Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published November 2018 | Submitted
Journal Article Open

Asymptotically Optimal Regenerating Codes Over Any Field

Abstract

The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size and, hence, may be hard to implement in practice. By restructuring a code construction by Rashmi et al. , we obtain two explicit families regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases and may be realized over any given finite field if the file size is large enough. Essentially, these codes constitute a constructive proof that the cut-set bound does not imply a field size restriction, unlike some known bounds for ordinary linear codes. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters. Even though these codes require a large file size, this restriction is trivially satisfied in most conceivable distributed storage scenarios, that are the prominent motivation for regenerating codes.

Additional Information

© 2018 IEEE. Manuscript received September 10, 2017; revised February 28, 2018; accepted March 4, 2018. Date of publication March 13, 2018; date of current version October 18, 2018. N. Raviv was supported in part by the Israeli Science Foundation, Jerusalem, Israel, under Grant 10/12, in part the IBM Ph.D. Fellowship, and in part by the Mitacs organization, through the Globalink Israel-Canada Innovation Initiative. This research was done while the author was a visiting student at the University of Toronto, under the supervision of Prof. F. Kschischang. This paper is a part of his Ph.D. dissertation that was submitted to the Technion under the supervision of Prof. T. Etzion. This paper was presented at the 2017 International Symposium on Information Theory.

Attached Files

Submitted - 1609.06420.pdf

Files

1609.06420.pdf
Files (263.3 kB)
Name Size Download all
md5:6c270a801f9b1e5936624bb7b0540b5a
263.3 kB Preview Download

Additional details

Created:
September 22, 2023
Modified:
October 23, 2023