On the Capacity of Private Information Retrieval from Coded, Colluding, and Adversarial Servers

In this work, we first prove the capacity of coded, linear symmetric private information retrieval (SPIR) in the presence of colluding, adversarial, and nonresponsive servers, giving a positive closure to the conjecture stated by Tajeddine et al. It is also shown that, further restricting to strongly-linear PIR schemes with linear interference cancellation, the so-called star product scheme proposed by Freij-Hollanti et al. is optimal. This observation enables to prove the capacity of strongly-linear (non-symmetric) PIR schemes for any number of files. Further, it also provides a positive proof in this practical special case for the conjectures stated in the asymptotic regime by Freij-Hollanti et al. and Tajeddine et al.