Bit Allocation in Spatially Correlated Sensor Fields: Shapley Value-Based Allocation vs. Heuristic Approaches

Bit allocation is a core design problem in spatially correlated sensor fields under limited communication resources since per-sensor bit depth determines quantization fidelity and thus the quality of acquired information. We address this problem by formulating bit allocation as a cooperative game whose payoff is given in the criterion of mutual information, and by using Shapley value to quantify each sensor’s contribution; to ensure this formulation scales well in larger networks, we approximate Shapley values via Neyman stratified sampling. We compare Shapley value-based allocation against four heuristic baselines – uniform allocation, greedy allocation, Voronoi-based geometry-aware allocation, and conditional variance-based allocation – with both randomly distributed and clustered deployments, using five complementary metrics: mutual information, global RMSE, boundary RMSE, worst-10% RMSE, and weighted posterior trace. Numerical experiments on sampled random fields show that stratified sampling achieves tight efficiency consistency with reasonable runtime and scales to larger sensor counts. Reconstruction performance is context-dependent: geometry-aware allocation often performs best under tight budgets, particularly on boundary and tail errors, while Shapley value-based allocation yields the best performance in stringent small-scale fields and becomes competitive under high budgets for global and tail errors. Overall, mutual information and weighted posterior trace provide complementary rankings, highlighting trade-offs between information-centric objectives and reconstruction-error objectives under heterogeneous spatial redundancy.