TY - GEN
T1 - Bounds on the Length of Functional PIR and Batch Codes
AU - Zhang, Yiwei
AU - Yaakobi, Eitan
AU - Etzion, Tuvi
N1 - Publisher Copyright: © 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - A functional k-PIR code of dimension s consists of n servers storing linear combinations of s linearly independent information symbols. Any linear combination of the s information symbols can be recovered by k disjoint subsets of servers (the reason for this somehow abused definition will be explained in the sequel). The goal is to find the smallest number of servers for given k and s. We provide lower bounds on the number of servers and constructions which yield upper bounds. For k ≤ 4 we provide exact bounds on the number of servers. Furthermore, we provide some asymptotic bounds. The problem coincides with the well known private information retrieval problem based on a coded database to reduce the storage overhead.If any multiset of size k of linear combinations from the linearly independent information symbols can be recovered by k disjoint subset of servers, then the servers form a functional k-batch code. A functional k-batch code is also a functional k-PIR, where all the k linear combinations in the multiset are equal. We provide some bounds on the number of servers for functional k-batch codes. In particular we present a random construction and a construction based on simplex codes, WOM codes, and RIO codes.
AB - A functional k-PIR code of dimension s consists of n servers storing linear combinations of s linearly independent information symbols. Any linear combination of the s information symbols can be recovered by k disjoint subsets of servers (the reason for this somehow abused definition will be explained in the sequel). The goal is to find the smallest number of servers for given k and s. We provide lower bounds on the number of servers and constructions which yield upper bounds. For k ≤ 4 we provide exact bounds on the number of servers. Furthermore, we provide some asymptotic bounds. The problem coincides with the well known private information retrieval problem based on a coded database to reduce the storage overhead.If any multiset of size k of linear combinations from the linearly independent information symbols can be recovered by k disjoint subset of servers, then the servers form a functional k-batch code. A functional k-batch code is also a functional k-PIR, where all the k linear combinations in the multiset are equal. We provide some bounds on the number of servers for functional k-batch codes. In particular we present a random construction and a construction based on simplex codes, WOM codes, and RIO codes.
UR - http://www.scopus.com/inward/record.url?scp=85073147420&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849453
DO - 10.1109/ISIT.2019.8849453
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2129
EP - 2133
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -