2013
Koch, Tobias; Lapidoth, Amos
At Low SNR, Asymmetric Quantizers are Better Artículo de revista
En: IEEE Transactions on Information Theory, vol. 59, no 9, pp. 5421–5445, 2013, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: 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
@article{Koch2013,
title = {At Low SNR, Asymmetric Quantizers are Better},
author = {Tobias Koch and Amos Lapidoth},
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.