Capacity of Private Linear Computation for Coded Databases

Document Type

Conference Proceeding

Publication Date

7-2-2018

Abstract

We consider the problem of private linear computation (PLC) in a distributed storage system. In PLC, a user wishes to compute a linear combination of f messages stored in noncolluding databases while revealing no information about the coefficients of the desired linear combination to the databases. In extension of our previous work we employ linear codes to encode the information on the databases. We show that the PLC capacity, which is the ratio of the desired linear function size and the total amount of downloaded information, matches the maximum distance separable (MDS) coded capacity of private information retrieval for a large class of linear codes that includes MDS codes. In particular, the proposed converse is valid for any number of messages and linear combinations, and the capacity expression depends on the rank of the coefficient matrix obtained from all linear combinations.

Identifier

85062882766 (Scopus)

ISBN

[9781538665961]

Publication Title

2018 56th Annual Allerton Conference on Communication Control and Computing Allerton 2018

External Full Text Location

https://doi.org/10.1109/ALLERTON.2018.8636039

First Page

813

Last Page

820

Grant

CNS-1526547

Fund Ref

National Science Foundation

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