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New Families of MDS Symbol-Pair codes From Matrix-Product codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第3期69卷 1567-1587页

作者： Luo, Gaojun Ezerman, Martianus Frederic Ling, San Pan, Xu Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore Sandhiguna Kota Batam 29461 Kepulauan Riau Indonesia Cent China Normal Univ Sch Math & Stat Wuhan 430079 Peoples R China

In emerging storage technologies, the outputs of the channels consist of overlapping pairs of symbols. The errors are no longer individual symbols. Controlling them calls for a different approach. Symbol-pair codes have been proposed as a solution. The error-correcting capability of such a code depends on its minimum pair distance instead of the usual minimum Hamming distance. Longer codes can be conveniently constructed from known shorter ones by a matrix-product approach. The parameters of a matrix-product code can be determined from the parameters of the ingredient codes. We construct a new family of maximum distance separable (MDS) symbol-pair matrix-product codes. codes which are permutation equivalent to matrix-product codes may have improved minimum pair distances. We present four new families of MDS symbol-pair codes and a new family of almost MDS symbol-pair codes. The codes in these five new families are permutation equivalent to matrix-product codes. Each of our five constructions identifies permutations that can increase the minimum pair distances. We situate the new families among previously known families of MDS symbol-pair codes to highlight the versatility of our matrix-product construction route.

关键词： codes Symbols Hamming distances codecs Writing Scholarships Reed-Solomon codes Matrix-product code maximum distance separable code symbol-pair code

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Elastic Resource Allocation for coded Distributed Computing Over Heterogeneous Wireless Edge Networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2023年第4期22卷 2636-2649页

作者： Nguyen, Cong T. Nguyen, Diep N. Hoang, Dinh Thai Phan, Khoa Tran Niyato, Dusit Pham, Hoang-Anh Dutkiewicz, Eryk Univ Technol Sydney Sch Elect & Data Engn Sydney NSW 2007 Australia Vietnam Natl Univ Ho Chi Minh City VNU HCM Ho Chi Minh City Univ Technol HCMUT Fac Comp Sci & Engn Ho Chi Minh City 700000 Vietnam La Trobe Univ Sch Engn & Math Sci Melbourne VIC 3086 Australia Nanyang Technol Univ Sch Comp Sci & Engn Singapore City 639798 Singapore

coded distributed computing (CDC) has recently emerged to be a promising solution to address the straggling effects in conventional distributed computing systems. By assigning redundant workloads to the computing nodes, CDC can significantly enhance the performance of the whole system. However, since the core idea of CDC is to introduce redundancies to compensate for uncertainties, it may lead to a large amount of wasted energy at the edge nodes. It can be observed that the more redundant workload added, the less impact the straggling effects have on the system. However, at the same time, the more energy is needed to perform redundant tasks. In this work, we develop a novel framework, namely CERA, to elastically allocate computing resources for CDC processes. Particularly, CERA consists of two stages. In the first stage, we model a joint coding and node selection optimization problem to minimize the expected processing time for a CDC task. Since the problem is NP-hard, we propose a linearization approach and a hybrid algorithm to quickly obtain the optimal solutions. In the second stage, we develop a smart online approach based on Lyapunov optimization to dynamically turn off straggling nodes based on their actual performance. As a result, wasteful energy consumption can be significantly reduced with minimal impact on the total processing time. Simulations using real-world datasets have shown that our proposed approach can reduce the system's total processing time by more than 200% compared to that of the state-of-the-art approach, even when the nodes' actual performance is not known in advance. Moreover, the results have shown that CERA's online optimization stage can reduce the energy consumption by up to 37.14% without affecting the total processing time.

关键词： Task analysis Servers Optimization Distributed computing Wireless communication Energy consumption codes coded distributed computing maximum distance separable code resource allocation INLP Lyapunov optimization edge computing straggling effects

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Latency-Aware Task Scheduling in Software-Defined Edge and Cloud Computing With Erasure-coded Storage Systems

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IEEE TRANSACTIONS ON CLOUD COMPUTING 2023年第2期11卷 1575-1590页

作者： Tang, Jianhang Jalalzai, Mohammad M. Feng, Chen Xiong, Zehui Zhang, Yang Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066104 Hebei Peoples R China Univ British Columbia Sch Engn Okanagan Campus Vancouver BC V6T 1Z4 Canada Singapore Univ Technol & Design Pillar Informat Syst Technol & Design Singapore 487372 Singapore Nanjing Univ Aeronaut & Astronaut Coll Comp Sci & Technol Nanjing 210016 Peoples R China

The collaborative edge and cloud computing system has emerged as a promising solution to fulfill the unprecedented high requirements of 5G application scenarios. Due to vendor variations, it is often difficult to manage hardware facilities in such a collaborative system. Moreover, the amount of data generated and tasks requested by end devices are increasing exponentially, which introduces storage and computation bottlenecks. To address these issues, a novel systematic framework called software-defined edge and cloud computing (SD-ECC) is designed to manage the underlying physical resources of edge and cloud layers via software. SD-ECC is combined with an erasure-coded storage system, for which a task scheduling problem is formulated by considering data access and task processing steps. Then, a joint data access and task processing (JDATP) algorithm is proposed to minimize the task response time including data access latency and task processing latency. A practical SD-ECC platform is developed on OpenStack, OpenDaylight, and Kubernetes to conduct experiments with real-world datasets. The experimental results demonstrate that our proposed JDATP algorithm can reduce 20.87% of the task response time and increase 14.16% of the remaining storage space on average by comparing it with alternative schemes.

关键词： Software-defined edge and cloud computing erasure-coded storage systems maximum distance separable code task scheduling

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Three New Constructions of Optimal Locally Repairable codes From Matrix-Product codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第1期69卷 75-85页

作者： Luo, Gaojun Ezerman, Martianus Frederic Ling, San Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore Sandhiguna Jalan Raya Batam Ctr Batam 29461 Kepulauan Riau Indonesia

repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with (r, delta)-locality that achieve equality in the Singleton-type bound. We use matrix-product codes to propose two constructions of q-ary optimal (r, delta) locally repairable codes of lengths up to q(2 )+ q. The ingredients in the matrix-product codes are linear maximum distance separable codes. We give another construction of optimal (r, delta) locally repairable codes by using optimal locally repairable codes as ingredients in the matrix-product approach. The codes in this third construction have unbounded lengths not divisible by (r +delta -1). The three constructions of optimal (r, delta) locally repairable codes constructed here are new. Previously constructed codes in the literature have not covered the same sets of parameters. Our construction proposals are flexible since one can easily vary r and delta to come up with particular parameters that can suit numerous scenarios.

关键词： Distributed storage system locally repairable code maximum distance separable code matrix-product code

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MDS codes based on orthogonality of quasigroups

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2023年 1-22页

作者： Kumar, Satish Singh, Harshdeep Gupta, Indivar Gupta, Ashok Ji Indian Inst Technol BHU Dept Math Sci Varanasi 221005 UP India Def R&D Org Sci Anal Grp New Delhi 110054 India

In this paper, we propose a novel method for constructing maximum distance separable (MDS) codes based on the extended invertibility and orthogonality of quasigroups. We provide various methods of constructing an orthogonal system of k-ary operations over Q(2) using a special type of k-ary operations over Q, where Q is any arbitrary finite set. Then we use concepts of strong orthogonality of k-ary operations to establish a connection between orthogonality and linear recursive MDS codes. We illustrate these new classes of MDS codes using the proposed techniques and enumerate such codes using SageMath.

关键词： i-invertible operation Orthogonal system of operations Extended i-invertibility Recursive code maximum distance separable code

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Robust, Private and Secure Cache-Aided Scalar Linear Function Retrieval From coded Servers

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2022年第3期40卷 968-981页

作者： Yan, Qifa Tuninetti, Daniela Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA Southwest Jiaotong Univ Informat Coding & Transmiss Key Lab Sichuan Prov CSNMT Int Cooperat Res Ctr MoST Chengdu 611756 Peoples R China

This work investigates a system where each user aims to retrieve a scalar linear function of the files of a library, which are maximum distance separable coded and stored at multiple distributed servers. The system needs to guarantee robust decoding in the sense that each user must decode its demanded function with signals received from any subset of servers whose cardinality exceeds a threshold. In addition, (a) the content of the library must be kept secure from a wiretapper who obtains all the signals from the servers;(b) any subset of users together can not obtain any information about the demands of the remaining users;and (c) the users' demands must be kept private against all the servers even if they collude. Achievable schemes are derived by modifying existing Placement Delivery Array (PDA) constructions, originally proposed for single-server single-file retrieval coded caching systems without any privacy or security or robustness constraints. It is shown that the PDAs describing the original Maddah-Ali and Niesen's coded caching scheme result in a load-memory tradeoff that is optimal to within a constant multiplicative gap, except for the small memory regime when the number of file is smaller than the number of users. As by-products, improved order optimality results are derived for three less restrictive systems in all parameter regimes.

关键词： Servers Privacy Security Handheld computers codes Libraries Robustness coded caching distributed storage maximum distance separable code placement delivery array privacy robust decoding scalar linear function retrieval security

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Optimize Coding and Node Selection for coded Distributed Computing over Wireless Edge Networks

Optimize Coding and Node Selection for Coded Distributed Com...

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IEEE Wireless Communications and Networking Conference (IEEE WCNC)

作者： Nguyen, Cong T. Nguyen, Diep N. Dinh Thai Hoang Hoang-Anh Pham Dutkiewicz, Eryk Univ Technol Sydney Sydney NSW Australia Ho Chi Minh City Univ Technol HCMUT Vietnam Natl Univ Ho Chi Minh City VNU HCM Ho Chi Minh City Vietnam

ISBN: (纸本)9781665442664

This paper aims to develop a highly-effective framework to significantly enhance the efficiency in using coded computing techniques for distributed computing tasks over heterogeneous wireless edge networks. In particular, we first formulate a joint coding and node selection optimization problem to minimize the expected total processing time for computing tasks, taking into account the heterogeneity in the nodes' computing resources and communication links. The problem is shown to be NP-hard. To circumvent it, we leverage the unique characteristic of the problem to develop a linearization approach and a hybrid algorithm based on binary search and branch-and-bound (BB) algorithms. This hybrid algorithm can not only guarantee to find the optimal solution, but also significantly reduce the computational complexity of the BB algorithm. Simulations based on real-world datasets show that the proposed approach can reduce the total processing time up to 2.4 times compared with that of state-of-the-art approach, even without perfect knowledge regarding the node's performance and their straggling parameters.

关键词： coded distributed computing maximum distance separable code INLP straggling effects

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Adaptive Task Offloading in coded Edge Computing: A Deep Reinforcement Learning Approach

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IEEE COMMUNICATIONS LETTERS 2021年第12期25卷 3878-3882页

作者： Nguyen Van Tam Nguyen Quang Hieu Nguyen Thi Thanh Van Nguyen Cong Luong Niyato, Dusit Kim, Dong In Phenikaa Univ Fac Comp Sci Hanoi 12116 Vietnam A&A Phoenix Grp JSC Phenikaa Res & Technol Inst PRATT Hanoi 11313 Vietnam Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore Phenikaa Univ Fac Elect & Elect Engn Hanoi 12116 Vietnam Sungkyunkwan Univ Dept Elect & Comp Engn Suwon 16419 South Korea

In this letter, we consider a coded Edge Computing (CEC) network in which a client encodes its computation subtasks using the maximum distance separable (MDS) code before offloading them to helpers. The CEC network is heterogeneous in which the helpers are different in computing capacity, wireless communication stability, and computing price. Thus, the client needs to determine a desirable size of MDS-coded subtasks and selects proper helpers such that the computation latency is within the deadline and the incentive cost is minimal. This problem is challenging since the helpers are generally dynamic and random in the computing, communication, and computing price. We thus propose to adopt a Deep Reinforcement Learning (DRL) algorithm that allows the client to learn and find optimal decisions without any prior knowledge of network environments. The experiment results reveal that the proposed algorithm outperforms the standard Q-learning and baseline algorithms in both terms of computation latency and incentive cost.

关键词： Task analysis Costs Reinforcement learning codes Edge computing Partitioning algorithms Optimization maximum distance separable code coded edge computing deep reinforcement learning

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MDS coded caching with MRT and its optimization

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ICT EXPRESS 2019年第1期5卷 60-64页

作者： Kim, Gibum Park, Hyuncheol Choi, Wan Korea Adv Inst Sci & Technol Sch Elect Engn 335 Gwahak Ro Daejeon South Korea

In conventional maximum distance separable (MDS) coded caching systems, storage-efficient caching strategy which minimizes unnecessarily redundant data is believed to be optimal. However, the conventional storage efficient caching strategy may not be optimal because redundantly stored data can be utilized as diversity sources to combat wireless channel impairments due to channel fading. This paper explores how MDS coded caching facilitates coordinated maximum ratio transmission (MRT) in cache enabled wireless networks. Optimizing the length of MDS coded sequence and the amount of redundant cached data, we demonstrate the gain of MDS coded caching leveraged by MRT outperforms conventional uncoded caching schemes. (C) 2018 The Korean Institute of Communications and Information Sciences (KICS). Publishing Services by Elsevier B.V.

关键词： Wireless caching coded caching maximum distance separable code maximum ratio transmission

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MDS and I-perfect poset block codes

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FINITE FIELDS AND THEIR APPLICATIONS 2020年 62卷 101620-000页

作者： Dass, B. K. Sharma, Namita Verma, Rashmi Univ Delhi Dept Math Delhi 110007 India Univ Delhi Mata Sundri Coll Women Mata Sundri Lane Delhi 110002 India

We obtain the Singleton bound for poset block codes and define a maximum distance separable poset block code (MDS (P, pi)-code) as a code meeting this bound. We extend the concept of I-balls to poset block metric and describe r-perfect and MDS (P, pi)-codes in terms of I-perfect codes. As a special case when all the blocks have the same dimension, we establish that MDS (P, pi)-codes are same as I-perfect codes for I is an element of In-k/m (P). We show that the duality result also holds for this case. Further, we determine the weight enumerator of an MDS (P, pi)-code. (C) 2019 Elsevier Inc. All rights reserved.

关键词： maximum distance separable code Poset block metric Perfect code

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