Optimal one-bit quantizers are asymmetric for additive uniform noise

In this paper, we consider one-bit output quantization of an amplitude bounded input-signal subject to arbitrary additive noise. Capacity is then represented in various ways, each demonstrating that finding the optimum quantization threshold q is an extremely difficult problem. For a class of noise distributions, of which a typical representative is the uniform distribution, it is shown that the optimum quantizer is asymmetric. This contradicts intuition, which for symmetric noise expects the optimum threshold to be the average of the input distribution.