Multi-access Coded Caching Scheme with Linear Sub-packetization using PDAs

Sasi, Shanuja; Rajan, B. Sundar

doi:10.48550/arxiv.2102.06616

Cited by 2 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and the application of PDA designs to the multi-access setting [51], [52]. To the best of our understanding, it is fair to say that, under the assumption of a cyclic wrap-around topology and under realistic assumptions on the cache resources Λγ and on λ, the impact of the MACC setting has remained relatively modest.…”

Section: A Multi-access Coded Cachingmentioning

confidence: 99%

Fundamental Limits of Combinatorial Multi-Access Caching

Brunero¹,

Elia²

2021

Preprint

View full text Add to dashboard Cite

This work identifies the fundamental limits of Multi-Access Coded Caching (MACC) where each user is connected to multiple caches in a manner that follows a generalized combinatorial topology. This topology stands out as it allows for unprecedented coding gains, even with very modest cache resources.First, we extend the setting and the scheme presented by Muralidhar et al. to a much more general topology that supports both a much denser range of users and the coexistence of users connected to different numbers of caches, all while maintaining the astounding coding gains -here proven to be exactly optimal -associated with the combinatorial topology. This is achieved, for this generalized topology, with a novel information-theoretic converse that we present here, which establishes, together with the scheme, the exact optimal performance under the assumption of uncoded placement. We subsequently consider different connectivity ensembles, including the very general scenario of the entire ensemble of all possible network connectivities/topologies, where any user can be connected to any subset of caches arbitrarily. For these settings, we develop novel converse bounds on the optimal performance averaged over the ensemble's different connectivities, considering the additional realistic scenario that the connectivity at delivery time is entirely unknown during cache placement. This novel analysis of topological ensembles leaves open the possibility that currently-unknown topologies may yield even higher gains, a hypothesis that is part of the bigger question of which network topology yields the most caching gains.

show abstract

Section: A Multi-access Coded Cachingmentioning

confidence: 99%

Fundamental Limits of Combinatorial Multi-Access Caching

Brunero¹,

Elia²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Also, there exists several other constructions that focus on reducing sub-packetization, some of which uses resolvable block design and linear block codes [18], the strong edge colouring of subset graphs [19], projective space [20] etc. Recently, a new class of PDA termed as consecutive and t-cyclic PDA were introduced [21] to describe the delivery scheme for a special class of multi-access coded caching problem.…”

Section: A Related Workmentioning

confidence: 99%

Coded Caching with Shared Caches from Generalized Placement Delivery Arrays

Peter¹,

Rajan²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider the coded caching problem with shared caches where several users share a cache, but each user has access to only a single cache. For this network, the fundamental limits of coded caching are known for centralized and decentralized settings under uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a subpacketization which increases exponentially with the number of caches. The dedicated cache networks had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to it. Using the PDA framework, we propose a procedure to obtain new coded caching schemes for shared caches with lower sub-packetization requirements. The advantage of this procedure is that we can transform all the existing PDA structures into coded caching schemes for shared caches, thus resulting in low sub-packetization schemes. We also show that the optimal scheme given by Parrinello, Ünsal and Elia (Fundamental Limits of Coded Caching with Multiple Antennas, Shared Caches and Uncoded Prefetching) can be recovered using a Maddah-Ali Niesen PDA.

show abstract

Multi-access Coded Caching Scheme with Linear Sub-packetization using PDAs

Cited by 2 publications

References 16 publications

Fundamental Limits of Combinatorial Multi-Access Caching

Fundamental Limits of Combinatorial Multi-Access Caching

Coded Caching with Shared Caches from Generalized Placement Delivery Arrays

Contact Info

Product

Resources

About