Optimal Thresholding Quantizer Maximizing Mutual Information of Discrete Multiple-Input Continuous One-Bit Output Quantization

In this paper, we consider the problem of one-bit (two-level) output-quantization maximizing mutual information between quantizer-output and channel-input using a single threshold for a discrete signal that is corrupted by a continuous additive noise. A necessary condition is constructed for which the thresholding quantizer is optimal. In addition, we show that if the distribution of the additive noise satisfies a mild condition, then a global optimal threshold can be found efficiently via a modified fixed-point algorithm.