Divergence-Based Soft Decision for Error Resilient Decentralized Signal Detection

In this paper, we consider decentralized detection where the transmission of local soft-decisions of the secondary users (SUs) to the fusion center (FC) is both rate-limited and error-prone. The quantized data to be sent from SUs should not only carry the local information but also need to be resilient to channel errors. With the assumption of independent and identical secondary user observations conditioned on signal hypothesis and binary symmetric channels (BSC) between SUs and the FC, we design local quantizers at a SU, based on two divergence metrics, namely Kullback-Leibler (KL) and Chernoff. Using convex duality, we show that a two-stage algorithm can be developed to take care of the quantization thresholding, codeword assignment, and error resilience. Specifically, we obtain the following results. First, we show that the proposed quantizer obtains increased divergence between the distributions of the demodulated data at the FC, when compared to the maximum entropy quantizer design. We also point out the fallacy of previously reported Gray code assignment to quantized data. Second, the quantizer optimally picks the repetition codeword in the case of "ideal" sensing at the sensors. Similar "channel blind" optimal quantizer design was observed in the literature for single-sensor case. Third, we derive new bit error probability (BEP) wall expression for D-bits soft-quantization, for specified probabilities of errors at the FC. The new result shows whether and when a majority logic rule is optimal at the FC.