Quantisation effects in PDMM: A first study for synchronous distributed averaging

Schellekens, Daan H. M.; Sherson, Thomas; Heusdens, Richard

doi:10.1109/icassp.2017.7952955

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…Dithering consists of adding a random additive signal n d , called dither, to the input signal x prior to quantization. Dithering is widely used in distributed signal processing [28], [31], [34], [47], which consists of iterative algorithms akin to distributed graph filtering. In subtractive dithered quantization, the dither signal is generated by a pseudo-random generator at the transmitter node and it is subtracted at the receiving node after transmission.…”

Section: B Dithered Quantizationmentioning

confidence: 99%

Quantization Analysis and Robust Design for Distributed Graph Filters

Saad

Beferull-Lozano

Isufi

2022

IEEE Trans. Signal Process.

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Distributed graph filters have recently found applications in wireless sensor networks (WSNs) to solve distributed tasks such as reaching consensus, signal denoising, and reconstruction. However, when implemented over WSNs, the graph filters should deal with network limited energy constraints as well as processing and communication capabilities. Quantization plays a fundamental role to improve the latter but its effects on distributed graph filtering are little understood. WSNs are also prone to random link losses due to noise and interference. In this instance, the filter output is affected by both the quantization error and the topological randomness error, which, if it is not properly accounted in the filter design phase, may lead to an accumulated error through the filtering iterations and significantly degrade the performance. In this paper, we analyze how quantization affects distributed graph filtering over both time-invariant and time-varying graphs. We bring insights on the quantization effects for the two most common graph filters: the finite impulse response (FIR) and autoregressive moving average (ARMA) graph filter. Besides providing a comprehensive analysis, we devise theoretical performance guarantees on the filter performance when the quantization stepsize is fixed or changes dynamically over the filtering iterations. For FIR filters, we show that a dynamic quantization stepsize leads to more reduction of the quantization noise than in the fixed-stepsize quantization. For ARMA graph filters, we show that decreasing the quantization stepsize over the iterations reduces the quantization noise to zero at the steady-state. In addition, we propose robust filter design strategies that minimize the quantization noise for both timeinvariant and time-varying networks. Numerical experiments on synthetic and two real data sets corroborate our findings and show the different trade-offs between quantization bits, filter order, and robustness to topological randomness.

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Section: B Dithered Quantizationmentioning

confidence: 99%

Quantization Analysis and Robust Design for Distributed Graph Filters

Saad

Beferull-Lozano

Isufi

2022

IEEE Trans. Signal Process.

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“…V. PROPOSED APPROACH After explaining why there is a trade-off between privacy and communication cost in noise insertion approaches, we now proceed to introduce the proposed approach which addresses this trade-off by using the adaptive differential quantization scheme of [39], [40]. The reason of choosing this quantization scheme is because it can help to save the communication cost without compromising privacy.…”

Section: Trade-off Between Privacy and Bitsmentioning

confidence: 99%

“…The main idea of applying adaptive differential quantization is based on the observation that for fixed point iterations the difference of successive iterations will converge to zero (i.e, it is a Cauchy sequence), which implies that the entropy of the difference of successive iterations will decrease to zero as the number of iteration increases. Motivated by this, the adaptive differential quantization scheme proposed in [39], [40] quantize the difference of the auxiliary variable at every two successive iterations with an adaptive cell-width decreasing with increasing iterations, details will be given below. By doing so, low data rate transmission between nodes can be achieved without compromising the accuracy of the algorithm.…”

Section: Trade-off Between Privacy and Bitsmentioning

confidence: 99%

Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

Li¹,

Heusdens²,

Christensen³

2021

Preprint

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Privacy issues and communication cost are both major concerns in distributed optimization. There is often a trade-off between them because the encryption methods required for privacy-preservation often incur expensive communication bandwidth. To address this issue, we, in this paper, propose a quantization-based approach to achieve both communication efficient and privacy-preserving solutions in the context of distributed optimization. By deploying an adaptive differential quantization scheme, we allow each node in the network to achieve its optimum solution with a low communication cost while keeping its private data unrevealed. Additionally, the proposed approach is general and can be applied in various distributed optimization methods, such as the primal-dual method of multipliers (PDMM) and the alternating direction method of multipliers (ADMM). Moveover, we consider two widely used adversary models: passive and eavesdropping. Finally, we investigate the properties of the proposed approach using different applications and demonstrate its superior performance in terms of several parameters including accuracy, privacy, and communication cost.

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“…where ϵ is a small positive number. In [34], [35], the convergence of PDMM was shown in the presence of quantization noise. Due to quantization, the dual variables exchanged among nodes are noisy, i.e.,μ…”

Section: Distributed Lcmv Beamforming With Quantization Noisementioning

confidence: 99%

“…Since the beamforming is performed iteratively with quantization, the quantization noise ζ (J) X k will accumulate at each iteration. However, in [34], it was shown that in case of quantization with sufficiently small fixed cell width (e.g., uniform quantization), the error accumulates but the growth is so slow that it can be considered constant over the iteration range of interest. That is, the primal MSE…”

Section: Proposed Distributed Rate Allocationmentioning

confidence: 99%

Distributed Rate-Constrained LCMV Beamforming

Zhang

Koutrouvelis

Heusdens

et al. 2019

IEEE Signal Process. Lett.

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In this letter, we propose a decentralized framework for rate-distributed linearly constrained minimum variance (LCMV) beamforming in wireless acoustic sensor networks (WASNs). To save the energy usage within the network, we propose to minimize the transmission cost and put a constraint on the noise reduction performance. Subsequently, we decentralize the obtained LCMV filter structure by exploiting an imposed block diagonal form of the noise correlation matrix. As a result, the beamformer weights are calculated in a decentralized fashion and each node can determine its quantization rate locally. Finally, numerical results validate the proposed method.

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Quantisation effects in PDMM: A first study for synchronous distributed averaging

Cited by 8 publications

References 12 publications

Quantization Analysis and Robust Design for Distributed Graph Filters

Quantization Analysis and Robust Design for Distributed Graph Filters

Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

Distributed Rate-Constrained LCMV Beamforming

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