Erasure codes in large-scale storage systems allow recovery of data from a failed node. A recently developed class of codes, locally repairable codes (LRCs), offers tradeoffs between storage overhead and repair cost. LRCs facilitate efficient recovery scenarios by adding parity blocks to the system. However, these additional blocks may eventually increase the number of blocks that must be reconstructed. Existing LRCs differ in their use of the parity blocks, in their locality semantics, and in their parameter space. Thus, existing theoretical models cannot directly compare different LRCs to determine which code offers the best recovery performance, and at what cost. We perform the first systematic comparison of existing LRC approaches. We analyze Xorbas, Azure’s LRCs, and Optimal-LRCs in light of two new metrics: average degraded read cost and normalized repair cost. We show the tradeoff between these costs and the code’s fault tolerance, and that different approaches offer different choices in this tradeoff. Our experimental evaluation on a Ceph cluster further demonstrates the different effects of realistic system bottlenecks on the benefit from each LRC approach. Despite these differences, the normalized repair cost metric can reliably identify the LRC approach that would achieve the lowest repair cost in each setup.

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Matters concerned with the application of correction devices containing delay elements are addressed. Such filters are proposed as an alternative to the high-pass filters and low-pass first-order filters that are widely used in control systems. It is shown that by using filters containing delay elements, the power of high-frequency interference in the controller output signal can be reduced by up to 30% in comparison with the conventional filters. It should be noted that these results are obtained in using the proposed filters in closed-loop continuous systems. Two filter configuration versions used in control applications were analyzed. In the first version, the filters are connected in series in the control loop (as applied to astatic systems with a proportional-differentiating controller in both linear and relay modes of operation). In the second version, a correction filter connected in the local feedback is used (taking a generalized representation of the instrument-assisted position tracking system as an example). The article proposes a fairly simple method for determining the parameters of filters with a delay element that make it possible to use conventional techniques for synthesizing controllers in the frequency domain and estimating their dynamic properties.

The article addresses the matter of reducing the power of high-frequency noise in the control signal produced by industrial automatic systems through the use of algorithms implementing the properties of comb filters in microprocessor controllers. The specific features relating to the frequency responses of open- and closed-loop automatic control systems of industrial facilities are analyzed - both taken alone and in combination with the characteristics of comb filters. The frequency properties of three filter groups that are conventionally used in continuous automatic control systems are compared with three groups of comb filters that implement similar functions. As applied to control tasks, such filters include real differentiating sections or first-order high-pass filters, first-order lag sections or low-pass filters, and proportional sections. The ratios between the parameters of continuous filters and comb filters at which their frequency properties coincide in the operating frequency band are determined. These ratios known, it becomes possible to synthesize the controllers of systems using the existing techniques. It is shown that the amplitude-frequency responses of comb filters have dips in the high-frequency band, due to which the high frequency noise power is finally decreased by up to 30%. The advantage of comb filters in control systems lies in simplicity of implementing them in digital form in a microprocessor controller. The application of comb filters in automatic control systems makes it possible to cut undesirable harmonic noise of large amplitude in the control signal.