In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for a discrete distribution estimation. This class not only recovers many known LDP schemes in a unified framework of combinatorial block design, but also suggests a novel way of finding new schemes achieving the optimal (or near-optimal) privacy-utility trade-off with lower communication costs. Indeed, we find many new LDP schemes that achieve both the optimal privacy-utility trade-off and the minimum communication cost among all the unbiased schemes for a certain set of input data size and LDP constraint. Furthermore, to partially solve the sparse existence issue of block design schemes, we consider a broader class of LDP schemes based on regular and pairwise-balanced designs, called RPBD schemes, which relax one of the symmetry requirements on block designs. By considering this broader class of RPBD schemes, we can find LDP schemes achieving near-optimal privacy-utility trade-off with reasonably low communication costs for a much larger set of input data size and LDP constraint.

翻译：本文提出了一类基于组合区组设计的全新局部差分隐私（LDP）方案，用于离散分布估计。该类方案不仅通过统一的组合区组设计框架囊括了众多已知LDP方案，还提出了一种创新方法，能够在较低通信成本下找到达到最优（或近最优）隐私-效用权衡的新方案。实际上，我们发现了众多全新LDP方案，这些方案在特定输入数据规模和LDP约束条件下，既实现了最优隐私-效用权衡，又在所有无偏方案中达到了最低通信成本。此外，为部分解决区组设计方案的稀疏存在性问题，我们考虑了基于正则和成对平衡设计（RPBD）的更广泛LDP方案类别——RPBD方案，它放松了区组设计在对称性上的部分要求。通过引入更广泛的RPBD方案类别，我们能够在更大范围的输入数据规模和LDP约束下，找到以合理较低通信成本实现近最优隐私-效用权衡的LDP方案。