An Optimal Linear Error Correcting Delivery Scheme for Coded Caching with Shared Caches

Karat, Nujoom Sageer; Dey, Spandan; Thomas, Anoop; Rajan, B. Sundar

doi:10.1109/isit.2019.8849406

Cited by 25 publications

(16 citation statements)

References 33 publications

(104 reference statements)

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“…There is a server with N = 45 files connected to K = 45 users and to Λ = 9 caches, each with a normalized size M N = 1 3 . Then for an association profile L = (8,7,6,6,5,4,4,3,2), sub-packetization and the worst-case delivery load achieved by our PDA-based construction and the PUE scheme are shown in Table II. We consider the same setting as in Example 2 with only change in the normalized cache size.…”

Section: Resultsmentioning

confidence: 99%

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Coded Caching with Shared Caches from Generalized Placement Delivery Arrays

Peter¹,

Rajan²

2021

Preprint

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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.

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Section: Resultsmentioning

confidence: 99%

“…In [5], the centralized setting is considered and an optimal coded caching scheme is proposed for distinct demand case. For non-distinct demands, an improved delivery scheme was introduced in [7]. A caching scheme based on coded placement was proposed in [8], which outperforms the scheme in [5] in certain memory regimes.…”

Section: A Related Workmentioning

confidence: 99%

Coded Caching with Shared Caches from Generalized Placement Delivery Arrays

Peter¹,

Rajan²

2021

Preprint

Self Cite

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show abstract

“…The centralized caching scheme in [3] provides the optimal delivery time for distinct demands, under uncoded prefetching. To accommodate redundant user demands, a new delivery scheme was introduced in [7] which provides an improved performance for non-distinct demands. A caching scheme based on coded placement was proposed in [10], which outperforms the scheme in [3] in certain memory regimes.…”

Section: A Related Workmentioning

confidence: 99%

Decentralized and Online Coded Caching with Shared Caches: Fundamental Limits with Uncoded Prefetching

Peter¹,

Rajan²

2021

Preprint

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Decentralized coded caching scheme, introduced by Maddah-Ali and Niesen, assumes that the caches are filled with no coordination. This work identifies a decentralized coded caching scheme -under the assumption of uncoded placement-for shared cache network, where each cache serves multiple users. Each user has access to only a single cache and the number of caches is less than or equal to the number of users. For this setting, we derive the optimal worst-case delivery time for any user-tocache association profile where each such profile describes the number of users served by each cache. The optimality is shown using an index-coding based converse. Further, we improve the delivery scheme to accommodate redundant demands. Also, an optimal linear error correcting delivery scheme is proposed for the worst-case demand scenario. Next, we consider the Least Recently Sent (LRS) online coded caching scheme where the caches need to be updated based on the sequence of demands made by the users. Cache update happens if any of the demanded file was not partially cached at the users. The update is done by replacing the least recently sent file with the new file. But, the least recently sent file need not be unique. In that case, there needs to be some ordering of the files which are getting partially cached, or else centralized coordination would have to be assumed which does not exist. If each user removes any of the least recently used files at random, then the next delivery phase will not serve the purpose. A modification is suggested for the scheme by incorporating the ordering of files. The fix is suggested so that the results on the error-correction for the online coded caching scheme introduced in [N. S. Karat, K. L. V. Bhargav and B. S. Rajan, "On the Optimality of Two Decentralized Coded Caching Schemes With and Without Error Correction," IEEE ISIT, Jun. 2020] are not affected. Moreover, all the above results with shared caches are extended to the online setting.

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“…For index coding problems satisfying α(I) = κ q (I), the concatenation scheme is optimal [19]. Error correcting index coding scheme has been used already in index coding [21] and coded caching [20], [22], [23], where optimal error correcting schemes are constructed by the concatenation scheme.…”

Section: B Index Coding Problemmentioning

confidence: 99%