A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes

Kazemi, Fatemeh; Karimi, Esmaeil; Soljanin, Emina; Sprintson, Alex

doi:10.1109/isit44484.2020.9174027

Cited by 10 publications

(8 citation statements)

References 32 publications

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“…(See Figure 7 for an example of the [7,3] Simplex code.) We note that has been shown in [1], [56], [58]. We present a brief proof for completeness.…”

Section: Using Graph Representations To Characterize Service Rate Reg...mentioning

confidence: 71%

“…Associating a recovery graph with a coding scheme allows us to relate the service allocation problem to the problem of finding a fractional matching in the recovery graph. (For the original observation and more details, see [56].) Let us consider a coding scheme G and its recovery graph Γ G .…”

Section: Service Allocation As a Fractional Matching In The Recovery ...mentioning

confidence: 99%

“…Since these codes are batch codes [58], the claim follows easily from the results in Section VI. Moreover, an algorithm is presented in [56] that takes an integer demand vector (λ a , λ b , λ c ) in the service rate region of the [7,3] Simplex code and produces an integral matching with λ a a-recovery edges, λ b b-recovery edges, and λ c c-recovery edges (see [56,Algorithm 1]). This algorithm can be easily extended to the binary [15,4] Simplex code, but a generalization to an arbitrary [2 k − 1, k] Simplex code is an open problem.…”

Section: B Coding Theory and Data Allocation Problemsmentioning

confidence: 99%

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Service Rate Region: A New Aspect of Coded Distributed System Design

Aktas

Joshi

Kadhe

et al. 2021

IEEE Trans. Inform. Theory

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Erasure coding has been recognized as a powerful method to mitigate delays due to slow or straggling nodes in distributed systems. This work shows that erasure coding of data objects can flexibly handle skews in the request rates. Coding can help boost the service rate region, that is, increase the overall volume of data access requests that the system can handle. This paper aims to postulate the service rate region as an important consideration in the design of erasure-coded distributed systems.We highlight several open problems that can be grouped into two broad threads: 1) characterizing the service rate region of a given code and finding the optimal request allocation, and 2) designing the underlying erasure code for a given service rate region. As contributions along the first thread, we find the rate regions of maximum-distance-separable, locally repairable, and simplex codes. We show the effectiveness of hybrid codes that combine replication and erasure coding in terms of code design. We also discover fundamental connections between multi-set batch codes and the problem of maximizing the service rate region.

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“…(See Figure 7 for an example of the [7,3] Simplex code.) We note that has been shown in [1], [56], [58]. We present a brief proof for completeness.…”

Section: Using Graph Representations To Characterize Service Rate Reg...mentioning

confidence: 71%

Section: Service Allocation As a Fractional Matching In The Recovery ...mentioning

confidence: 99%

Section: B Coding Theory and Data Allocation Problemsmentioning

confidence: 99%

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Service Rate Region: A New Aspect of Coded Distributed System Design

Aktas

Joshi

Kadhe

et al. 2021

IEEE Trans. Inform. Theory

Self Cite

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“…The service rate region of the systems with arbitrary n when k = 3 was determined in [9]. A connection between the service rate problem and the fractional matching problem is established in [10]. Also, it has been shown that the service rate problem can be viewed as a generalization of the batch codes problem.…”

Section: Introduction Motivationmentioning

confidence: 99%

Efficient Storage Schemes for Desired Service Rate Regions

Kazemi

Kurz

Soljanin

et al. 2021

2020 IEEE Information Theory Workshop (ITW)

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A major concern in cloud/edge storage systems is serving a large number of users simultaneously. The service rate region is introduced recently as an important performance metric for coded distributed systems, which is defined as the set of all data access requests that can be simultaneously handled by the system. This paper studies the problem of designing a coded distributed storage system storing k files where a desired service rate region R of the system is given and the goal is 1) to determine the minimum number of storage nodes n(R) for serving all demand vectors inside the set R and 2) to design the most storage-efficient redundancy scheme with the service rate region covering the set R. Towards this goal, we propose three general lower bounds for n(R). Also, for k = 2, we characterize n(R), i.e., we show that the proposed lower bounds are tight, via designing a novel storage-efficient redundancy scheme with n(R) storage nodes and the service rate region covering R.

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“…The service rate region of the systems with arbitrary n when k = 3 was determined in [23]. A connection between the service rate problem and the fractional matching problem is established in [24]. Also, it has been shown that the service rate problem can be viewed as a generalization of the multiset primitive batch codes problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient Storage Schemes for Desired Service Rate Regions

Kazemi¹,

Kurz²,

Soljanin³

et al. 2020

Preprint

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A major concern in cloud/edge storage systems is serving a large number of users simultaneously.The service rate region is introduced recently as an important performance metric for coded distributed systems, which is defined as the set of all data access requests that can be simultaneously handled by the system. This paper studies the problem of designing a coded distributed storage system storing k files where a desired service rate region R of the system is given and the goal is 1) to determine the minimum number of storage nodes n(R) (or a lower bound on n(R)) for serving all demand vectors inside the set R and 2) to design the most storage-efficient redundancy scheme with the service rate region covering R. Towards this goal, we propose three general lower bounds for n(R). Also, for k = 2, we characterize n(R), i.e., we show that the proposed lower bounds are tight via designing a novel storage-efficient redundancy scheme with n(R) storage nodes and the service rate region covering R.

show abstract

A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes

Cited by 10 publications

References 32 publications

Service Rate Region: A New Aspect of Coded Distributed System Design

Service Rate Region: A New Aspect of Coded Distributed System Design

Efficient Storage Schemes for Desired Service Rate Regions

Efficient Storage Schemes for Desired Service Rate Regions

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