Private Information Retrieval (PIR) is a fundamental problem in the broader fields of security and privacy. In recent years, the problem has garnered significant attention from the research community, leading to achievability schemes and converse results for many important PIR settings. This paper focuses on the Multi-message Private Information Retrieval (MPIR) setting, where a user aims to retrieve \(D\) messages from a database of \(K\) messages, with identical copies of the database available on \(N\) remote servers. The user's goal is to maximize the download rate while keeping the identities of the retrieved messages private. Existing approaches to the MPIR problem primarily focus on either scalar-linear solutions or vector-linear solutions, the latter requiring a high degree of subpacketization. Furthermore, prior scalar-linear solutions are restricted to the special case of \(N = D+1\). This limitation hinders the practical adoption of these schemes, as real-world applications demand simple, easily implementable solutions that support a broad range of scenarios. In this work, we present a solution for the MPIR problem, which applies to a broader range of system parameters and requires a limited degree of subpacketization. In particular, the proposed scheme applies to all values of \(N=DL+1\) for any integer \(L\geq 1\), and requires a degree of subpacketization \(L\). Our scheme achieves capacity when \(D\) divides \(K\), and in all other cases, its performance matches or comes within a small additive margin of the best-known scheme that requires a high degree of subpacketization.

翻译：私有信息检索（PIR）是安全与隐私领域的一个基础性问题。近年来，该问题受到研究界的广泛关注，针对许多重要的PIR场景已提出了可实现方案与逆定理结果。本文聚焦于多消息私有信息检索（MPIR）场景，该场景中用户需要从包含K条消息的数据库中检索D条消息，且该数据库的相同副本存储在N个远程服务器上。用户的目标是在保持所检索消息身份私密性的同时最大化下载速率。现有的MPIR解决方案主要集中于标量线性方案或矢量线性方案，后者需要高度的子分组化处理。此外，现有的标量线性方案仅限于N = D+1的特殊情况。这一限制阻碍了这些方案的实际应用，因为现实应用需要支持广泛场景的简单、易实现的解决方案。本文提出了一种适用于更广泛系统参数且仅需有限子分组化程度的MPIR解决方案。具体而言，所提方案适用于所有满足N=DL+1（其中L为任意大于等于1的整数）的参数配置，且仅需L级的子分组化程度。当D可整除K时，本方案达到容量极限；在所有其他情况下，其性能与当前已知需要高度子分组化的最优方案相当或仅存在微小可加性差距。