UC Irvine

In many applications, one is interested in optimally deploying a network of unidentical agents to a certain area of interest; examples include heterogeneous sensor networks and cellular networks. Such deployment problems can equivalently be formulated as quantizer design problems, where different distortion measures should be associated with different quantization indices. In this paper, we consider the case where the distortion measure is the rth power (r≥ 1) of the distance between the reproduction point and the source sample weighted by a factor that varies from one index to another. For a uniform distribution of source samples, we determine the corresponding optimal scalar quantizers and their average distortions. For nonuniform distributions and vector quantization, we provide a high-resolution analysis of the minimum possible average distortion. Applications to sensor and cellular networks are also discussed together with numerical design examples.