Capacity of Single-Server Single-Message Private Information Retrieval with Coded Side Information

This paper considers the problem of single-server single-message private information retrieval with coded side information (PIR-CSI). In this problem, there is a server storing a database, and a user which knows a linear combination of a subset of messages in the database as a side information. The number of messages contributing to the side information is known to the server, but the indices and the coefficients of these messages are unknown to the server. The user wishes to download a message from the server privately, i.e., without revealing which message it is requesting, while minimizing the download cost. In this work, we consider two different settings for the PIR-CSI problem depending on the demanded message being or not being one of the messages contributing to the side information. For each setting, we prove an upper bound on the maximum download rate as a function of the size of the database and the size of the side information, and propose a protocol that achieves the rate upper-bound.

[1]  Sennur Ulukus,et al.  The Capacity of Private Information Retrieval From Coded Databases , 2016, IEEE Transactions on Information Theory.

[2]  Sennur Ulukus,et al.  Fundamental Limits of Cache-Aided Private Information Retrieval With Unknown and Uncoded Prefetching , 2017, IEEE Transactions on Information Theory.

[3]  Swanand Kadhe,et al.  Private information retrieval with side information: The single server case , 2017, 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[4]  Hua Sun,et al.  The Capacity of Private Information Retrieval , 2017, IEEE Transactions on Information Theory.

[5]  Eyal Kushilevitz,et al.  Private information retrieval , 1998, JACM.

[6]  Hua Sun,et al.  The Capacity of Robust Private Information Retrieval With Colluding Databases , 2016, IEEE Transactions on Information Theory.

[7]  Syed Ali Jafar,et al.  The Capacity of Private Information Retrieval with Private Side Information , 2017, ArXiv.

[8]  Mahdi Jafari Siavoshani,et al.  Multi-Message Private Information Retrieval with Private Side Information , 2018, 2018 IEEE Information Theory Workshop (ITW).

[9]  Ron M. Roth,et al.  Introduction to Coding Theory , 2019, Discrete Mathematics.

[10]  Ravi Tandon,et al.  The capacity of cache aided private information retrieval , 2017, 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[11]  Camilla Hollanti,et al.  Private information retrieval schemes for codec data with arbitrary collusion patterns , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[12]  Sennur Ulukus,et al.  Cache-Aided Private Information Retrieval With Partially Known Uncoded Prefetching: Fundamental Limits , 2017, IEEE Journal on Selected Areas in Communications.

[13]  Michael Gastpar,et al.  Single-server Multi-message Private Information Retrieval with Side Information , 2018, 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Fatemeh Kazemi,et al.  Capacity of Single-Server Single-Message Private Information Retrieval with Private Coded Side Information , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[15]  Sennur Ulukus,et al.  Multi-message private information retrieval , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[16]  Swanand Kadhe,et al.  Private Information Retrieval With Side Information , 2017, IEEE Transactions on Information Theory.

[17]  Swanand Kadhe,et al.  On the Capacity of Single-Server Multi-Message Private Information Retrieval with Side Information , 2018, 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton).