The exact rate-memory tradeoff for caching with uncoded prefetching

Yu, Qian; Maddah-Ali, Mohammad Ali; Avestimehr, A. Salman

doi:10.1109/isit.2017.8006802

Cited by 156 publications

(449 citation statements)

References 27 publications

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“…Remark 3. R u and R u,ave , as defined in Definition 1, are the optimum peak rate and the optimum average rate that can be achieved using uncoded prefetching, as we proved in [20]. This indicates that for the coded caching problem, using uncoded prefetching schemes is within a factor of 2.00884 optimal for both peak rate and average rate.…”

Section: Resultssupporting

confidence: 51%

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)

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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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Section: Resultssupporting

confidence: 51%

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)

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163

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“…The server has access to a database of N files W 1 , ..., W N , each of size F bits. 1 We denote the jth bit in file i by B i,j , and we assume that all bits in the database are i.i.d. Bernoulli random variables with p = 0.5.…”

Section: A System Modelmentioning

confidence: 99%

The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Maddah-Ali

Avestimehr

2018

IEEE Trans. Inform. Theory

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305

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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“…We would like to note that the capacity of the above caching network remains an open problem even when the delivery channel is an error-free shared bit pipe except for the network with an uncoded cache placement phase [11]. Here, our goal is to identify achievable memory-rate pairs that improve upon the state-of-the-art.…”

Section: System Model and Preliminariesmentioning

confidence: 99%

Cache-Aided Content Delivery Over Erasure Broadcast Channels

Amiri

Gündüz

2018

IEEE Trans. Commun.

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A cache-aided broadcast network is studied, in which a server delivers contents to a group of receivers over a packet erasure broadcast channel (BC). The receivers are divided into two sets with regards to their channel qualities: the weak and strong receivers, where all the weak receivers have statistically worse channel qualities than all the strong receivers. The weak receivers, in order to compensate for the high erasure probability they encounter over the channel, are equipped with cache memories of equal size, while the receivers in the strong set have no caches. Data can be pre-delivered to weak receivers' caches over the off-peak traffic period before the receivers reveal their demands.Allowing arbitrary erasure probabilities for the weak and strong receivers, a joint caching and channel coding scheme, which divides each file into several subfiles, and applies a different caching and delivery scheme for each subfile, is proposed. It is shown that all the receivers, even those without any cache memories, benefit from the presence of caches across the network. An information theoretic trade-off between the cache size and the achievable rate is formulated. It is shown that the proposed scheme improves upon the state-of-the-art in terms of the achievable trade-off.

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The exact rate-memory tradeoff for caching with uncoded prefetching

Cited by 156 publications

References 27 publications

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

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

The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching

Cache-Aided Content Delivery Over Erasure Broadcast Channels

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