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离散分布估计本地差分隐私（LDP）方案。该类方案不仅将众多已知LDP方案统一纳入组合区组设计框架，还提出了一种在较低通信成本下实现最优（或近最优）隐私-效用权衡的新方案发现途径。事实上，针对特定输入数据规模和LDP约束条件，我们发现多种新型LDP方案能够同时实现最优隐私-效用权衡与无偏方案中的最小通信成本。此外，为部分解决区组设计的存在性稀疏问题，我们考虑了一类基于正则设计与成对平衡设计的更广义LDP方案——RPBD方案，该方案放宽了区组设计中的对称性要求。通过引入这一更广义的RPBD方案类别，我们能够在更广泛的输入数据规模和LDP约束条件下，以较低的通信成本实现近最优隐私-效用权衡的LDP方案。