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arxiv: 2604.11492 · v2 · submitted 2026-04-13 · 💻 cs.IT · math.IT

On Demand-Private Coded Caching With Multiple Demands

Qinyi Lu , Nan Liu , Wei Kang This is my paper

Pith reviewed 2026-05-10 15:52 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords coded cachingdemand privacymultiple demandsachievable schemeconverse boundorder optimalitytransformation
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The pith

A transformation from non-private single-demand caching produces an order-optimal demand-private scheme for users requesting multiple files.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a coded caching setup in which a server holds N files and serves K users, each requesting L distinct files, while ensuring that no user can infer any other user's demands. It constructs a new scheme that works for any values of N and K by converting an existing non-private caching design meant for a much larger number of single-request users into one that meets the privacy requirement. A converse bound is derived to prove that the resulting communication rate stays within a factor of six of the minimum possible rate. This result matters because it gives a concrete, scalable way to add demand privacy to multi-request caching without the cost growing unboundedly with system size.

Core claim

The authors establish that any non-private coded caching scheme with uncoded placement designed for N files and K·min{N,KL} single-demand users whose demands are restricted to a subset can be transformed into a demand-private scheme for the original K users each requesting L files, while keeping the same rate. They derive a new converse bound on the rate needed under the privacy constraint and conclude that the transformed scheme achieves a rate at most six times this lower bound for arbitrary N and K.

What carries the argument

The transformation that converts a non-private uncoded-placement single-demand scheme for an expanded user count into a demand-private multi-demand scheme while preserving rate and enforcing privacy.

If this is right

  • The construction applies to arbitrary numbers of files and users without further restrictions on the parameters.
  • Demand privacy is achieved with no extra rate cost beyond what the base non-private scheme already requires.
  • The gap between achievable and optimal rate remains bounded by a constant independent of N and K.
  • The scheme reuses existing single-demand caching designs after a simple demand-mapping step.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If improved non-private schemes appear for the expanded single-demand case, the private multi-demand version improves by the same factor.
  • The bounded gap implies that adding demand privacy changes only the constant factor in rate scaling, not the fundamental dependence on system size.
  • The method may apply to variants where users request overlapping but not identical sets of files.

Load-bearing premise

The transformation from the non-private uncoded-placement scheme for N files and K min{N,KL} single-demand users preserves both the rate and the demand-privacy constraint when mapped back to the original multi-demand setting.

What would settle it

An explicit demand-private scheme whose rate is strictly less than one-sixth of the transformed scheme's rate for some fixed N, K, and L, or a tighter converse bound showing the optimal rate exceeds one-sixth of the achieved rate, would disprove the factor-of-6 order optimality.

read the original abstract

We consider a coded caching problem with multiple demands under a privacy constraint. In this problem, a server with access to \(N\) files serves \(K\) users over a shared link, and each user requests \(L\) distinct files. The privacy constraint requires that each user obtain no information about the demands of the other users. We propose a new achievable scheme for arbitrary numbers of files and users. The scheme is obtained via a transformation from a non-private coded caching scheme under uncoded placement for \(N\) files and \(K \cdot \min\{N,KL\}\) users, where each user requests one file and the demands are restricted to a subset of all possible demands. We then derive a converse bound, and the proposed scheme is shown to be order optimal within a factor of 6 of this bound.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper addresses the demand-private coded caching problem in which a server holding N files serves K users over a broadcast link, with each user requesting L distinct files, subject to the constraint that each user obtains no information about the demand vectors of the other users. It proposes an achievable scheme obtained by transforming a non-private uncoded-placement coded caching scheme designed for N files and K·min{N,KL} single-demand users whose demands are restricted to a suitable subset; a converse bound is then derived, and the resulting rate is shown to be within a constant factor of 6 of the converse for arbitrary N, K, L.

Significance. If the transformation is shown to preserve both the delivery rate and the demand-privacy constraint, the construction supplies a general achievable scheme for arbitrary parameters together with a parameter-independent constant-factor optimality guarantee. This would constitute a concrete advance in the literature on privacy-constrained coded caching, extending known single-demand results to the multi-demand setting while providing an explicit, albeit loose, approximation to the optimal rate.

major comments (1)
  1. The central claim rests on the transformation from the non-private single-demand scheme (with restricted demands) to the multi-demand private setting. The manuscript asserts that this mapping preserves the rate and enforces that each user learns nothing about other users' L-file demand vectors, yet supplies no explicit argument, rate calculation, or small-case verification demonstrating that distinct demand vectors consistent with a given user's own requests produce identical delivery messages. This step is load-bearing for both the achievable rate and the privacy guarantee.
minor comments (1)
  1. The abstract and introduction would benefit from an explicit statement of the achieved rate expression (in terms of N, K, L) rather than only the order-optimality factor.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. The major comment identifies a genuine gap in the exposition of the transformation, which we will address by adding explicit arguments, rate calculations, and verification in the revised manuscript.

read point-by-point responses

  1. Referee: [—] The central claim rests on the transformation from the non-private single-demand scheme (with restricted demands) to the multi-demand private setting. The manuscript asserts that this mapping preserves the rate and enforces that each user learns nothing about other users' L-file demand vectors, yet supplies no explicit argument, rate calculation, or small-case verification demonstrating that distinct demand vectors consistent with a given user's own requests produce identical delivery messages. This step is load-bearing for both the achievable rate and the privacy guarantee.

    Authors: We agree that the manuscript would benefit from a more explicit and self-contained argument for the transformation. In the revision we will add a dedicated section that (i) formally defines the mapping from the multi-demand private instance to the single-demand non-private instance with restricted demands, (ii) proves that the delivery message produced by the underlying scheme is identical for any two global demand vectors that are consistent with a given user's own L-file request (thereby establishing the privacy guarantee), and (iii) shows that the broadcast rate is exactly the same as that of the original single-demand scheme. We will also include a small illustrative example (N=3, K=2, L=2) that explicitly computes the delivery messages for distinct compatible demand vectors and verifies they coincide. These additions will make the central claim fully rigorous while leaving the stated rate and order-optimality results unchanged. revision: yes

Circularity Check

0 steps flagged

No circularity: scheme from external transformation plus independent converse

full rationale

The derivation constructs an achievable scheme via an explicit transformation from a cited non-private uncoded-placement coded caching scheme (with restricted single demands) and separately derives a converse bound; the final order-optimality claim (within factor 6) is obtained by comparing these two independent quantities. No equation or rate expression is shown to reduce by construction to a fitted parameter, self-definition, or self-citation chain whose validity depends on the present paper. The transformation is asserted to preserve rate and demand privacy, but this is presented as a mapping property rather than a tautological renaming or fit. The paper is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The result rests on the existence of a suitable non-private uncoded-placement scheme for the expanded user count and on the correctness of the privacy-preserving mapping; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption A non-private coded caching scheme under uncoded placement exists for N files and K·min{N,KL} users with single-file demands restricted to a subset of possible demand vectors.
    The transformation explicitly invokes this prior construction to obtain the private multi-demand scheme.

pith-pipeline@v0.9.0 · 5433 in / 1211 out tokens · 41219 ms · 2026-05-10T15:52:24.238607+00:00 · methodology

discussion (0)

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Reference graph

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    For the caseN≥3sL:Letr=⌊ K ¯N(N−L(t−1)) N Ls ⌋. Then, we have K ¯N r − K ¯N−L r K ¯N r N≤ N Lr K ¯N ≤ N−L(t−1) s =M s,t, which shows that the corresponding memory size in Theo- rem 1 is no larger thanM s,t. It follows from Theorem 1 that Rp N,K,L(Ms,t)≤ K ¯N r+1 − (K−1) ¯N r+1 K ¯N r ≤ K ¯N−r r+ 1 ≤ K ¯N r+ 1 ≤ N Ls N−L(t−1) ,(29) where the last step foll...

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