Quantization for decentralized hypothesis testing under communication constraints

Quantizer design for distributed estimation with communication constraints and unknown observation statistics

“…In the case where the joint distribution p(x 1 , x 2 , θ) is known and continuous, necessary conditions for optimal Q 1 , Q 2 , and h for the mse distortion function are given by Lam and Reibman [10]. In order to find the solution, the Cyclic Generalized Lloyd's Algorithm (CGLA) proposed by Longo, et al [13] in the framework of decentralized hypothesis testing under capacity constraints and for a known joint distribution is used [13], [9], [10], [6]. The CGLA is a variation of the Generalized Lloyd Algorithm (GLA) [11], [12], [5].…”

“…The fusion center estimates the parameter θ based onX b k . Many researchers have studied the problem of quantization for distributed estimation in the case where the joint distribution p(x 1 , x 2 , θ), is known [13], [9], [10], [4], [3], [1], [6]. Here, we consider a more realistic model where the observation statistics are unknown.…”

“…We follow the concept of Cooperative Design-Separate Encoding (see [13]). In the case where the joint distribution p(x 1 , x 2 , θ) is known and continuous, necessary conditions for optimal Q 1 , Q 2 , and h for the mse distortion function are given by Lam and Reibman [10].…”

Optimization of decentralized quantizers in rate constrained data fusion systems

“…Hence one is lead to renounce to global optimality and to study suboptimal strategies. Joint design of soft (multi-bit) quantizers has been studied by Longo et al in [3], where an alternate optimization technique is proposed. Specifically, the approach in [3] is to maximize the Bhattacharyya distance between the multivariate conditional probabilities of quantized data given the hypotheses.…”

“…Joint design of soft (multi-bit) quantizers has been studied by Longo et al in [3], where an alternate optimization technique is proposed. Specifically, the approach in [3] is to maximize the Bhattacharyya distance between the multivariate conditional probabilities of quantized data given the hypotheses. The potential weakness of this approach is that the Bhattacharyya distance is not the natural measure of performance of detection systems.…”