{"ID":2892381,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15818","arxiv_id":"2507.15818","title":"The Capacity of Semantic Private Information Retrieval with Colluding Servers","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 $T \u003c N$. 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.","short_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...","url_abs":"https://arxiv.org/abs/2507.15818","url_pdf":"https://arxiv.org/pdf/2507.15818v1","authors":"[\"Mohamed Nomeir\",\"Alptug Aytekin\",\"Sennur Ulukus\"]","published":"2025-07-21T17:24:40Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"cs.CR\",\"cs.NI\",\"eess.SP\"]","methods":"[]","has_code":false}