In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive nonconforming finite element method. In each step of the algorithm, the iterative solution of the discrete system is controlled by ...
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In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive nonconforming finite element method. In each step of the algorithm, the iterative solution of the discrete system is controlled by an adaptive stopping criterion, and the local refinement is based on either a simple edge residual or a volume term, depending on an adaptive marking strategy. We prove that this marking strategy guarantees a strict reduction of the error, augmented by the volume term and an additional oscillation term, and quasi-optimal complexity of the generated sequence of meshes.
In this article, we propose an enhanced random access preamble (PA) detector for the low earth orbit (LEO) satellite-based non-terrestrial network (NTN) Internet-of-Things (IoT) that efficiently detects non-orthogonal...
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In this article, we propose an enhanced random access preamble (PA) detector for the low earth orbit (LEO) satellite-based non-terrestrial network (NTN) Internet-of-Things (IoT) that efficiently detects non-orthogonal PAs while suppressing interference. The proposed detector operates in two stages to efficiently suppress the interference caused by non-orthogonal PAs. In the first stage, reconstruction and cancellation of non-orthogonal PAs are performed. In the second stage, final PA detection is performed iteratively using the reconstructed PAs and received signal. In addition, we theoretically derive the probability of PA misdetection, PA collision, and successful PA detection under typical NTN line-of-sight (LoS) channel conditions. Simulation results verify that the proposed two-stage PA detector (TSPD) achieves performance close to the theoretical upper bound in terms of successful PA detection probability. The TSPD also shows a significantly greater successful PA detection probability than the conventional PA detector using orthogonal PAs while satisfying the random access requirement for the 3rd generation partnership project (3GPP) standard. Moreover, compared to the conventional PA detector for non-orthogonal PA, which adopts an interference cancellation scheme, the TSPD achieves up to 25.6 times lower detection complexity.
In this paper we formally introduce the distinction between strong and weak precedence relation in scheduling for the case of trees. We demonstrate that this distinction in precedence relation for trees (as demonstrat...
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In this paper we formally introduce the distinction between strong and weak precedence relation in scheduling for the case of trees. We demonstrate that this distinction in precedence relation for trees (as demonstrated in earlier work for chains) is a proper one in the sense that some problems are solvable in polynomial time if weak tree relation is assumed and are NP-hard in the case of strong tree relations. For some other problems, both weak tree and strong tree relations are NP-hard, and for yet other problems both weak and strong tree relations are polynomially solvable. Since the distinction between strong and weak tree precedence was not clearly recognized in the past, this work establishes the existence of new problem categories in scheduling. (C) 1999 Elsevier Science B.V. All rights reserved.
We introduce the maximum agreement phylogenetic subnetwork problem (MASN) for finding branching structure shared by a set of phylogenetic networks. We prove that the problem is NP-hard even if restricted to three phyl...
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We introduce the maximum agreement phylogenetic subnetwork problem (MASN) for finding branching structure shared by a set of phylogenetic networks. We prove that the problem is NP-hard even if restricted to three phylogenetic networks and give an O(n(2))-time algorithm for the special case of two level-1 phylogenetic networks, where n is the number of leaves in the input networks and where N is called a level-f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of N containing at most f nodes with indegree 2. We also show how to extend our technique to yield a polynomial-time algorithm for any two level-f phylogenetic networks N-1, N-2 satisfying f = O(log n);more precisely, its running time is O(vertical bar V(N-1)vertical bar (.) vertical bar V(N-2)vertical bar (.) 2(f1+f2)), where V(N-i) and f(i) denote the set of nodes in Ni and the level of N-i, respectively, for i is an element of {1, 2}. (c) 2005 Elsevier B.V. All rights reserved.
Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run averag...
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Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function.
We observe that the problem of deciding the winner in mean payoff games is in the complexity class UP boolean AND co-UP. We also show a simple reduction from parity games to mean payoff games. From this it follows tha...
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We observe that the problem of deciding the winner in mean payoff games is in the complexity class UP boolean AND co-UP. We also show a simple reduction from parity games to mean payoff games. From this it follows that deciding the winner in parity games and the modal mu-calculus model checking are in UP boolean AND co-UP. (C) 1998 Elsevier Science B.V. All rights reserved.
Reversible digital watermarking techniques enable the recovery of the original 'cover image' from a watermarked image in a distortion-free way. Reversible watermarking techniques find application in military a...
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Reversible digital watermarking techniques enable the recovery of the original 'cover image' from a watermarked image in a distortion-free way. Reversible watermarking techniques find application in military and medical imagery, where integrity of the cover image is of utmost importance. In this study, we propose a reversible digital image watermarking algorithm that predicts a pixel greyscale value exploiting its correlation with its neighbouring pixels, and embeds watermark bits into the prediction errors. Our algorithm succeeds in providing high embedding capacity with very low distortion, without 'multilayer embedding', hence reducing the computational burden compared with existing state-of-the-art algorithms. In addition, our results indicate that the resulting data overhead requirement is extremely low.
This paper presents a novel low-complexity sequential, blind, pilot-assisted estimator for the sampling frequency offset (SFO) and the carrier frequency offset (CFO), for orthogonal frequency-division multiplexing (OF...
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This paper presents a novel low-complexity sequential, blind, pilot-assisted estimator for the sampling frequency offset (SFO) and the carrier frequency offset (CFO), for orthogonal frequency-division multiplexing (OFDM) communications. The proposed algorithm processes the received subcarriers to obtain a cost function which depends only on a single unknown parameter at a time, either the SFO or the CFO, as well as on a specifically designed auxiliary parameter, while ignoring the noise. Then, by computing the cost function at a few selected values of the auxiliary parameter, an explicit estimator for each unknown parameter is derived, thereby avoiding the need for a search. To the best of our knowledge, this is the first time such a deterministic approach is applied to the joint estimation of the SFO and the CFO. Moreover, the proposed estimator does not require knowledge of the channel coefficients at the pilot subcarriers, and achieves good performance with a relatively small number of pilot symbols, which results in a low computational complexity. Simulation results show that at low computational complexity, there are many scenarios in which the new estimator achieves smaller estimation errors compared to other existing methods.
Layered decoding is well appreciated in low-density parity-check (LDPC) decoder implementation since it can achieve effectively high decoding throughput with low computation complexity. This work, for the first time, ...
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Layered decoding is well appreciated in low-density parity-check (LDPC) decoder implementation since it can achieve effectively high decoding throughput with low computation complexity. This work, for the first time, addresses low-complexity column-layered decoding schemes and very-large-scale integration (VLSI) architectures for multi-Gb/s applications. At first, the min-sum algorithm is incorporated into the column-layered decoding. Then algorithmic transformations and judicious approximations are explored to minimise the overall computation complexity. Compared to the original column-layered decoding, the new approach can reduce the computation complexity in check node processing for high-rate LDPC codes by up to 90% while maintaining the fast convergence speed of layered decoding. Furthermore, a relaxed pipelining scheme is presented to enable very high clock speed for VLSI implementation. Equipped with these new techniques, an efficient decoder architecture for quasi-cyclic LDPC codes is developed and implemented with 0.13 mu m VLSI implementation technology. It is shown that a decoding throughput of nearly 4 Gb/s at a maximum of 10 iterations can be achieved for a (4096, 3584) LDPC code. Hence, this work has facilitated practical applications of column-layered decoding and particularly made it very attractive in high-speed, high-rate LDPC decoder implementation.
We present an alternative explicit expression for the Moore-Penrose inverse of a matrix. Based on this expression, we propose a Gauss-Jordan elimination method for the computation of A(dagger). Its computational compl...
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We present an alternative explicit expression for the Moore-Penrose inverse of a matrix. Based on this expression, we propose a Gauss-Jordan elimination method for the computation of A(dagger). Its computational complexity indicates that this method is more efficient than the existing Gauss-Jordan elimination method in the literature for a large class of problems. An example is included to illustrate the new method. (C) 2012 Elsevier Inc. All rights reserved.
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