The Capacity of Semantic Private Information Retrieval with Colluding Servers

Mohamed Nomeir; Alptug Aytekin; Sennur Ulukus

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arXiv · 2507.15818

The Capacity of Semantic Private Information Retrieval with Colluding Servers

Mohamed Nomeir·Alptug Aytekin·Sennur Ulukus

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Abstract

We study the problem of semantic private information retrieval (Sem-PIR) with $T$ colluding servers (Sem-TPIR), i.e., servers that collectively share user queries. In Sem-TPIR, the message sizes are different, and message retrieval probabilities by any user are not uniform. This is a generalization of the classical PIR problem where the message sizes are equal and message retrieval probabilities are identical. The earlier work on Sem-PIR considered the case of no collusions, i.e., the collusion parameter of $T=1$. In this paper, we consider the general problem for arbitrary $T < N$. We find an upper bound on the retrieval rate and design a scheme that achieves this rate, i.e., we derive the exact capacity of Sem-TPIR.

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Mohamed Nomeir, Alptug Aytekin, Sennur Ulukus. 2025-07-21. The Capacity of Semantic Private Information Retrieval with Colluding Servers. https://arxiv.org/abs/2507.15818

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