One of the design objectives in distributed storage system is the minimization of the data traffic during the repair of failed storage nodes. By repairing multiple failures simultaneously and cooperatively rather than successively and independently, further reduction of repair traffic is made possible. A closed-form expression of the optimal tradeoff between the repair traffic and the amount of storage in each node for cooperative repair is given. We show that the points on the tradeoff curve can be achieved by linear cooperative regenerating codes, with an explicit bound on the required finite-field size. The proof relies on a max-flow-min-cut-type theorem from combinatorial optimization for submodular flows. Two families of explicit constructions are given.
Abstract-To provide fault tolerance for cloud storage, recent studies propose to stripe data across multiple cloud vendors. However, if a cloud suffers from a permanent failure and loses all its data, we need to repair the lost data with the help of the other surviving clouds to preserve data redundancy. We present a proxy-based storage system for fault-tolerant multiple-cloud storage called NCCloud, which achieves cost-effective repair for a permanent single-cloud failure. NCCloud is built on top of a network-coding-based storage scheme called the functional minimum-storage regenerating (FMSR) codes, which maintain the same fault tolerance and data redundancy as in traditional erasure codes (e.g., RAID-6), but use less repair traffic and hence incur less monetary cost due to data transfer. One key design feature of our FMSR codes is that we relax the encoding requirement of storage nodes during repair, while preserving the benefits of network coding in repair. We implement a proof-of-concept prototype of NCCloud and deploy it atop both local and commercial clouds. We validate that FMSR codes provide significant monetary cost savings in repair over RAID-6 codes, while having comparable response time performance in normal cloud storage operations such as upload/download.
Purpose: Due to the low contrast, blurry boundaries, and large amount of shadows in breast ultrasound (BUS) images, automatic tumor segmentation remains a challenging task. Deep learning provides a solution to this problem, since it can effectively extract representative features from lesions and the background in BUS images. Methods: A novel automatic tumor segmentation method is proposed by combining a dilated fully convolutional network (DFCN) with a phase-based active contour (PBAC) model. The DFCN is an improved fully convolutional neural network with dilated convolution in deeper layers, fewer parameters, and batch normalization techniques; and has a large receptive field that can separate tumors from background. The predictions made by the DFCN are relatively rough due to blurry boundaries and variations in tumor sizes; thus, the PBAC model, which adds both region-based and phase-based energy functions, is applied to further improve segmentation results. The DFCN model is trained and tested in dataset 1 which contains 570 BUS images from 89 patients. In dataset 2, a 10-fold support vector machine (SVM) classifier is employed to verify the diagnostic ability using 460 features extracted from the segmentation results of the proposed method. Results: Advantages of the present method were compared with three state-of-the-art networks; the FCN-8s, U-net, and dilated residual network (DRN). Experimental results from 170 BUS images show that the proposed method had a Dice Similarity coefficient of 88.97 AE 10.01%, a Hausdorff distance (HD) of 35.54 AE 29.70 pixels, and a mean absolute deviation (MAD) of 7.67 AE 6.67 pixels, which showed the best segmentation performance. In dataset 2, the area under curve (AUC) of the 10-fold SVM classifier was 0.795 which is similar to the classification using the manual segmentation results. Conclusions: The proposed automatic method may be sufficiently accurate, robust, and efficient for medical ultrasound applications.
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 crossrack 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 crossrack 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.
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