Capacity Achieving Quantizer Design for Binary Channels

We consider a communication channel with a binary input X being distorted by an arbitrary continuous-valued noise which results in a continuous-valued signal Y at the receiver. A quantizer Q is used to quantize Y back to a binary output Z. Our goal is to determine the optimal quantizer Q∗ and the corresponding input probability mass function pX that achieve the capacity. We present a new lower bound and a new upper bound on the capacity in terms of quantization parameters and the structure of the associated channel matrix. Based on these theoretical results, we propose an efficient algorithm for finding the optimal quantizer.

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