Computer Science – Information Theory
Scientific paper
2012-01-12
Computer Science
Information Theory
41 pages, 3 figures. Submitted to IEEE Transactions on Information Theory
Scientific paper
We study the capacity of the discrete-time Gaussian channel when its output is quantized with a one-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 2/pi, i.e., to cause an asymptotic power loss of approximately two decibels. Here it is shown that this power loss can be entirely avoided by using asymmetric threshold quantizers and asymmetric signaling constellations. We prove that in order to avoid this power loss flash-signaling input-distributions are essential. Consequently, one-bit output quantization of the Gaussian channel reduces spectral efficiency. Threshold quantizers are not only asymptotically optimal: as we prove, at every fixed SNR, a threshold quantizer maximizes capacity among all one-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case we show that a one-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.
Koch Tobias
Lapidoth Amos
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