At Low SNR Asymmetric Quantizers Are Better

TL;DR

This paper demonstrates that asymmetric quantizers and signaling can eliminate power loss in low SNR Gaussian channels with one-bit quantization, challenging the traditional symmetric approach.

Contribution

It shows that asymmetric threshold quantizers and flash signaling can avoid power loss at low SNR, and that threshold quantizers are optimal at every fixed SNR.

Findings

Asymmetric quantizers eliminate asymptotic power loss at low SNR.

Threshold quantizers maximize capacity among one-bit quantizers at fixed SNR.

Power loss in Rayleigh-fading channels depends on coherence and quantizer adaptation.

Abstract

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 a factor of 2/pi, i.e., to cause an asymptotic power loss of approximately two decibels. 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, one-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 one-bit output quantizers. The picture changes on the Rayleigh-fading channel. In the noncoherent case 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.