Coded caching with linear subpacketization is possible using Ruzsa-Szeméredi graphs

Shanmugam, Karthikeyan; Tulino, Antonia M.; Dimakis, Alexandros G.

doi:10.1109/isit.2017.8006726

Cited by 64 publications

(74 citation statements)

References 30 publications

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“…Similar conclusions were also drawn in [19] [20] which took a hyper-graph theoretic approach to show that there do not exist caching algorithms that achieve a constant T (T is independent of K) with subpacketization that grows linearly 3 with K. This work also provided constructions which nicely tradeoff performance with subpacketization, which require though (Construction 6) that K > 4/γ 2 (approximately) in order 4 to have gains bigger than 1. Another milestone of a more theoretical nature was the very recent work in [21] which employed the Ruzsa-Szeméredi graphs to show for the first time that, under the assumption of (an unattainably) large K, one can get a (suboptimal) gain that scales with K, with a subpacketization that scales with K 1+δ for some arbitrarily small positive δ.…”

Section: A Subpacketization Bottleneck Of Coded Cachingmentioning

confidence: 99%

“…We recall that the scheme that we have presented, involved 'elevating' the original MN algorithm in [1], from the single-stream scenario (L = 1) with K = K/L users, to the L-antenna case with K groups of L-users per group. This same idea can apply directly to other centralized coded caching algorithms like those in [18], [19], [21], in which case the steps are almost identical:…”

Section: F Elevating Different Coded Caching Algorithms To the L Antmentioning

confidence: 99%

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Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

Lampiris

Elia

2018

IEEE J. Select. Areas Commun.

140

177

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In the context of coded caching in the K-user BC, our work reveals the surprising fact that having multiple (L) transmitting antennas, dramatically ameliorates the long-standing subpacketization bottleneck of coded caching by reducing the required subpacketization to approximately its Lth root, thus boosting the actual DoF by a multiplicative factor of up to L. In asymptotic terms, this reveals that as long as L scales with the theoretical caching gain, then the full cumulative (multiplexing + full caching) gains are achieved with constant subpacketization. This is the first time, in any known setting, that unbounded caching gains appear under finite file-size constraints. The achieved caching gains here are up to L times higher than any caching gains previously experienced in any single-or multiantenna fully-connected setting, thus offering a multiplicative mitigation to a subpacketization problem that was previously known to hard-bound caching gains to small constants.The proposed scheme is practical and it works for all values of K, L and all cache sizes. The scheme's gains show in practice: e.g. for K = 100, when L = 1 the theoretical caching gain of G = 10, under the original coded caching algorithm, would have needed subpacketization S 1 = K G = 100 10 > 10 13 , while if extra transmitting antennas were added, the subpacketization was previously known to match or exceed S 1 . Now for L = 5, our scheme offers the theoretical (unconstrained) cumulative DoF d L = L + G = 5 + 10 = 15, with subpacketization S L = K/L G/L = 100/5 10/5 = 190. The work extends to the multi-server and cache-aided IC settings, while the scheme's performance, given subpacketization S L = K/L G/L , is within a factor of 2 from the optimal linear sum-DoF.

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Section: A Subpacketization Bottleneck Of Coded Cachingmentioning

confidence: 99%

Section: F Elevating Different Coded Caching Algorithms To the L Antmentioning

confidence: 99%

Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

Lampiris

Elia

2018

IEEE J. Select. Areas Commun.

140

177

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“…The remaining precoders scalars depend on ν η 4,5 [t] and can be computed by using (52) in (48) and (49)- (51). To this end, we compute the precoders along the r-th alignment chain [44], r ∈ [3], of the graph (the first chain in Fig.…”

Section: Rn and Denb Denb Onlymentioning

confidence: 99%

“…A practical proof-of-concept implementation allows to verify to what extent the theoretically postulated delivery times in this paper are achievable. Further, implementation issues such as large subpacketization levels [52], practicality of centralized cache placement [10] and selfinterference cancelation in full-duplex communication [53] have to be handled.…”

Section: Proof-of-concept Implementationmentioning

confidence: 99%

Cache-Assisted Broadcast-Relay Wireless Networks: A Delivery-Time Cache-Memory Tradeoff

et al. 2019

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An emerging trend of next generation communication systems is to provide network edges with additional capabilities such as storage resources in the form of caches to reduce file delivery latency.To investigate this aspect, we study the fundamental limits of a cache-aided broadcast-relay wireless network consisting of one central base station, M cache-equipped transceivers and K receivers from a latency-centric perspective. We use the normalized delivery time (NDT) to capture the per-bit latency for the worst-case file request pattern at high signal-to-noise ratios (SNR), normalized with respect to a reference interference-free system with unlimited transceiver cache capabilities. The objective is to design the schemes for cache placement and file delivery in order to minimize the NDT. To this end, we establish a novel converse (for arbitrary M and K) and two types of achievability schemes applicable to both time-variant and invariant channels. The first scheme is a general one-shot scheme for any M and K that synergistically exploits both multicasting (coded) caching and distributed zero-forcing opportunities. Apart from the obvious advantage of low signaling complexity, we show that the proposed one-shot scheme (i) attains gains attributed to both individual and collective transceiver caches (ii) is NDT-optimal for various parameter settings, particularly at higher cache sizes. The second scheme, on the other hand, designs beamformers to facilitate both subspace interference alignment and zero-forcing at lower cache sizes. Exploiting both schemes, we are able to characterize for various special cases of M and K which satisfy K + M ≤ 4 the optimal tradeoff between cache storage and latency. The tradeoff illustrates that the NDT is the preferred choice to capture the latency of a system rather than the commonly used sum degrees-of-freedom (DoF). In fact, our optimal tradeoff refutes the popular belief that increasing cache sizes translates to increasing the achievable sum DoF. As such, we identify and discuss cases where increasing cache sizes decreases both the delivery time and the achievable DoF. DRAFT 2 Index TermsCaching, interference alignment, degrees-of-freedom, latency, delivery time. DRAFT 4 with an arbitrary number of edge nodes and users. With these bounds, the optimality of schemes presented in [21] for certain regimes of cache sizes was shown under uncoded prefetching of the cached content. These concepts have been recently applied to Fog radio access networks (F-RAN) that consist of a centralized cloud server, cache-assisted edge nodes and mobile users.The NDT of F-RANs has been first fully characterized for two edge nodes and two mobile users [23]. Later on for the setting of arbitrary number of edge nodes and receivers a constant factor characterization of 2 has been established in [24]. The effect of channel strength and fading on the delivery time of partially connected F-RANs has been investigated in [25], [26], [27] on the basis of the binary fading model [28] and the linear deterministi...

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“…A key factor that limits the application of all forms of coded caching in practice, is the required high subpacketization level [13], i.e., the number of subpackets must grow exponentially with the number of users. In contrast, [14]- [18] proposed new caching schemes that have much lower subpacketization levels but slightly increased transmission rate. A useful tool for representing these new schemes are placement delivery arrays (PDA) introduced in [14].…”

Section: Introductionmentioning

confidence: 99%

Placement Delivery Array Design for Combination Networks with Edge Caching

Yan

Wigger

Yang

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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A major practical limitation of the Maddah-Ali-Niesen coded caching techniques is their high subpacketization level. For the simple network with a single server and multiple users, Yan et al. proposed an alternative scheme with the so-called placement delivery arrays (PDA). Such a scheme requires slightly higher transmission rates but significantly reduces the subpacketization level. In this paper, we extend the PDA framework and propose three low-subpacketization schemes for combination networks, i.e., networks with a single server, multiple relays, and multiple cache-aided users that are connected to subsets of relays. One of the schemes achieves the cutset lower bound on the link rate when the cache memories are sufficiently large. Our other two schemes apply only to resolvable combination networks. For these networks and for a wide range of cache sizes, the new schemes perform closely to the coded caching schemes that directly apply Maddah-Ali-Niesen scheme while having significantly reduced subpacketization levels.

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Coded caching with linear subpacketization is possible using Ruzsa-Szeméredi graphs

Cited by 64 publications

References 30 publications

Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

Cache-Assisted Broadcast-Relay Wireless Networks: A Delivery-Time Cache-Memory Tradeoff

Placement Delivery Array Design for Combination Networks with Edge Caching

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