Privacy in Index Coding: K -Limited-Access Schemes

Mohammed Karmoose, Linqi Song, Martina Cardone, Christina Fragouli

Research output: Contribution to journalArticlepeer-review

Abstract

In the traditional index coding problem, a server employs coding to send messages to a set of clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation comes from the work by Karmoose et al., which shows that learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. We start by showing that this approach can indeed help mitigate that privacy concern. We do so by considering two different privacy metrics. The first one shows the attained privacy benefits based on a geometric interpretation of the problem. Differently, the second metric, referred to as maximal information leakage, provides upper bounds on: (i) the guessing power of the adversaries (i.e., curious clients) when our proposed approach is employed, and (ii) the effect of decreasing the number of accessible rows on the attained privacy. Then, we propose the use of $k$ -limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$ -limited-access scheme with $T_{k}\geq T$ transmissions, and with the property that each client needs at most $k$ transmissions to decode her message. We derive upper and lower bounds on $T_{k}$ for all values of $k$ , and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal for some parameter regimes, and we propose heuristics that complement the universal schemes for the remaining regimes.

Original languageEnglish (US)
Article number8922781
Pages (from-to)2625-2641
Number of pages17
JournalIEEE Transactions on Information Theory
Volume66
Issue number5
DOIs
StatePublished - May 2020

Bibliographical note

Funding Information:
Manuscript received September 19, 2018; revised August 31, 2019; accepted November 16, 2019. Date of publication December 4, 2019; date of current version April 21, 2020. This work was supported in part by NSF under Award 1527550, Award 1514531, Award 1423271, Award 1314937, and Award 1740047; and in part by the Research Grants Council (RGC) of Hong Kong under Grant ECS 9048149. This work was presented in part at the 2017 International Symposium on Information Theory, in part at the 2017 Information Theory Workshop, and in part at the 2018 International Symposium on Information Theory.

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Index coding
  • broadcasting
  • k-limited-access scheme
  • maximal information leakage
  • privacy

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