Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1703.01548

Coded Caching Schemes with Low Rate and Subpacketizations

Minquan Cheng·Qifa Yan·Xiaohu Tang·Jing Jiang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Coded caching scheme, which is an effective technique to increase the transmission efficiency during peak traffic times, has recently become quite popular among the coding community. Generally rate can be measured to the transmission in the peak traffic times, i.e., this efficiency increases with the decreasing of rate. In order to implement a coded caching scheme, each file in the library must be split in a certain number of packets. And this number directly reflects the complexity of a coded caching scheme, i.e., the complexity increases with the increasing of the packet number. However there exists a tradeoff between the rate and packet number. So it is meaningful to characterize this tradeoff and design the related Pareto-optimal coded caching schemes with respect to both parameters. Recently, a new concept called placement delivery array (PDA) was proposed to characterize the coded caching scheme. However as far as we know no one has yet proved that one of the previously known PDAs is Pareto-optimal. In this paper, we first derive two lower bounds on the rate under the framework of PDA. Consequently, the PDA proposed by Maddah-Ali and Niesen is Pareto-optimal, and a tradeoff between rate and packet number is obtained for some parameters. Then, from the above observations and the view point of combinatorial design, two new classes of Pareto-optimal PDAs are obtained. Based on these PDAs, the schemes with low rate and packet number are obtained. Finally the performance of some previously known PDAs are estimated by comparing with these two classes of schemes.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Minquan Cheng, Qifa Yan, Xiaohu Tang, Jing Jiang. 2017-10-02. Coded Caching Schemes with Low Rate and Subpacketizations. https://arxiv.org/abs/1703.01548

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

KEEP EXPLORING

Related papers

arXiv2026

Bistatic Target Detection by Exploiting Both Deterministic Pilots and Unknown Random Data Payloads

Integrated sensing and communication (ISAC) plays a crucial role in 6G, to enable innovative applications such as drone surveillance, urban air mobility, and low-altitude logistics. However, the hybrid ISAC signal, which comprises deterministic pilot and random data payload components, poses challenges for target detection due to two reasons: 1) these two components cause coupled shifts in both the mean and variance of the received signal, and 2) the random data payloads are typically unknown to the sensing receiver in the bistatic setting. Unfortunately, these challenges could not be tackled by existing target detection algorithms. In this paper, a generalized likelihood ratio test (GLRT)-based detector is derived, by leveraging the known deterministic pilots and the statistical characteristics of the unknown random data payloads. Due to the analytical intractability of exact performance characterization, we perform an asymptotic analysis for the false alarm probability and detection probability of the proposed detector. The results highlight a critical trade-off: both deterministic and random components improve detection reliability, but the latter also brings statistical uncertainty that hinders detection performance. Simulations validate the theoretical findings and demonstrate the effectiveness of the proposed detector, which highlights the necessity of designing a dedicated detector to fully exploited the signaling resources assigned to random data payloads.

cs.IT↗
arXiv2026

On Unbiased Parameter Estimation and Signal Reconstruction

In this paper, we extend the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction for an arbitrary number of non-zero parameters. The topic touches on exact reconstructibility, most commonly studied in compressed sensing and multisource estimation across various imaging problems. The theoretical results derive upper bounds on the number of recoverable parameters in the noiseless case, and define a probability measure to assess the likelihood of recovering all non-zero parameters with correct magnitude order. The work provides a mathematical explanation of the open question regarding the noise robustness of standardized and unbiased methods. The paper also reveals a trade-off between the number of sensors and the signal-to-noise ratio. Numerical experiments demonstrate the theoretical findings.

cs.IT↗
arXiv2026

Minimum enclosing Bregman balls made easy

In this work, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) of finite sets of parameters. First, we show that Bregman MEBs are equivalent to MEBs of corresponding weighted point sets with respect to the power distance. We then report an efficient Frank--Wolfe $(1+ε)$-approximation algorithm for computing power MEBs, for any $ε>0$. This power MEB approximation algorithm coincides with the Bregman MEB approximation algorithm of Nock and Nielsen (2005) when expressed in the dual gradient space. Finally, we show that the Bregman potential lifting transforms used to construct Bregman Voronoi diagrams can be reinterpreted as the classical paraboloid lifting transform applied to corresponding weighted point sets. In particular, Bregman MEB circumcenters lie on the farthest Bregman Voronoi diagrams or equivalently on the corresponding farthest power diagrams.

cs.IT↗