TY - GEN

T1 - Multiset combinatorial batch codes

AU - Zhang, Hui

AU - Yaakobi, Eitan

AU - Silberstein, Natalia

N1 - Publisher Copyright: © 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of n data items on m servers, in such a way that any batch of k data items can be retrieved by reading at most some t symbols from each server. Combinatorial batch codes, are replication-based batch codes in which each server stores a subset of the data items. In this paper, we propose a generalization of combinatorial batch codes, called multiset combinatorial batch codes (MCBCs), in which n data items are stored in m servers, such that any multiset request of k items, where any item is requested at most r times, can be retrieved by reading at most t items from each server. The setup of this new family of codes is motivated by recent work on codes which enable high availability and parallel reads in distributed storage systems. The main problem under this paradigm is to minimize the number of items stored in the servers, given the values of n, m, k, r, t, which is denoted by N(n, k, m, t; r). We first give a necessary and sufficient condition for the existence of MCBCs. Then, we present several bounds on N(n, k, m, t; r) and constructions of MCBCs. In particular, we determine the value of N(n, k, m, 1; r) for any n ≥ |k-1/r| (mk-1) - (m - k + 1)A(m, 4, k - 2), where A(m, 4, k - 2) is the maximum size of a binary constant weight code of length m, distance four and weight k - 2. We also determine the exact value of N(n, k, m, 1; r) when r {k, k - 1} or k = m.

AB - Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of n data items on m servers, in such a way that any batch of k data items can be retrieved by reading at most some t symbols from each server. Combinatorial batch codes, are replication-based batch codes in which each server stores a subset of the data items. In this paper, we propose a generalization of combinatorial batch codes, called multiset combinatorial batch codes (MCBCs), in which n data items are stored in m servers, such that any multiset request of k items, where any item is requested at most r times, can be retrieved by reading at most t items from each server. The setup of this new family of codes is motivated by recent work on codes which enable high availability and parallel reads in distributed storage systems. The main problem under this paradigm is to minimize the number of items stored in the servers, given the values of n, m, k, r, t, which is denoted by N(n, k, m, t; r). We first give a necessary and sufficient condition for the existence of MCBCs. Then, we present several bounds on N(n, k, m, t; r) and constructions of MCBCs. In particular, we determine the value of N(n, k, m, 1; r) for any n ≥ |k-1/r| (mk-1) - (m - k + 1)A(m, 4, k - 2), where A(m, 4, k - 2) is the maximum size of a binary constant weight code of length m, distance four and weight k - 2. We also determine the exact value of N(n, k, m, 1; r) when r {k, k - 1} or k = m.

UR - http://www.scopus.com/inward/record.url?scp=85034109746&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/ISIT.2017.8006916

DO - https://doi.org/10.1109/ISIT.2017.8006916

M3 - Conference contribution

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2183

EP - 2187

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -