[Paper Review] Demand Private Coded Caching

Sneha Kamath|arXiv (Cornell University)|Sep 7, 2019

Caching and Content Delivery14 references34 citations

TL;DR

This paper introduces demand-private coded caching, providing an achievable scheme that preserves demand privacy among users, and proves order-optimality within a constant factor relative to no-privacy bounds.

ABSTRACT

The work by Maddah-Ali and Niesen demonstrated the benefits in reducing the transmission rate in a noiseless broadcast network by joint design of caching and delivery schemes. In their setup, each user learns the demands of all other users in the delivery phase. In this paper, we introduce the problem of demand private coded caching where we impose a privacy requirement that no user learns any information about the demands of other users. We provide an achievable scheme and compare its performance using the existing lower bounds on the achievable rates under no privacy setting. For this setting, when $N\leq K$ we show that our scheme is order optimal within a multiplicative factor of 8. Furthermore, when $N > K$ and $M\geq N/K$, our scheme is order optimal within a multiplicative factor of 4.

Motivation & Objective

• Motivate privacy in coded caching to prevent users from learning others' demands.
• Propose an achievable demand-private caching scheme derived from a non-private scheme.
• Establish lower bounds and demonstrate order-optimality factors under privacy constraints.

Proposed method

• Construct a demand-private scheme from a known non-private scheme by incorporating per-user shared randomness during placement.
• Define cache encoding, transmission, and decoding functions under privacy constraints with mutual information and conditional entropy conditions.
• Show the privacy guarantee: I(D_rest; Z_k, X, D_k) = 0 and decoding correctness: H(W_{D_k} | Z_k, X, D_k) = 0.
• Use the NK-user non-private scheme as a backbone and map demands with a c-vector derived from s_k and d_k to preserve privacy.
• Prove that the rate with privacy R^{*p}(N,K,M) is bounded by the expression in Theorem 1 and relate it to the lower convex envelope R^{p}_{c}(N,K,M).

Experimental results

Research questions

• RQ1 How can one achieve demand privacy in coded caching without sacrificing recoverability of the demanded file?
• RQ2 What is the achievable memory-rate trade-off under the demand privacy constraint?
• RQ3 How close is the privacy-preserving scheme to the best known non-private bounds (in terms of order optimality)?

Key findings

• An explicit achievable demand-private memory-rate pair is given: R^{*p}(N,K,M) ≤ R^{p}(N,K,M) = ( {NK choose KM+1} - {NK-N choose KM+1} ) / {NK choose KM}, for M ∈ {0, 1/K, 2/K, ..., N}.
• The rate regional envelope R^{p}_{c}(N,K,M), the lower convex envelope of the points in (8), is achievable.
• For N ≤ K, the scheme is within a multiplicative factor of 8 from the optimal privacy-containing region.
• For N > K, and M ≥ N/K, the scheme is within a multiplicative factor of 4 from the optimal privacy-containing region.
• The scheme is exact (optimal) for M ≥ (NK-1)/K (i.e., all but a tiny fraction of the library cached).
• Any converse under privacy bounds the no-privacy converses, so the presented private-bounded rates align with known non-private lower bounds up to constants.