Abstract

This talk discusses the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power limited Gaussian channel. This problem is relevant for communication systems where the receiver uses digital signal processing techniques, especially when high-resolution analog-to-digital converters are not feasible. The focus is on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread Spectrum and Ultra-Wideband communications. It is well known that, in this regime, a symmetric one-bit quantizer reduces capacity by a factor of 2/pi, which translates to a power loss of approximately two decibels. Hence the rule of thumb that “hard decisions cause a 2dB power loss.”

We show that the power loss of 2dB is not a consequence of the hard-decision decoder but of the suboptimal quantizer. In fact, if an asymmetric quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.

(Joint work with Amos Lapidoth)