Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1809.09861 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929490819547136 |
|---|---|
| author | Li, Su Gastpar, Michael |
| author_facet | Li, Su Gastpar, Michael |
| contents | Multi-server single-message private information retrieval is studied in the presence of side information. In this problem, $K$ independent messages are replicatively stored at $N$ non-colluding servers. The user wants to privately download one message from the servers without revealing the index of the message to any of the servers, leveraging its $M$ side information messages. We assume that the servers only know the number of the side information messages available at the user but not their indices. We prove a converse bound on the maximum download rates, which coincides with the known achievability scheme proposed by Kadhe {\it et. al.}. Hence, we characterize the capacity for this problem, which is $(1+\frac{1}{N}+\frac{1}{N^2}+\dots+\frac{1}{N^{\left\lceil \frac{K}{M+1}\right\rceil-1}})^{-1}$. The proof leverages a novel concept that we call {\it virtual side information}, which, for a fixed query and any message, identifies the side information that would be needed in order to recover that message. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_09861 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Converse for Multi-Server Single-Message PIR with Side Information Li, Su Gastpar, Michael Information Theory Multi-server single-message private information retrieval is studied in the presence of side information. In this problem, $K$ independent messages are replicatively stored at $N$ non-colluding servers. The user wants to privately download one message from the servers without revealing the index of the message to any of the servers, leveraging its $M$ side information messages. We assume that the servers only know the number of the side information messages available at the user but not their indices. We prove a converse bound on the maximum download rates, which coincides with the known achievability scheme proposed by Kadhe {\it et. al.}. Hence, we characterize the capacity for this problem, which is $(1+\frac{1}{N}+\frac{1}{N^2}+\dots+\frac{1}{N^{\left\lceil \frac{K}{M+1}\right\rceil-1}})^{-1}$. The proof leverages a novel concept that we call {\it virtual side information}, which, for a fixed query and any message, identifies the side information that would be needed in order to recover that message. |
| title | Converse for Multi-Server Single-Message PIR with Side Information |
| topic | Information Theory |
| url | https://arxiv.org/abs/1809.09861 |