Relation of signal set choice to the performance of optimal non-Gaussian detectors

Johnson, Don H.; Orsak, G.C.

doi:10.1109/26.237850

Cited by 31 publications

(18 citation statements)

References 10 publications

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“…While the Chernoff bound [11] proves an upper bound on error probability with respect to KL divergence in hypothesis testing, the bound has been found to be loose [9]. Though not a provable bound (upper or lower) on error probability, KL does provide a close proxy; supporting arguments in addition to that given above can be found in [9], [10].…”

Section: B Pairwise Error Using Kullback-leibler Divergencesupporting

confidence: 49%

“…This problem arises when trying to calculate the probability of error between two distributions parameterized by different target locations x m . In lieu of a closed-form expression, Kullback-Leibler (KL) divergence has been used as a close proxy to pairwise error probability [7], [9], [10]. We motivate this relationship by returning to the two-target case of the ML decode rule (5) and rewriting it as…”

Section: B Pairwise Error Using Kullback-leibler Divergencementioning

confidence: 99%

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Optimal Target Placement for Neural Communication Prostheses

Cunningham

Shenoy

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-Neural prosthetic systems have been designed to estimate continuous reach trajectories as well as discrete reach targets. In the latter case, reach targets are typically decoded from neural activity during an instructed delay period, before the reach begins. We have recently characterized the decoding speed and accuracy achievable by such a system. The results were obtained using canonical target layouts, independent of the tuning properties of the neurons available. Here we seek to increase decode accuracy by judiciously selecting the locations of the reach targets based on the characteristics of the neural population at hand. We present an optimal target placement algorithm that approximately maximizes decode accuracy with respect to target locations. Using maximum likelihood decoding, the optimal target placement algorithm yielded up to 11 and 12% improvement for two and sixteen targets, respectively. For four and eight targets, gains were more modest (5 and 3%, respectively) as the target layouts found by the algorithm closely resembled the canonical layouts. Thus, the algorithm can serve not only to find target layouts that outperform canonical layouts, but it can also confirm or help select among multiple canonical layouts. These results indicate that the optimal target placement algorithm is a valuable tool for designing highperformance prosthetic systems.Index Terms-Brain-machine interface, neural coding and decoding, motor control, pre-motor cortex, Kullback-Leibler divergence.

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Section: B Pairwise Error Using Kullback-leibler Divergencesupporting

confidence: 49%

Section: B Pairwise Error Using Kullback-leibler Divergencementioning

confidence: 99%

Optimal Target Placement for Neural Communication Prostheses

Cunningham

Shenoy

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

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“…Ultimately, for a given γ, σ 2 , number of signal points, and an average transmit power constraint, one might want to find the optimal signal constellation set that minimizes the SER. However, it is known that for non-Gaussian noise statistics, no analytical results for the optimal signal set exist [18], and numerical methods that are developed in solving such optimization problems are rather complicated [19]. Therefore, we only focus on four-point signal constellation optimization with some symmetry constraints such that the problem is more tractable, and the solution is more attractive for practical implementation purposes.…”

Section: Signal Constellation Optimizationmentioning

confidence: 99%

Signal Design and Detection in Presence of Nonlinear Phase Noise

Lau

Kahn

2007

J. Lightwave Technol.

119

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Abstract-In optical fiber transmission systems using inline amplifiers, the interaction of a signal and amplifier noise through the Kerr effect leads to nonlinear phase noise that can impair the detection of phase-modulated signals. We present analytical expressions for the maximum-likelihood (ML) decision boundaries and symbol-error rate (SER) for phase-shift keying and differential phase-shift keying systems with coherent and differentially coherent detection, respectively. The ML decision boundaries are in the form θ(r) = c 2 r 2 + c 1 r + c 0 , where θ and r are the phase and the amplitude of the received signal, respectively. Using the expressions for the SER, we show that the impact of phase error from carrier synchronization is small, particularly for transoceanic links. For modulation formats such as 16-quadrature amplitude modulation, we propose various transmitter and receiver phase rotation strategies such that the ML detection is well approximated by using straight-line decision boundaries. The problem of signal constellation design for optimal SER performance is also studied for a system with four signal points.Index Terms-Maximum likelihood (ML) detection, nonlinear optics, optical fiber communication, optical Kerr effect, phase noise, quadrature amplitude modulation (QAM).

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“…Owing to the noisy Poisson model, particular spike counts will erroneously decode a target mЈ when in fact the presented target was m. There is no closed-form expression for the probability of decode error between two Poisson noise distributions (Verdu 1986). Kullback-Leibler (KL) divergence is often used as a close proxy to pairwise error probability (Gockenbach and Kearsley 1999;Johnson and Orsak 1993;Johnson et al 2001). KL divergence measures how different two probability distributions are.…”

Section: Optimal Target Placement Algorithmmentioning

confidence: 99%

“…The use of KL as a proxy to error probability is intuitively sound, and our simulations have shown that increasing KL divergence (making the two distributions more different) corresponds well to decreasing error probability. KL is commonly used when error probability is not closed form (Gockenbach and Kearsley 1999;Johnson and Orsak 1993;Johnson et al 2001) with the understanding that making distributions more distinguishable (increasing the KL divergence) will generally reduce probability of error also. The relationship between KL and error probability can be motivated mathematically by returning to the two-target case of the ML decode rule (Eq.…”

Section: Optimal Target Placement Algorithmmentioning

confidence: 99%