QUANTIZATION FOR DECENTRALIZED HYPOTHESIS-TESTING UNDER COMMUNICATION CONSTRAINTS

In a decentralized hypothesis testing network, several peripheral nodes observe an environment and communicate their observations to a central node for the final decision. The presence of capacity constraints introduces novel theoretical and practical problems. The problem is addressed: Given that the peripheral encoders that satisfy these constraints are scalar quantizers, how should they be designed in order that the central test to be performed on their output indices is most powerful? The scheme is called Cooperative Design-Separate Encoding since the quantizers process separate observations but have a common goal; they seek to maximize—by possibly exploiting the spatial correlation of the observations—a system-wide performance measure, not individual performance measures. The Bhattacharyya distance of the joint index space as such a criterion is suggested, and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed: each optimization step is an alternating minimization based on Lloyd's design for minimum distortion. A simplified version of the algorithm, namely an Independent Design-Separate Encoding scheme, where the correlation is either absent or neglected for sake of simplicity is outlined. Performances are compared through worked examples. © 1990 IEEE