TY - GEN

T1 - Almost Optimal Construction of Functional Batch Codes Using Hadamard Codes

AU - Yohananov, Lev

AU - Yaakobi, Eitan

N1 - Funding Information:
ACKNOWLEDGMENTS This work was partially supported by the ISF grant 1817/18 and by the TechnionHiroshi Fujiwara cyber security research center and the Israel cyber directorate.
Publisher Copyright:
© 2021 IEEE.

PY - 2021/7/12

Y1 - 2021/7/12

N2 - A functional k-batch code of dimension s consists of n servers storing linear combinations of s linearly independent information bits. Any multiset request of size k of linear combinations (or requests) of the information bits can be recovered by k disjoint subsets of the servers. The goal under this paradigm is to find the minimum number of servers for given values of s and k. A recent conjecture states that for any k=2^{s-1} requests the optimal solution requires 2^{s}-1 servers. This conjecture is verified for s\leqslant 5 but previous work could only show that codes with n=2^{s}-1 servers can support a solution for k=2^{s-2}+2^{s-4}+ \left\lfloor\frac{2^{s/2{\sqrt{24 \right\rfloor requests. This paper reduces this gap and shows the existence of codes for k= \lfloor\frac{2}{3}2^{s-1}\rfloor requests with the same number of servers. Another construction in the paper provides a code with n=2^{s+1}-2 servers and k=2^{s} requests, which is an optimal result. These constructions are mainly based on Hadamard codes and equivalently provide constructions for parallel Random I/O (RIO) codes.

AB - A functional k-batch code of dimension s consists of n servers storing linear combinations of s linearly independent information bits. Any multiset request of size k of linear combinations (or requests) of the information bits can be recovered by k disjoint subsets of the servers. The goal under this paradigm is to find the minimum number of servers for given values of s and k. A recent conjecture states that for any k=2^{s-1} requests the optimal solution requires 2^{s}-1 servers. This conjecture is verified for s\leqslant 5 but previous work could only show that codes with n=2^{s}-1 servers can support a solution for k=2^{s-2}+2^{s-4}+ \left\lfloor\frac{2^{s/2{\sqrt{24 \right\rfloor requests. This paper reduces this gap and shows the existence of codes for k= \lfloor\frac{2}{3}2^{s-1}\rfloor requests with the same number of servers. Another construction in the paper provides a code with n=2^{s+1}-2 servers and k=2^{s} requests, which is an optimal result. These constructions are mainly based on Hadamard codes and equivalently provide constructions for parallel Random I/O (RIO) codes.

UR - http://www.scopus.com/inward/record.url?scp=85115054751&partnerID=8YFLogxK

U2 - 10.1109/ISIT45174.2021.9518215

DO - 10.1109/ISIT45174.2021.9518215

M3 - Conference contribution

AN - SCOPUS:85115054751

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 3139

EP - 3144

BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021

Y2 - 12 July 2021 through 20 July 2021

ER -