$X$-secure $T$-private Information Retrieval from MDS Coded Storage with Byzantine and Unresponsive Servers

Understand

The problem of $X$-secure $T$-private information retrieval from MDS coded storage is studied in this paper, where the user wishes to privately retrieve one out of $K$ independent messages that are distributed over $N$ servers according to an MDS code.

• It is guaranteed that any group of up to $X$ colluding servers learn nothing about the messages and that any group of up to $T$ colluding servers learn nothing about the identity of desired message.
• A lower bound of achievable rates is proved by presenting a novel scheme based on \emph{cross-subspace alignment} and a successive decoding with interference cancellation strategy.
• For large number of messages $(K\rightarrow\infty)$ the achieved rate, which we conjecture to be optimal, improves upon the best known rates previously reported in the literature by Raviv and Karpuk, and generalizes an achievable rate for MDS-TPIR previously found by Freij-Hollanti et al.