6 problems

Let $ASP(k,t,q)$ and $ASB(k,t,q)$ denote the minimum lengths of, respectively, all-symbol PIR and all-symbol batch codes with parameters $k,t,q$. For all $k,q$ and $t_1,t_2\geq 1$,…

Finite-file PIR rate conjecture. Any such PIR scheme has rate at most

Asymptotic PIR capacity conjecture. The asymptotic capacity as the number of files $m$ tends to infinity is

Let an $[n,k]$ MDS storage code store a database accessed by a Symmetric Private Information Retrieval scheme, with $t$-colluding servers, $b$ Byzantine servers, and $r$ unresponsi…

Let $\mathcal{C}$ be an $[n,k]$ code, and let $d_s^{\mathcal{C}}$ denote the quantity appearing in the necessary condition … An MDS-PIR capacity-achieving matrix…

Let $s>2$, and consider the PIR array codes produced by the B-E Construction. B-E optimality conjecture. These PIR array codes have optimal rate. The preceding discussion is based…