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Private information retrieval from MDS coded data with colluding servers: Settling a conjecture by Freij-Hollanti et al

  • Author(s): Sun, H
  • Jafar, SA
  • et al.

A (K, N, T, Kc) instance of private information retrieval from MDS coded data with colluding servers (in short, MDS-TPIR), is comprised of K messages and N distributed servers. Each message is separately encoded through a (Kc, N) MDS storage code. A user wishes to retrieve one message, as efficiently as possible, while revealing no information about the desired message index to any colluding set of up to T servers. The fundamental limit on the efficiency of retrieval, i.e., the capacity of MDS-TPIR is known only at the extremes where either T or Kc belongs to {1, N}. The focus of this work is a recent conjecture by Freij-Hollanti, Gnilke, Hollanti, and Karpuk which offers a general capacity expression for MDS-TPIR.We prove that the conjecture is false by presenting as a counterexample a PIR scheme for the setting (K, N, T, Kc) = (2, 4, 2, 2), which achieves the rate 3/5, exceeding the conjectured capacity, 4/7. Insights from the counterexample lead us to capacity characterizations for various instances of MDS-TPIR, including all cases with (K, N, T, Kc) = (2, N, T, N -1), where N and T can be arbitrary.

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