Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.06311

The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching

Han Fang·Nan Liu·Wei Kang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We determine the exact zero-error memory-rate tradeoff for secure coded caching with three users and any number $N\ge2$ of independent files. Each user recovers its requested file, while its cache and the broadcast jointly reveal no information about the complete tuple of unrequested files. For $N\ge4$, two converse inequalities establish the optimality of the known achievable points and the memory-sharing segments between them. For $N=3$, two additional bounds identify a new corner at $(M,R)=(3/2,2)$, where memory and rate are measured in file units. An explicit linear code over $\mathbb{F}_3$ attains this corner and reduces the rate by one quarter of a file relative to memory sharing between the known points. The converse links the information held by cache pairs and triples to delivery under repeated and distinct requests. Its equality conditions guide the construction: users cancel the keys to recover their requested files, while uniform masking protects the complete tuple of unrequested files.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Han Fang, Nan Liu, Wei Kang. 2026-11-04. The Exact Memory-Rate Tradeoff for Three-User Secure Coded Caching. https://arxiv.org/abs/2611.06311

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A class of asymptotically optimal authentication codes with secrecy

In this paper, a class of linear authentication codes with secrecy, which are equipped with simple encoding rules, is constructed. By means of a special Weil sum, the maximum success probabilities of impersonation attack (denoted by $P_I$) and of substitution attack (denoted by $P_S$) for these codes are explicitly derived. It is further proven that the codes are asymptotically optimal, in the sense that both the information theoretic bound and the combinatorial bound for authentication codes are asymptotically attained by $P_I$ and $P_S$.

cs.IT↗
arXiv2026

Fluid Antenna-Aided Robust Secure Uplink Transmission in LEO Satellite Constellations

Secure uplink transmission in low-earth orbit (LEO) satellite constellations faces significant challenges due to the time-varying spatial distributions of serving and potential eavesdropping satellites, particularly when their angular separations are small and eavesdropper channel state information (CSI) is imperfect. To address these challenges, this paper investigates fluid antenna (FA)-aided robust secure uplink transmission in LEO satellite constellations. To avoid frequent antenna reconfiguration, the FA positions are optimized over an observation interval and remain fixed throughout the interval, while transmit beamforming dynamically adapts to the time-varying satellite channels. We formulate an average worst-case secrecy rate maximization problem by jointly optimizing FA positions and time-varying beamforming under norm-bounded eavesdropper CSI uncertainties and per-slot secrecy rate constraints. Two new alternating optimization (AO) algorithms are developed to solve the resulting non-convex problem. For robust beamforming optimization, the S-procedure, semidefinite relaxation (SDR), and first-order approximation are employed to construct a tractable convex problem, followed by Gaussian randomization for rank-one recovery. For FA position optimization, we derive concave surrogate functions for successive convex approximation (SCA) and develop a differential evolution (DE)-based search strategy to reduce computational complexity. Numerical results demonstrate that both FA-aided schemes consistently outperform conventional fixed-position antenna arrays across different constellation configurations and CSI uncertainty levels. Moreover, the two algorithms exhibit different performance-complexity tradeoffs as the number of FA elements increases, with DE offering a computational advantage for larger arrays while SCA can achieve higher secrecy rates.

cs.IT↗
arXiv2026

Product Expansion of Random Codes via Analytic Techniques

Beginning with the work of Dinur, Lin, and Vidick (FOCS, 2024), tensor codes with constant product expansion have been foundational to recent advances in quantum locally testable codes (qLTCs) based on cubical complexes. Informally, product expansion says that any low-weight parity check of the tensor code can be written as the sum of few parity checks of each component code in each dimension. Recent work of Kalachev and Panteleev (FOCS, 2025) showed that tensors of random linear codes have constant product expansion. In this work we initiate the study of random linear codes with prescribed automorphism groups. For every sufficiently large prime $k$, we construct pairs of rate $1/2$ MDS codes of length $2k$, over finite fields whose size depends on $k$, that have constant two-sided product expansion and are invariant under the simultaneous cyclic shift of two cycles of length $k$. This shift is the local action in the cube complexes of Rungtanapirom, Stix, and Vdovina (Internat. J. Algebra Comput., 2019). Along the way we give a proof of the existence of two-sided product expanding codes which, unlike the earlier result of [KP25], does not rely on explicit constructions of asymptotically optimal locally testable codes. Our proof relies on several new techniques that we view as interesting in their own right. Instead of working directly over finite fields, we work over the reals and use random Rademacher matrices for the generator matrices of the component codes. From here, we show how to relate product expansion to the operator norm of sparse restrictions of carefully chosen Gram matrices, which we bound using tools from random matrix theory. More generally, we propose a method for studying properties of random linear codes by lifting to random codes over $\mathbb{R}$ and $\mathbb{C}$, which we anticipate will be applicable more broadly to existential problems in coding theory.

cs.IT↗