@article{Koch2013,
title = {At Low SNR, Asymmetric Quantizers are Better},
author = {Koch, Tobias and Lapidoth, Amos},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6545291},
issn = {0018-9448},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {9},
pages = {5421--5445},
abstract = {We study the capacity of the discrete-time Gaussian channel when its output is quantized with a 1-bit quantizer. We focus on the low signal-to-noise ratio (SNR) regime, where communication at very low spectral efficiencies takes place. In this regime, a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2/$pi$, i.e., to cause an asymptotic power loss of approximately 2 dB. Here, it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. To avoid this power loss, flash-signaling input distributions are essential. Consequently, 1-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: at every fixed SNR, a threshold quantizer maximizes capacity among all 1-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case, a 1-bit output quantizer causes an unavoidable low-SNR asymptotic power loss. In the coherent case, however, this power loss is avoidable provided that we allow the quantizer to depend on the fading level.},
keywords = {1-bit quantizer, asymmetric signaling constellation, asymmetric threshold quantizers, asymptotic power loss, Capacity per unit energy, channel capacity, discrete-time Gaussian channel, flash-signaling input distribution, Gaussian channel, Gaussian channels, low signal-to-noise ratio (SNR), quantisation (signal), quantization, Rayleigh channels, Rayleigh-fading channel, signal-to-noise ratio, SNR, spectral efficiency},
pubstate = {published},
tppubtype = {article}
}

We study the capacity of the discrete-time Gaussian channel when its output is quantized with a 1-bit quantizer. We focus on the low signal-to-noise ratio (SNR) regime, where communication at very low spectral efficiencies takes place. In this regime, a symmetric threshold quantizer is known to reduce channel capacity by a factor of 2/$pi$, i.e., to cause an asymptotic power loss of approximately 2 dB. Here, it is shown that this power loss can be avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. To avoid this power loss, flash-signaling input distributions are essential. Consequently, 1-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: at every fixed SNR, a threshold quantizer maximizes capacity among all 1-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case, a 1-bit output quantizer causes an unavoidable low-SNR asymptotic power loss. In the coherent case, however, this power loss is avoidable provided that we allow the quantizer to depend on the fading level.

@inproceedings{Koch2011,
title = {Asymmetric Quantizers are Better at Low SNR},
author = {Koch, Tobias and Lapidoth, Amos},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6034037},
issn = {2157-8095},
year = {2011},
date = {2011-01-01},
booktitle = {2011 IEEE International Symposium on Information Theory Proceedings},
pages = {2592--2596},
publisher = {IEEE},
address = {St. Petersburg},
abstract = {We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/$pi$, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.},
keywords = {asymmetric one-bit quantizer, asymmetric signal constellations, channel capacity, Channel Coding, Constellation diagram, Decoding, discrete-time average-power-limited Gaussian chann, Gaussian channels, quantization, Signal to noise ratio, signal-to-noise ratio, SNR, spread spectrum communication, spread-spectrum communications, ultra wideband communication, ultrawideband communications, Upper bound},
pubstate = {published},
tppubtype = {inproceedings}
}

We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/$pi$, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.

2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 81–84, IEEE, San Juan, 2011, ISBN: 978-1-4577-2105-2.

@inproceedings{Achutegui2011,
title = {A Parallel Resampling Scheme and its Application to Distributed Particle Filtering in Wireless Networks},
author = {Achutegui, Katrin and Miguez, Joaquin},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6136051},
isbn = {978-1-4577-2105-2},
year = {2011},
date = {2011-01-01},
booktitle = {2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
pages = {81--84},
publisher = {IEEE},
address = {San Juan},
abstract = {We address the design of a particle filter (PF) that can be implemented in a distributed manner over a network of wireless sensor nodes, each of them collecting their own local data. This is a problem that has received considerable attention lately and several methods based on consensus, the transmission of likelihood information, the truncation and/or the quantization of data have been proposed. However, all existing schemes suffer from limitations related either to the amount of required communications among the nodes or the accuracy of the filter outputs. In this work we propose a novel distributed PF that is built around the distributed resampling with non-proportional allocation (DRNA) algorithm. This scheme guarantees the properness of the particle approximations produced by the filter and has been shown to be both efficient and accurate when compared with centralized PFs. The standard DRNA technique, however, places stringent demands on the communications among nodes that turn out impractical for a typical wireless sensor network (WSN). In this paper we investigate how to reduce this communication load by using (i) a random model for the spread of data over the WSN and (ii) methods that enable the out-of-sequence processing of sensor observations. A simple numerical illustration of the performance of the new algorithm compared with a centralized PF is provided.},
keywords = {Approximation algorithms, Approximation methods, Artificial neural networks, distributed resampling, DRNA technique, Markov processes, nonproportional allocation algorithm, parallel resampling scheme, PF, quantization, Signal processing, Vectors, Wireless sensor network, Wireless Sensor Networks, WSN},
pubstate = {published},
tppubtype = {inproceedings}
}

We address the design of a particle filter (PF) that can be implemented in a distributed manner over a network of wireless sensor nodes, each of them collecting their own local data. This is a problem that has received considerable attention lately and several methods based on consensus, the transmission of likelihood information, the truncation and/or the quantization of data have been proposed. However, all existing schemes suffer from limitations related either to the amount of required communications among the nodes or the accuracy of the filter outputs. In this work we propose a novel distributed PF that is built around the distributed resampling with non-proportional allocation (DRNA) algorithm. This scheme guarantees the properness of the particle approximations produced by the filter and has been shown to be both efficient and accurate when compared with centralized PFs. The standard DRNA technique, however, places stringent demands on the communications among nodes that turn out impractical for a typical wireless sensor network (WSN). In this paper we investigate how to reduce this communication load by using (i) a random model for the spread of data over the WSN and (ii) methods that enable the out-of-sequence processing of sensor observations. A simple numerical illustration of the performance of the new algorithm compared with a centralized PF is provided.

@inproceedings{Koch2010,
title = {Increased Capacity per Unit-Cost by Oversampling},
author = {Koch, Tobias and Lapidoth, Amos},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5662127},
isbn = {978-1-4244-8681-6},
year = {2010},
date = {2010-01-01},
booktitle = {2010 IEEE 26-th Convention of Electrical and Electronics Engineers in Israel},
pages = {000684--000688},
publisher = {IEEE},
address = {Eliat},
abstract = {It is demonstrated that doubling the sampling rate recovers some of the loss in capacity incurred on the bandlimited Gaussian channel with a one-bit output quantizer.},
keywords = {AWGN, AWGN channels, bandlimited Gaussian channel, channel capacity, Gaussian channels, increased capacity per unit cost, Information rates, one bit output quantizer, oversampling, quantisation (signal), quantization, sampling rate recovery, signal sampling},
pubstate = {published},
tppubtype = {inproceedings}
}

It is demonstrated that doubling the sampling rate recovers some of the loss in capacity incurred on the bandlimited Gaussian channel with a one-bit output quantizer.