In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver only checks whether a message of special interest to him has been sent or not. In contrast to Shannon transmission codes, the size of ID codes for a Discrete Memoryless Channel (DMC) grows doubly exponentially fast with the blocklength, if randomized encoding is used. This groundbreaking result makes the ID paradigm more efficient than the classical Shannon transmission in terms of necessary energy and hardware components. Further gains can be achieved by taking advantage of additional resources such as feedback. We study the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. The sender simultaneously sends an ID message over the DMC with a random state and estimates the channel state via a strictly causal channel output. The random channel state is available to neither the sender nor the receiver. For the proposed system model, we establish a lower bound on the ID capacity-distortion function.
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We consider the problems of testing and learning quantum $k$-junta channels, which are $n$-qubit to $n$-qubit quantum channels acting non-trivially on at most $k$ out of $n$ qubits and leaving the rest of qubits unchanged. We show the following. 1. An $\widetilde{O}\left(k\right)$-query algorithm to distinguish whether the given channel is $k$-junta channel or is far from any $k$-junta channels, and a lower bound $\Omega\left(\sqrt{k}\right)$ on the number of queries; 2. An $\widetilde{O}\left(4^k\right)$-query algorithm to learn a $k$-junta channel, and a lower bound $\Omega\left(4^k/k\right)$ on the number of queries. This gives the first junta channel testing and learning results, and partially answers an open problem raised by Chen et al. (2023). In order to settle these problems, we develop a Fourier analysis framework over the space of superoperators and prove several fundamental properties, which extends the Fourier analysis over the space of operators introduced in Montanaro and Osborne (2010).
This paper examines asymmetric and time-varying dependency structures between financial returns, using a novel approach consisting of a combination of regime-switching models and the local Gaussian correlation (LGC). We propose an LGC-based bootstrap test for whether the dependence structure in financial returns across different regimes is equal. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime-switching models with copula theory. Furthermore, the LGC is a semi-parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using returns from the US-UK stock markets and the US stock and government bond markets. Using a two-regime model for the US-UK stock returns, the test rejects equality of the dependence structure in the two regimes. Furthermore, we find evidence of lower tail dependence in the regime associated with financial downturns in the LGC structure. For a three-regime model fitted to US stock and bond returns, the test rejects equality of the dependence structures between all regime pairs. Furthermore, we find that the LGC has a primarily positive relationship in the time period 1980-2000, mostly a negative relationship from 2000 and onwards. In addition, the regime associated with bear markets indicates less, but asymmetric dependence, clearly documenting the loss of diversification benefits in times of crisis.
In this paper, we design a novel two-phase unsourced random access (URA) scheme in massive multiple input multiple output (MIMO). In the first phase, we collect a sequence of information bits to jointly acquire the user channel state information (CSI) and the associated information bits. In the second phase, the residual information bits of all the users are partitioned into sub-blocks with a very short length to exhibit a higher spectral efficiency and a lower computational complexity than the existing transmission schemes in massive MIMO URA. By using the acquired CSI in the first phase, the sub-block recovery in the second phase is cast as a compressed sensing (CS) problem. From the perspective of the statistical physics, we provide a theoretical framework for our proposed URA scheme to analyze the induced problem based on the replica method. The analytical results show that the performance metrics of our URA scheme can be linked to the system parameters by a single-valued free entropy function. An AMP-based recovery algorithm is designed to achieve the performance indicated by the proposed theoretical framework. Simulations verify that our scheme outperforms the most recent counterparts.
We explore two differentiable deep declarative layers, namely least squares on sphere (LESS) and implicit eigen decomposition (IED), for learning the principal matrix features (PMaF). This can be used to represent data features with a low-dimension vector containing dominant information from a high-dimension matrix. We first solve the problems with iterative optimization in the forward pass and then backpropagate the solution for implicit gradients under a bi-level optimization framework. Particularly, adaptive descent steps with the backtracking line search method and descent decay in the tangent space are studied to improve the forward pass efficiency of LESS. Meanwhile, exploited data structures are used to greatly reduce the computational complexity in the backward pass of LESS and IED. Empirically, we demonstrate the superiority of our layers over the off-the-shelf baselines by comparing the solution optimality and computational requirements.
Verification and safety assessment of neural network controlled systems (NNCSs) is an emerging challenge. To provide guarantees, verification tools must efficiently capture the interplay between the neural network and the physical system within the control loop. In this paper, a compositional approach focused on inclusion preserving long term symbolic dependency modeling is proposed for the analysis of NNCSs. First of all, the matrix structure of symbolic zonotopes is exploited to efficiently abstract the input/output mapping of the loop elements through (inclusion preserving) affine symbolic expressions, thus maintaining linear dependencies between interacting blocks. Then, two further extensions are studied. Firstly, symbolic polynotopes are used to abstract the loop elements behaviour by means of polynomial symbolic expressions and dependencies. Secondly, an original input partitioning algorithm takes advantage of symbol preservation to assess the sensitivity of the computed approximation to some input directions. The approach is evaluated via different numerical examples and benchmarks. A good trade-off between low conservatism and computational efficiency is obtained.
In this paper, due to the important value in practical applications, we consider the coded distributed matrix multiplication problem of computing $AA^\top$ in a distributed computing system with $N$ worker nodes and a master node, where the input matrices $A$ and $A^\top$ are partitioned into $m$-by-$p$ and $p$-by-$m$ blocks of equal-size sub-matrices respectively. For effective straggler mitigation, we propose a novel computation strategy, named \emph{folded polynomial code}, which is obtained by modifying the entangled polynomial codes. Moreover, we characterize a lower bound on the optimal recovery threshold among all linear computation strategies when the underlying field is the real number field, and our folded polynomial codes can achieve this bound in the case of $m=1$. Compared with all known computation strategies for coded distributed matrix multiplication, our folded polynomial codes outperform them in terms of recovery threshold, download cost, and decoding complexity.
This paper introduces a novel approach to active feature acquisition for classification, which is the task of sequentially selecting the most informative subset of features to achieve optimal prediction performance during testing while minimizing cost. The proposed approach involves a new lazy model that is significantly faster and more efficient compared to existing methods, while still producing comparable accuracy results. During the test phase, the proposed approach utilizes Fisher scores for feature ranking to identify the most important feature at each step. In the next step the training dataset is filtered based on the observed value of the selected feature and then we continue this process to reach to acceptable accuracy or limit of the budget for feature acquisition. The performance of the proposed approach was evaluated on synthetic and real datasets, including our new synthetic dataset, CUBE dataset and also real dataset Forest. The experimental results demonstrate that our approach achieves competitive accuracy results compared to existing methods, while significantly outperforming them in terms of speed. The source code of the algorithm is released at github with this link: //github.com/alimirzaei/FCwSFS.
Strong secrecy communication over a discrete memoryless state-dependent multiple access channel (SD-MAC) with an external eavesdropper is investigated. The channel is governed by discrete memoryless and i.i.d. channel states and the channel state information (CSI) is revealed to the encoders in a causal manner. Inner and outer bounds are provided. To establish the inner bound, we investigate coding schemes incorporating wiretap coding and secret key agreement between the sender and the legitimate receiver. Two kinds of block Markov coding schemes are proposed. The first one is a new coding scheme using backward decoding and Wyner-Ziv coding and the secret key is constructed from a lossy description of the CSI. The other one is an extended version of the existing coding scheme for point-to-point wiretap channels with causal CSI. A numerical example shows that the achievable region given by the first coding scheme can be strictly larger than the second one. However, these two schemes do not outperform each other in general and there exists some numerical examples that in different channel models each coding scheme achieves some rate pairs that cannot be achieved by another scheme. Our established inner bound reduces to some best-known results in the literature as special cases. We further investigate some capacity-achieving cases for state-dependent multiple access wiretap channels (SD-MAWCs) with degraded message sets. It turns out that the two coding schemes are both optimal in these cases.
Estimating the output size of a join query is a fundamental yet longstanding problem in database query processing. Traditional cardinality estimators used by database systems can routinely underestimate the true join size by orders of magnitude, which leads to significant system performance penalty. Recently, size upper bounds have been proposed that are based on information inequalities and incorporate sizes and max-degrees from input relations, yet they grossly overestimate the true join size. This paper puts forward a general class of size bounds that are based on information inequalities involving Lp-norms on the degree sequences of the join columns. They generalise prior efforts and can be asymptotically tighter than the known bounds. We give two types of lower and upper bounds: some hold for all entropic vectors, while others hold for all polymatroids. Whereas the former are asymptotically tight but possibly not computable, the latter are computable but not even asymptotically tight. In the case when all degree constraints are over a single variable then we call them "simple", and prove that the polymatroid and entropic bounds are equal, they are tight up to a query-dependent constant (which is stronger than asymptotically tight), are computable in exponential time in the size of the query, and that the worst case database instance that matches the bound has a simple structure called a "normal database".
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework and derive a finite-dimensional approximating system via pseudospectral discretization. For renewal equations, via integration we consider a reformulation in a space of absolutely continuous functions that ensures that point evaluation is well defined. We prove the one-to-one correspondence of equilibria between the original equation and its approximation, and that linearization and discretization commute. Our most important result is the proof of convergence of the characteristic roots of the pseudospectral approximation of the linear(ized) equations, which ensures that the finite-dimensional system correctly reproduces the stability properties of the original linear equation if the dimension of the approximation is large enough. This result is illustrated with several numerical tests, which also demonstrate the effectiveness of the approach for the bifurcation analysis of equilibria of nonlinear equations.
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