English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The problem of private information retrieval with graph-based replicatedstorage was recently introduced by Raviv, Tamo and Yaakobi. Its capacityremains open in almost all cases. In this work the asymptotic (large number ofmessages) capacity of this problem is studied along with its generalizations toinclude arbitrary $T$-privacy and $X$-security constraints, where the privacyof the user must be protected against any set of up to $T$ colluding serversand the security of the stored data must be protected against any set of up to$X$ colluding servers. A general achievable scheme for arbitrary storagepatterns is presented that achieves the rate $(\rho_{\min}-X-T)/N$, where $N$is the total number of servers, and each message is replicated at least$\rho_{\min}$ times. Notably, the scheme makes use of a special structureinspired by dual Generalized Reed Solomon (GRS) codes. A general converse isalso presented. The two bounds are shown to match for many settings, includingsymmetric storage patterns. Finally, the asymptotic capacity is fullycharacterized for the case without security constraints $(X=0)$ for arbitrarystorage patterns provided that each message is replicated no more than $T+2$times. As an example of this result, consider PIR with arbitrary graph basedstorage ($T=1, X=0$) where every message is replicated at exactly $3$ servers.For this $3$-replicated storage setting, the asymptotic capacity is equal to$2/\nu_2(G)$ where $\nu_2(G)$ is the maximum size of a $2$-matching in astorage graph $G[V,E]$. In this undirected graph, the vertices $V$ correspondto the set of servers, and there is an edge $uv\in E$ between vertices $u,v$only if a subset of messages is replicated at both servers $u$ and $v$.

On the Asymptotic Capacity of $X$-Secure $T$-Private Information Retrieval with Graph Based Replicated Storage