Optimum quantization for detection with side information

Abstract

In this work, we considered the problem of binary detection with side information. The receiver, observes the transmitted data which is corrupted by Gaussian noise, and tries to make a decision between two hypotheses where it has the knowledge of noise statistics of the channel and partial information about the data. Here the partial information is obtained via passing the original data through a quantizer, thus the partial information is simply the reproduction value of the bin that the corresponding data is in. We derived the optimal decision rule and corresponding probability of error. We presented and illustrated the optimal quantizers for several quantization levels. Next, we compare quantizers (optimal quantizer, Lloyd-Max, Uniform,a suboptimal quantizer obtained by approximation), with respect to bin constellations and their corresponding probability of detection errors. Finally, from the comparison it has been shown empirically that Lloyd-Max quantizers are suboptimal yet good choice for detection with side information problem under proposed setup.