Bit Allocation in Spatially Correlated Sensor Fields: A Comparative Study of Contribution-Aware and 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. In this paper, we investigate several regime-dependent bit allocation strategies and compare them under various deployment geometries, bit budgets, and performance metrics. We consider a per-reporting-round integer bit-allocation problem in which a total bit budget is distributed among sensors as nonnegative quantization bits, allowing zero-bit allocation to represent sensor silencing. To examine different allocation principles, we compare five strategies: Shapley-value-based contribution-aware allocation and four other heuristic approaches-uniform allocation, Voronoi-based geometry-aware allocation, greedy mutual information-driven allocation, and conditional variance-based allocation. We implement the contribution-aware allocation as a two-stage framework: a mutual information-based cooperative game first quantifies each sensor's spatial redundancy-aware contribution using Shapley value, and the value is then mapped to integer bit allocations. To mitigate the intractability of this formulation in larger networks, we approximate Shapley values via Neyman stratified sampling. Numerical experiments on sampled random fields show that 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. Furthermore, mutual information and weighted posterior trace provide complementary rankings, highlighting trade-offs between information-centric objectives and reconstruction-error objectives under heterogeneous spatial redundancy. These results show trade-offs among allocation strategies in accordance with different regimes and performance metrics.