum error-correcting code able to correct up to one generic qubit error plus one Z error in arbitrary positions. This, according to the generalized quantum Hamming bound, is the shortest code with the specified error correction capability. Finally, we evaluate analytically the performance of the new codes over asymmetric channels
Enumeration and Identification of Active Users for Grant-Free NOMA Using Deep Neural Networks
Full text linkIn next-generation mobile radio systems, multiple access schemes will support a massive number of uncoordinated devices exhibiting sporadic traffic, transmitting short packets to a base station. Grant-free non-orthogonal multiple access (NOMA) has been introduced to provide services to a large number of devices and to reduce the communication overhead in massive machine-type communication (mMTC) scenarios. In grant-free communication, there is no coordination between the device and base station (BS) before the data transmission; therefore, the challenging task of active users detection (AUD) must be conducted at the BS. For NOMA with sparse spreading, we propose a deep neural network (DNN)-based approach for AUD called active users enumeration and identification (AUEI). It consists of two phases: firstly, a DNN is used to estimate the number of active users; then in the second phase, another DNN identifies them. To speed up the training process of the DNNs, we propose a multi-stage transfer learning technique. Our numerical results show a remarkable performance improvement of AUEI in comparison to previously proposed approaches
Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
Full text linkOne of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution
Spectral Shape of Non-Binary LDPC Code Ensembles with Separated Variable Nodes
No full textThe non-binary weight distribution and its spectral
shape is developed for a partially-structured ensemble of low-density parity-check codes over finite fields. The ensemble is characterized by all degree-2 variable nodes and some of the degree-3 variable nodes being separated. It is shown that, under node separation, the typical minimum distance is strictly positive and significantly higher than the one of the corresponding unstructured ensemble
Logical Error Rates of XZZX and Rotated Quantum Surface Codes
Full text linkSurface codes are versatile quantum error- correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli X or Pauli Z operators in a square structure, these codes can be improved by rotating the lattice or incorporating a mix of generators in the XZZX variant. However, a comprehensive theoretical analysis of the logical error rate for these variants has been lacking. To address this gap, we present theoretical formulas based on recent advancements in understanding the weight distribution of stabilizer codes. For example, over an asymmetric channel with asymmetry A = 10 and a physical error rate p → 0, we observe that the logical error rate asymptotically approaches pL → 10p^2 for the rotated [[9, 1, 3]] XZZX code and pL → 18.3p^2 for the [[13, 1, 3]] surface code. Additionally, we observe a particular behavior regarding rectangular lattices in the presence of asymmetric channels. Our findings demonstrate that implementing both rotation and XZZX modifications simultaneously can lead to suboptimal performance. Thus, in scenarios involving a rectangular lattice, it is advisable to avoid using both modifications simultaneously
On-Line Construction of Irregular Repeat Accumulate Codes for Packet Erasure Channels
No full textIn many applications erasure correcting codes are used to recover packet losses at high protocol stack layers. The objects (e.g. files) to be transmitted often have variable sizes, resulting in a variable number of packets to be encoded by the packet-level encoder. In this paper, algorithms for the (on-line) flexible design of parity-check matrices for irregular-repeat-accumulate codes are investigated. The proposed algorithms allow designing in fast manner parity-check matrices that are suitable for low-complexity maximum-likelihood decoding. The code ensembles generated by the algorithms are analyzed via extrinsic information transfer charts. Numerical results show how the designed codes can attain codeword error rates as low as 10^{-5} without appreciable losses w.r.t. the performance of idealized maximum-distance separable codes. Finally, we apply the proposed codes to the upcoming aeronautical communication standard, showing large performance improvements and proving the efficiency and the flexibility of the developed method
A Joint PHY and MAC Layer Design for Coded Random Access with Massive MIMO
No full textGrant-free access schemes are candidates to support future massive multiple access applications owing to their capability to reduce control signaling and latency. As a promising class of grant-free schemes, coded random access schemes can achieve high reliabilities also with uncoordinated transmissions and therefore in presence packet collisions. In this paper, an analysis tool for coded random access, based on density evolution, is proposed and exploited for system design and optimization. In sharp contrast with the existing literature, where such tools have been developed under simplified channel assumptions, the proposed tool captures not only MAC layer features, but also the physical wireless fading channel and a realistic physical layer signal processing based on multiple antennas and randomlychosen orthogonal pilots. Theoretical results are validated by comparison with symbol-level Monte Carlo simulations
IMPROVING THE PERFORMANCE OF AEROMACS BY COOPERATIVE COMMUNICATIONS
No full textCooperative communications have gained in the past years an increasing attention, showing promising outcomes on the performance of the systems. The future airport surface communication system represents a potential candidate for the exploitation of these techniques. Focusing on the airport context, we analyze low complexity single-relay cooperative methods. Moreover, we implement a simple amplify and forward scheme showing its performance in the airport communication context
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