At low SNR, asymmetric quantizers are better Articles uri icon

publication date

  • September 2013

start page

  • 5421

end page

  • 5445


  • 9


  • 59

International Standard Serial Number (ISSN)

  • 0018-9448

Electronic International Standard Serial Number (EISSN)

  • 1557-9654


  • 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.


  • Electronics
  • Telecommunications


  • capacity per unit energy; channel capacity; gaussian channel; low signal-to-noise ratio (snr) quantization