# Technical Program

## Paper Detail

Paper Title Private Information Retrieval from Locally Repairable Databases with Colluding Servers TU3.R3.4 Umberto Martinez-Penas, University of Toronto, Canada Private Information Retrieval II Monge, Level 3 Tuesday, 09 July, 14:30 - 16:10 Tuesday, 09 July, 15:30 - 15:50 Click here to download the manuscript Information-theoretical private information retrieval (PIR) is considered from a coded database with colluding servers. The storage code is a locally repairable code (LRC) with maximal recoverability (MR), and in particular, with optimal global minimum distance, for arbitrary code parameters: Number of local groups $g$, locality $r$, local distance $\delta$, dimension $k \leq gr$ and length $n = g(r + \delta - 1)$. Servers are identified bijectively with local groups, and only locally non-redundant information is considered and downloaded from each server, that is, only $r$ nodes (out of $r+\delta-1$) are considered per server. When the remaining MDS code, after removing all locally redundant nodes, is a linearized Reed-Solomon code, a PIR scheme is provided achieving the (download) rate $R = (N - k - rt + 1)/N$, where $N = gr = n - g(\delta - 1)$ is the length of the restricted MDS code, for any $t$ colluding servers such that $k + rt \leq N$. The field size is roughly $g^r$, polynomial in the number of servers $g$. Assume an arbitrarily large number of stored files. If $N - k - rt = 0$, the rate $R = 1/N$ is the highest known and coincides with that of previous PIR schemes that work for any MDS storage code. If $N - k - rt > 0$, the achieved rate $R > 1/N$ coincides with the best known rate of PIR schemes for MDS storage codes (but which do not work for LRCs or linearized Reed-Solomon storage codes) and is always strictly higher than that of known PIR schemes that work for arbitrary MDS storage codes.