Symmetric PIR capacity conjecture for MDS-coded colluding and adversarial servers
Symmetric PIR capacity conjecture for MDS-coded colluding and adversarial servers
Assume , where , , and are the numbers of colluding, Byzantine, and nonresponsive servers, respectively. Consider symmetric private information retrieval (SPIR) from an MDS storage code with -collusion, Byzantine servers, and nonresponsive servers.
Symmetric PIR capacity conjecture. The capacity of SPIR is
The conjecture is one of the claims for the known-parameter cases or , where symmetric capacity is observed to coincide with asymptotic nonsymmetric capacity. The source notes that an earlier formulation used denominator because nonresponsive servers were excluded from the download cost; the paper counts them, while stating that the results apply under both conventions. Its resolution is not established in the supplied text.
Sources & referencesView supporting material
Primary source
Lukas Holzbaur, Ragnar Freij-Hollanti, Jie Li and Camilla Hollanti, “Towards the Capacity of Private Information Retrieval from Coded and Colluding Servers”, arXiv:1903.12552 (2021).
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