Almost Optimal Construction of Functional Batch Codes Using Extended Simplex Codes

Lev Yohananov, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review

Abstract

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=2s-1 requests the optimal solution requires 2s-1 servers. This conjecture is verified for s ≤ 5 but previous work could only show that codes with n=2s-1 servers can support a solution for k=2s-2 + 2s-4 + ⌊2s/2/24⌋ requests. This paper reduces this gap and shows the existence of codes for k=⌊5/6 2s-1⌋ - s requests with the same number of servers. Another construction in the paper provides a code with n=2s+1-2 servers and k=2s requests, which is an optimal result. These constructions are mainly based on extended Simplex codes and equivalently provide constructions for parallel Random I/O (RIO) codes.

Original languageEnglish
Pages (from-to)6434-6451
Number of pages18
JournalIEEE Transactions on Information Theory
Volume68
Issue number10
DOIs
StatePublished - 1 Oct 2022
Externally publishedYes

Keywords

  • Batch codes
  • Private Information Retrieval (PIR)
  • Simplex codes
  • codes with availability

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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