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Blaum–Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring F 2 [ x ] / (M p (x)) , where M p (x) = 1 + x + ⋯ + x p − 1 , and p is a prime number. Two existing all-erasure decoding methods for Blaum–Roth codes are the syndrome-based decoding method and the interpolation-based decoding method. In this paper, we propose a modified syndrome-based decoding method and a modified interpolation-based decoding method that have lower decoding complexity than the syndrome-based decoding method and the interpolation-based decoding method, respectively. Moreover, we present a fast decoding method for Blaum–Roth codes based on the LU decomposition of the Vandermonde matrix that has a lower decoding complexity than the two modified decoding methods for most of the parameters. [ABSTRACT FROM AUTHOR]

In this paper, we consider the update bandwidth in distributed storage systems (DSSs). The update bandwidth, which measures the transmission efficiency of the update process in DSSs, is defined as the average amount of data symbols transferred in the network when the data symbols stored in a node are updated. This paper contains the following contributions. First, we establish the closed-form expression of the minimum update bandwidth attainable by irregular array codes. Second, after defining a class of irregular array codes, called Minimum Update Bandwidth (MUB) codes, which achieve the minimum update bandwidth of irregular array codes, we determine the smallest code redundancy attainable by MUB codes. Third, the code parameters, with which the minimum code redundancy of irregular array codes and the smallest code redundancy of MUB codes can be equal, are identified, which allows us to define MR-MUB codes as a class of irregular array codes that simultaneously achieve the minimum code redundancy and the minimum update bandwidth. Fourth, we introduce explicit code constructions of MR-MUB codes and MUB codes with the smallest code redundancy. Fifth, we establish a lower bound of the update complexity of MR-MUB codes, which can be used to prove that the minimum update complexity of irregular array codes may not be achieved by MR-MUB codes. Last, we construct a class of $(n = k + 2, k)$ vertical maximum-distance separable (MDS) array codes that can achieve all of the minimum code redundancy, the minimum update bandwidth and the optimal repair bandwidth of irregular array codes. [ABSTRACT FROM AUTHOR]

An $m\times (k+r)$ binary maximum distance separable (MDS) array code contains $k$ information columns and $r$ parity columns with each entry being a bit, where any $k$ out of $k+r$ columns can recover the $k$ information columns. When there is a failed column, it is critical to minimize the repair bandwidth that is the total number of bits downloaded from $d$ out of $k+r-1$ surviving columns in repairing the failed column. In this article, we first propose two explicit constructions of binary MDS array codes that have asymptotically optimal repair bandwidth for any information column, where $r\geq 2$ and $d=k+r-1$ for the first construction, and $r\geq 4$ is an even number and $d=k+\frac {r}{2}-1$ for the second construction. By applying a generic transformation for the proposed two classes of binary MDS array codes, we then obtain two classes of new binary MDS array codes that also have optimal repair bandwidth for any parity column and asymptotically optimal repair bandwidth for any information column. [ABSTRACT FROM AUTHOR]

Zigzag-decodable codes have been proposed for distributed storage systems to achieve fast decoding of uncoded data packets through the iterative decoding of data bits from coded packets. To maintain high data availability, it is critical to minimize the repair bandwidth by downloading the least amount of bits for repairing any lost packet. In this work, we propose zigzag-decodable reconstruction (ZDR) codes which achieve asymptotically minimum repair bandwidth for repairing a single node, while preserving the high computational efficiency due to zigzag decoding. We present two explicit constructions of ZDR codes such that any node of ZDR codes can be repaired with asymptotically minimum repair bandwidth. The first construction is based on the well-designed encoding matrix and a generic transformation, while the second construction is designed by recursively employing the proposed generic transformation for any existing zigzag-decodable code. Moreover, we show that the proposed two classes of ZDR codes can be decoded by the zigzag decoding algorithm and have less computational complexity than the existing codes with asymptotically or exactly minimum repair bandwidth. [ABSTRACT FROM AUTHOR]

Consider a binary maximum distance separable (MDS) array code composed of an $m\times (k+r)$ array of bits with $k$ information columns and $r$ parity columns, such that any $k$ out of $k+r$ columns suffice to reconstruct the $k$ information columns. Our goal is to provide optimal repair access for binary MDS array codes, meaning that the bandwidth triggered to repair any single failed information or parity column is minimized. In this paper, we propose a generic transformation framework for binary MDS array codes, using EVENODD codes as a motivating example, to support optimal repair access for $k+1\le d \le k+r-1$ , where $d$ denotes the number of non-failed columns that are connected for repair; note that when $d< k+r-1$ , some of the chosen $d$ columns in repairing a failed column are specific. In addition, we show how our transformation framework applies to an example of binary MDS array codes with asymptotically optimal repair access of any single information column and enables asymptotically or exactly optimal repair access for any column. Furthermore, we present a new transformation for EVENODD codes with two parity columns such that the existing efficient repair property of any information column is preserved and the repair access of parity column is optimal. [ABSTRACT FROM AUTHOR]

Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provides fault tolerance with minimum storage redundancy but also achieves low computational complexity. They are constructed by encoding $k$ information columns into $r$ parity columns, in which each element in a column is a bit, such that any $k$ out of the $k+r$ columns suffice to recover all information bits. In addition to providing fault tolerance, it is critical to improve repair performance in practical applications. Specifically, if a single column fails, then our goal is to minimize the repair bandwidth by downloading the least amount of bits from $d$ healthy columns, where $k\leq d\leq k+r-1$. If one column of an MDS code is failed, it is known that we need to download at least $1/(d-k+1)$ fraction of the data stored in each of the $d$ healthy columns. If this lower bound is achieved for the repair of the failure column from accessing arbitrary $d$ healthy columns, we say that the MDS code has optimal repair. However, if such lower bound is only achieved by $d$ specific healthy columns, then we say the MDS code has weak-optimal repair. In this paper, we propose two explicit constructions of binary MDS array codes with more parity columns (i.e., $r\geq 3$) that achieve asymptotically weak-optimal repair, where $k+1\leq d\leq k+\lfloor (r-1)/2\rfloor $ , and “asymptotic” means that the repair bandwidth achieves the minimum value asymptotically in $d$. Codes in the first construction have odd number of parity columns and asymptotically weak-optimal repair for anyone information failure, while codes in the second construction have even number of parity columns and asymptotically weak-optimal repair for any one column failure. [ABSTRACT FROM AUTHOR]

Erasure coding is widely used for massive storage in data centers to achieve high fault tolerance and low storage redundancy. Since the cross-rack communication cost is often high, it is critical to design erasure codes that minimize the cross-rack repair bandwidth during failure repair. In this paper, we analyze the optimal trade-off between storage redundancy and cross-rack repair bandwidth specifically for data centers, subject to the condition that the original data can be reconstructed from a sufficient number of any non-failed nodes. We characterize the optimal trade-off curve under functional repair, and propose a general family of erasure codes called rack-aware regenerating codes (RRC), which achieve the optimal trade-off. We further propose exact repair constructions of RRC that have minimum storage redundancy and minimum cross-rack repair bandwidth, respectively. We show that (i) the minimum storage redundancy constructions support a wide range of parameters and have cross-rack repair bandwidth that is strictly less than that of the classical minimum storage regenerating codes in most cases, and (ii) the minimum cross-rack repair bandwidth constructions support all the parameters and have less cross-rack repair bandwidth than that of the minimum bandwidth regenerating codes for almost all of the parameters. [ABSTRACT FROM AUTHOR]

Abstract In this work, we study unmanned aerial vehicle (UAV) relaying networks with multi-hop, where one source communicates with one destination through the help of L relay hops. Cache is employed at the relay nodes nearby the destination. Then the destination can acquire the data directly through the cache instead of communicating with the source. For the multi-hop relaying networks with cache, we not only analyze the transmission performance of the considered system by deriving the analytical expressions for the outage probability as well as symbol error rate (SER), but also provide the asymptotic outage probability and SER, in the large region of transmit power. The proposed caching method is proved by simulation and numerical results, and validates that the usage of cache can provide ultra-reliable and low-latency communications for UAV systems. [ABSTRACT FROM AUTHOR]

Array codes are used widely in data storage systems such as redundant array of independent disks. The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. The increasing capacity of hard disks demands better fault tolerance by using array codes with three or more parity disks. Although many extensions of RDP and EVENODD codes have been proposed, their main drawback is high decoding complexity. In this paper, we propose a unified form of RDP and EVENODD codes under which RDP codes can be treated as shortened EVENODD codes. Moreover, an efficient decoding algorithm based on an LU factorization of a Vandermonde matrix is proposed. The LU decoding method is applicable to all the erasure patterns of RDP and EVENODD codes with three parity columns. It is also applicable to the erasure decoding of RDP and EVENODD codes with more than three parity columns when the number of continuous surviving parity columns is no less than the number of erased information columns and the first parity column has not failed. The proposed efficient decoding algorithm is also applicable to other Vandermonde array codes, with less decoding complexity than that of the existing method. [ABSTRACT FROM AUTHOR]

In this paper, we study the delay-constrained input-queued switch, where each packet has a deadline and it will expire if it is not delivered before its deadline. Such new scenario is motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems. The delay-constrained input-queued switch is completely different from the well-understood delay-unconstrained one and thus poses new challenges. We focus on three fundamental problems centering around the performance metric oftimely throughput: (i) how to characterize the capacity region? (ii) how to design a feasibility/throughput-optimal scheduling policy? and (iii) how to design a network-utility-maximization scheduling policy? We use three different approaches to solve these three fundamental problems. The first approach is based on Markov Decision Process (MDP) theory, which can solve all three problems. However, it suffers from the curse of dimensionality. The second approach breaks the curse of dimensionality by exploiting the combinatorial features of the problem. It gives a new capacity region characterization with only a polynomial number of linear constraints. The third approach is based on the framework of Lyapunov optimization, where we design a polynomial-time maximum-weight $T$ -disjoint-matching scheduling policy which is proved to be feasibility/throughput-optimal. Our three approaches apply to the frame-synchronized traffic pattern but our MDP-based approach can be extended to more general traffic patterns. [ABSTRACT FROM AUTHOR]

EVENODD codes are binary array codes for correcting double disk failures in RAID-6 with asymptotically optimal encoding and decoding complexities. However, the update complexity of EVENODD is sub-optimal. We propose a new construction of binary maximum distance separable array codes, namely EVENODD+, such that the encoding, decoding, and update complexities of EVENODD+ are less than those of EVENODD in general. Moreover, EVENODD+ achieves asymptotically optimal update complexity. [ABSTRACT FROM AUTHOR]

Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only exclusive OR operations are used in the encoding and decoding processes. Cauchy Reed–Solomon codes, Rabin-like codes, and circulant Cauchy codes are existing Cauchy maximum-distance separable (MDS) array codes that employ Cauchy matrices over finite fields, circular permutation matrices, and circulant Cauchy matrices, respectively. All these codes can correct any number of failures; however, a critical drawback of existing codes is the high decoding complexity. In this paper, we propose a new construction of Rabin-like codes based on a quotient ring with a cyclic structure. The newly constructed Rabin-like codes have more supported parameters (prime $p$ is extended to an odd number), such that the world sizes of them are more flexible than the existing Cauchy MDS array codes. An efficient decoding method using LU factorization of the Cauchy matrix can be applied to the newly constructed Rabin-like codes. It is shown that the decoding complexity of the proposed approach is less than that of existing Cauchy MDS array codes. Hence, the Rabin-like codes based on the new construction are attractive to distributed storage systems. [ABSTRACT FROM PUBLISHER]

Measurement traces from real-world production environment show that the execution time of tasks within a MapReduce job varies widely due to the variability in machine service capacity. This variability issue makes efficient job scheduling over large-scale MapReduce clusters extremely challenging. To tackle this problem, we adopt the task cloning approach to mitigate the effect of machine variability and design corresponding scheduling algorithms so as to minimize the overall job flowtime in different scenarios. For offline scheduling where all jobs arrive at the same time, we design an $O(1)$ -competitive algorithm, which gives priorities to jobs with small effective workload. We then extend this offline algorithm to yield the so-called Smallest Remaining Effective Workload based \beta$ -fraction Sharing plus Cloning algorithm (SREW+C(\beta$ )) for the online case. We also show that SREW+C(\beta$ ) is (1+ 2\beta + \epsilon) -competitive with respect to the sum of job flowtime within a cluster. We demonstrate via trace-driven simulations that SREW+C( $\beta$ ) can significantly reduce the overall job flowtime by cutting down the elapsed time of small jobs substantially. In particular, SREW+C($\beta$ ) reduces the total job flowtime by 14, 10 and 11 percent respectively when comparing to Mantri, Dolly and Grass. [ABSTRACT FROM PUBLISHER]

In distributed storage systems, regenerating codes can achieve the optimal tradeoff between storage capacity and repair bandwidth. However, a critical drawback of existing regenerating codes, in general, is the high coding and repair complexity, since the coding and repair processes involve expensive multiplication operations in finite field. In this paper, we present a design framework of regenerating codes, which employ binary addition and bitwise cyclic shift as the elemental operations, named BASIC regenerating codes. The proposed BASIC regenerating codes can be regarded as a concatenated code with the outer code being a binary parity-check code, and the inner code being a regenerating code utilizing the binary parity-check code as the alphabet. We show that the proposed functional-repair BASIC regenerating codes can achieve the fundamental tradeoff curve between the storage and repair bandwidth asymptotically of functional-repair regenerating codes with less computational complexity. Furthermore, we demonstrate that the existing exact-repair product-matrix construction of regenerating codes can be modified to exact-repair BASIC product-matrix regenerating codes with much less encoding, repair, and decoding complexity from the theoretical analysis, and with less encoding time, repair time, and decoding time from the implementation results. [ABSTRACT FROM AUTHOR]

Binary maximum distance separable (MDS) array codes are widely used in storage systems. EVENODD code and row-diagonal parity (RDP) code are two well-known binary MDS array codes with two parity columns. The Blaum–Bruck–Vardy (BBV) code is an extension of the double-erasure-correcting EVENODD code. It is known that the BBV code is always MDS for three parity columns, and sufficient conditions for up to eight parity columns to be MDS are also known. However, the MDS condition for more than eight parity columns is an open problem since then. In this letter, we study the MDS condition of BBV code and give a sufficient MDS condition of the BBV code with more than eight parity columns. [ABSTRACT FROM PUBLISHER]

In order to provide fault-tolerance and guarantee reliability, data redundancy should be introduced in distributed storage systems. The emerging coding techniques for storage such as fractional repetition codes, provide the required redundancy more efficiently than the conventional replication scheme. In this letter, we extend the construction of fractional repetition codes and present a new coding scheme, termed general fractional repetition codes. The proposed codes can be applied to storage systems in which the storage capacities of nodes may be different. Based on a combinatorial structure known as group divisible design, the new code construction is available for a large set of parameters. The performance of the proposed codes is evaluated by a metric called node repair alternativity, which measures the number of different subsets of nodes that enable the repair of a specific failed node. [ABSTRACT FROM PUBLISHER]

Aim: Lung adenocarcinoma (LUAD) and lung squamous-cell carcinoma (LUSC) are two major subtypes of lung cancer and constitute about 70% of all the lung cancer cases. The patient's lifespan and living quality will be significantly improved if they are diagnosed at an early stage and adequately treated., Methods & Results: This study comprehensively screened the proteomic dataset of both LUAD and LUSC, and proposed classification models for the progression stages of LUAD and LUSC with accuracies 86.51 and 89.47%, respectively., Discussion & Conclusion: A comparative analysis was also carried out on related transcriptomic datasets, which indicates that the proposed biomarkers provide discerning power for accurate stage prediction, and will be improved when larger-scale proteomic quantitative technologies become available.