In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for 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 exactly optimal (or near-optimal) privacy-utility trade-off with lower communication costs. Indeed, we find many new LDP schemes that achieve the exactly optimal privacy-utility trade-off, with the minimum communication cost among all the unbiased or consistent 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局部差分隐私（LDP）方案，用于离散分布估计。此类方案不仅能够在统一的组合区组设计框架下涵盖多种已知的LDP方案，还提出了一种新的途径，用于发现能够以更低通信成本实现精确最优（或近似最优）隐私-效用权衡的新方案。事实上，我们发现了许多新的LDP方案，对于特定的输入数据规模及LDP约束条件，这些方案在无偏或一致方案中实现了精确最优的隐私-效用权衡，且通信成本最小。此外，为部分解决区组设计方案中存在的稀疏性问题，我们考虑了一类更广泛的基于正则且成对平衡设计的LDP方案，称为RPBD方案，该方案放宽了区组设计中对对称性的某一要求。通过考虑这类更广泛的RPBD方案，我们能够找到适用于更广泛输入数据规模及LDP约束条件的LDP方案，这些方案以相当低的通信成本实现了近似最优的隐私-效用权衡。