@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}

}