A lower bound on the error probability for signals in white Gaussian noise

Seguin, G.

doi:10.1109/18.737550

Cited by 45 publications

(39 citation statements)

References 7 publications

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“…Constraint (25) means that the weight of the noncritical vector is necessary smaller than the weight of a (strongly or weakly) critical vector. On the contrary, constraint (26) means that the weight of the noncritical vector does not be too small compared to the weight of a critical vector. Constraint (27) means that the difference between the weights of two noncritical vectors and must be balanced in regard to the geometric distances between them.…”

Section: Constrained Epsilon-equalizer Test For Simple Hypothesesmentioning

confidence: 99%

“…It follows that but with a larger threshold. In fact, the right hand term in the constraint (28) has increased (the other constraints (26) and (27) do not depend on ). It means that the 's for remain constants or become larger, which implies that increases and, also, .…”

Section: False Alarm Probabilitymentioning

confidence: 99%

“…Let us consider the problem (LP) defined by (24)- (26). It is straightforward to verify that (39) for all .…”

Section: A Optimal Weight Vectormentioning

confidence: 99%

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Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Fillatre

2011

IEEE Trans. Inform. Theory

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Abstract-A constrained epsilon-minimax test is proposed to detect and classify nonorthogonal vectors in Gaussian noise, with a general covariance matrix, and in presence of linear interferences. This test is epsilon-minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability. This loss is even more negligible as the signal-to-noise ratio is large. Furthermore, it is also an epsilon-equalizer test since its classification error probabilities are equalized up to a negligible difference. When the signal-to-noise ratio is sufficiently large, an asymptotically equivalent test with a very simple form is proposed. This equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of Euclidean distance. Numerical experiments on active user identification in a multiuser system confirm the theoretical findings.Index Terms-Constrained minimax test, generalized likelihood ratio test, linear nuisance parameters, multiple hypothesis testing, statistical classification, user activity detection.

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Section: Constrained Epsilon-equalizer Test For Simple Hypothesesmentioning

confidence: 99%

Section: False Alarm Probabilitymentioning

confidence: 99%

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Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Fillatre

2011

IEEE Trans. Inform. Theory

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“…We use Seguin's bound [11] to provide a lower bound on the decoder performance which states that the probability of error given that the signal s u is transmitted through an AWGN channel with variance N 0 /2, denoted by P(ε|s u ), is lower bounded as…”

Section: B Performance Lower Boundsmentioning

confidence: 99%

“…Furthermore, we construct randomized serially concatenated convolutional codes (RSCCCs) based on the proposed randomized convolutional codes. Finally, using existing algorithms for computing the distance spectra of convolutional codes [10], we provide lower and upper bounds on the performance of the randomized convolutional codes in terms of codeword error probabilities, by utilizing Seguin's lower bound and tangential sphere bound [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Randomized Convolutional Codes for the Wiretap Channel

Nooraiepour¹,

Duman²

2017

IEEE Trans. Commun.

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Abstract-We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper's channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap.

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Electromyographic (EMG) Decomposition

Marateb

McGill

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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An electromyographic (EMG) signal is a biomedical signal derived from measuring electrical potentials generated in contracting muscles. EMG signals can be recorded using either intramuscular (iEMG) or surface electrodes (sEMG). EMG signals are composed of motor unit action potential (MUAP) trains, the MUAP being the signal detected in response to the discharge of a group of muscle fibers innervated by a single motoneuron. The process of extracting the MUAP trains from an EMG signal is referred to as EMG decomposition. EMG decomposition makes it possible to study the behavior of individual motoneurons and thus to decode the neural drive to a muscle at a very precise level. This article reviews the different electrodes used to record iEMG and sEMG signals, the main steps in pattern‐matching decomposition algorithms (filtering, segmentation, clustering, classification, and resolving superpositions), the blind‐source separation techniques used for decomposing high‐density sEMG signals, the principal decomposition programs that have been described in the literature, including those that are publicly available, and approaches for assessing the accuracy of decomposition algorithms and particular decomposition results. Finally, an interactive tutorial on iEMG decomposition is provided.

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A lower bound on the error probability for signals in white Gaussian noise

Cited by 45 publications

References 7 publications

Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Constrained Epsilon-Minimax Test for Simultaneous Detection and Classification

Randomized Convolutional Codes for the Wiretap Channel

Electromyographic (EMG) Decomposition

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