eng
Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-01-25
117:1
117:19
10.4230/LIPIcs.ITCS.2022.117
article
Low-Bandwidth Recovery of Linear Functions of Reed-Solomon-Encoded Data
Shutty, Noah
1
Wootters, Mary
1
Stanford University, CA, USA
We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions F:F^k β F of some data π± β F^k, given access to an encoding π β FβΏ of π± under an error correcting code. In our model - relevant in distributed storage, distributed computation and secret sharing - each symbol of π is held by a different party, and we aim to minimize the total amount of information downloaded from each party in order to compute F(π±). Special cases of this problem have arisen in several domains, and we believe that it is fruitful to study this problem in generality.
Our main result is a low-bandwidth scheme to compute linear functions for Reed-Solomon codes, even in the presence of erasures. More precisely, let Ξ΅ > 0 and let π: F^k β FβΏ be a full-length Reed-Solomon code of rate 1 - Ξ΅ over a field F with constant characteristic. For any Ξ³ β [0, Ξ΅), our scheme can compute any linear function F(π±) given access to any (1 - Ξ³)-fraction of the symbols of π(π±), with download bandwidth O(n/(Ξ΅ - Ξ³)) bits. In contrast, the naive scheme that involves reconstructing the data π± and then computing F(π±) uses Ξ(n log n) bits. Our scheme has applications in distributed storage, coded computation, and homomorphic secret sharing.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol215-itcs2022/LIPIcs.ITCS.2022.117/LIPIcs.ITCS.2022.117.pdf
Reed-Solomon Codes
Regenerating Codes
Coded Computation