On caching with more users than files

Wan, Kai; Tuninetti, Daniela; Piantanida, Pablo

doi:10.1109/isit.2016.7541276

Cited by 83 publications

(67 citation statements)

References 17 publications

(68 reference statements)

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“…However in the case of uniform file popularity, the achievable rates provided in these works reduce to the results of [10] or [17], while our proposal strictly improves the state of the arts in both [10] and [17] by developing a novel delivery strategy that exploits the commonality of the user demands. There have also been several proposed schemes that aim to minimize the peak rates [12], [16]. The main novelty of our work compared to their results is that we not only propose an optimal design that strictly improves upon all these works through a leader based strategy, but also provide an intuitive proof for its decodability.…”

Section: Resultsmentioning

confidence: 91%

“…The problem of caching with uncoded prefetching was initiated in [12], [51], which showed that the scheme in [10] is optimal when considering peak rate and centralized caching, if there are more files than users. Although not stated in [12], [51], the converse bound in our paper for the special case of peak rate and centralized setting could have also been derived using their approach.…”

Section: Introductionmentioning

confidence: 99%

“…Although not stated in [12], [51], the converse bound in our paper for the special case of peak rate and centralized setting could have also been derived using their approach. In this paper however, we introduce the novel idea of demand types, which allows us to go beyond and characterize the rate-memory tradeoff for both peak rate and average rate for all possible parameter values, in both centralized and decentralized settings.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Maddah-Ali

Avestimehr

2018

IEEE Trans. Inform. Theory

302

278

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Abstract-We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

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Section: Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Maddah-Ali

Avestimehr

2018

IEEE Trans. Inform. Theory

302

278

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“…If A < 0, let s = = 1, we have (N, 0) ∈ S Lower from (15). Hence A + BN ≤ 0, and for any M ∈ [0, N ] we have…”

Section: Proof Of Theorem 1 and Theoremmentioning

confidence: 99%

Characterizing the rate-memory tradeoff in cache networks within a factor of 2

Maddah-Ali

Avestimehr

2017

2017 IEEE International Symposium on Information Theory (ISIT)

163

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We consider a basic caching system, where a single server with a database of N files (e.g. movies) is connected to a set of K users through a shared bottleneck link. Each user has a local cache memory with a size of M files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), where the best proved characterization in the current literature gives a factor of 4 and 4.7 respectively. Moreover, in the practically important case where the number of files (N ) is large, we exactly characterize the tradeoff for systems with no more than 5 users, and characterize the tradeoff within a factor of 2 otherwise. We establish these results by developing novel information theoretic outer-bounds for the caching problem, which improves the state of the art and gives tight characterization in various cases. I. INTRODUCTIONCaching is a common strategy to mitigate heavy peak-time communication load in a distributed network, via duplicating parts of the content in memories distributed across the network during off-peak times. In other words, caching allows us to trade distributed memory in the network for communication load reduction. Characterizing this fundamental rate-memory tradeoff is of great practical interest, and has been a research subject for several decades. For single-cache networks, the ratememory tradeoff has been characterized for various scenarios in 80th [1]. However, those techniques were found insufficient to tackle the multiple-cache cases. There has been a surge of recent results in information theory that aim at formalizing and characterizing such rate-memory tradeoff in cache networks [2]- [13]. In particular, the peak rate vs. memory tradeoff was formulated and characterized within a factor of 12 in a basic cache network with a shared bottleneck link [2]. This result has been extended to many scenarios, including decentralized caching [3] Essentially, many of these extensions share similar ideas in terms of the achievability and the converse bounds. Therefore, if we can improve the results for the basic bottleneck caching network, the ideas can be used to improve the results in other cases as well.In the literature, various approaches have been proposed for improving the bounds on rate-memory tradeoff for the bottleneck network. Several caching schemes have been proposed in [14]-[21], and converse bounds have also been introduced in [9], [22]-[26]. For the case, where the prefetching is uncoded, the exact rate-memory tradeoff for both peak and average rate (under uniform file popularity) and for both centra...

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“…5 Recall that in Section I-B we defined the XOR operation⊕ over the binary representations of the two messages of same length.…”

Section: Generalized Coded-cachingmentioning

confidence: 99%

Benefits of cache assignment on degraded broadcast channels

Bidokhti

Wigger

Yener

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Degraded K-user broadcast channels (BC) are studied when receivers are facilitated with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate of reliable communication over the BC as a function of the receivers' cache sizes, and the bounds are shown to match for some special cases.The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. Lower and upper bounds are also established on the global capacity-memory tradeoff, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers' cache sizes subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, characterized in terms of the BC statistics. For small cache memories, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows as the total cache memory budget divided by the number of files in the system. In other words, a perfect global caching gain is achievable in this regime and the performance corresponds to a system where all cache contents in the network are available to all receivers. For large cache memories, it is optimal to assign a positive cache memory to every receiver such that the weaker receivers are assigned larger cache memories compared to the stronger receivers. In this regime, the growth rate of the global capacity-memory tradeoff is further divided by the number of users, which corresponds to a local caching gain.Numerical indicate suggest that a uniform cache-assignment of the total cache memory is suboptimal in all regimes unless the BC is completely symmetric. For erasure BCs, this claim is proved analytically in the regime of small cache-sizes.

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On caching with more users than files

Cited by 83 publications

References 17 publications

The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Characterizing the rate-memory tradeoff in cache networks within a factor of 2

Benefits of cache assignment on degraded broadcast channels

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