A Mismatched Decoding Perspective of Channel Output Quantization

Channel output quantization to a smaller number of outputs is modeled as a mismatched decoding problem. The conditions that a mismatched decoding metric should satisfy in order to represent an output quantizer are derived. In addition, a mismatched decoding metric and hypothesis test that minimizes the average error probability are found. It is shown that the best possible mismatched decoder is equivalent to maximum-likelihood decoding for the channel between the channel input and the quantized output. This gives a class of mismatched decoding problems where the mismatch capacity is known. This result supports previous studies on quantizer design and optimization over the quantized channel.