Mean estimation from adaptive one-bit measurements

Kipnis, Alon; Duchi, John C.

doi:10.1109/allerton.2017.8262847

Cited by 4 publications

(2 citation statements)

References 46 publications

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“…In simulations, we demonstrate that by choosing b large enough, the approximation of analog measurements holds and the MSE from ( 18) is achieved by b-bit quantized data. In addition to the power constraints in (25), systems may also have other physical constraints on the number of measurements. This can be due to system design or available workspace, such as a field in which sensors are deployed, requiring a minimal distance from each other to avoid interference.…”

Section: B Constraintsmentioning

confidence: 99%

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Berman,

Routtenberg

2020

Preprint

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Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation performance that is based on quantized data. In order to maintain physical constraints and simultaneously bring substantial performance gain, in this work we consider systems with mixedresolution, 1-bit quantized and continuous-valued, data. First, we describe the linear minimum mean-squared error (LMMSE) estimator and its associated mean-squared error (MSE) for the general mixed-resolution model. However, the MSE of the LMMSE requires matrix inversion in which the number of measurements defines the matrix dimensions and thus, is not a tractable tool for optimization and system design. Therefore, we present the linear Gaussian orthonormal (LGO) measurement model and derive a closed-form analytic expression for the MSE of the LMMSE estimator under this model. In addition, we present two common special cases of the LGO model: 1) scalar parameter estimation and 2) channel estimation in mixed-ADC multiple-input multiple-output (MIMO) communication systems. We then solve the resource allocation optimization problem of the LGO model with the proposed tractable form of the MSE as an objective function and under a power constraint using a one-dimensional search. Moreover, we present the concept of dithering for mixed-resolution models and optimize the dithering noise as part of the resource allocation optimization problem for two dithering schemes: 1) adding noise only to the quantized measurements and 2) adding noise to both measurement types. Finally, we present simulations that demonstrate the advantages of using mixed-resolution measurements and the possible improvement introduced with dithering and resource allocation.

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Section: B Constraintsmentioning

confidence: 99%

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Berman,

Routtenberg

2020

Preprint

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“…In particular, such an encoder is agnostic to the relationship between X and θ. This situation is in contrast to optimal quantization schemes in indirect source coding [14], [15] and in problems involving estimation from compressed date [7], [10], [12], [13], [35], [36], where the specification of the model θ → X is needed for the design of compression and estimation schemes. As a result, the random spherical coding scheme we rely on is sub-optimal in general, although it can be applied in situations where the model θ → X is unknown at the compressor.…”

Section: B Background and Related Workmentioning

confidence: 99%

Gaussian Approximation of Quantization Error for Estimation from Compressed Data

Kipnis

Reeves

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that the Wasserstein distance between a bitrate-R compressed version of X and its observation under an AWGN-channel of signal-to-noise ratio 2 2R −1 is sub-linear in the problem dimension. We utilize this fact to connect the risk of an estimator based on an AWGN-corrupted version of X to the risk attained by the same estimator when fed with its bitrate-R quantized version. We demonstrate the usefulness of this connection by deriving various novel results for inference problems under compression constraints, including noisy source coding and limited-bitrate parameter estimation.

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Mean Estimation From One-Bit Measurements

Kipnis¹,

Duchi

2022

IEEE Trans. Inform. Theory

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Mean estimation from adaptive one-bit measurements

Cited by 4 publications

References 46 publications

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Gaussian Approximation of Quantization Error for Estimation from Compressed Data

Mean Estimation From One-Bit Measurements

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