Row-Diagonal-Parity (RDP) codes and EVENODD codes are classical systematic array codes and most attention in the literature has been on the generalization of RDP codes. In this work, as generalization of not only RDP codes but also EVENODD codes, we present new construction of$\phi (L)$-dimensional$(k+r, k)$systematic array codes with$r \leq 4$, where L is an odd integer and$\phi (L)$represents the Euler’s totient function of L. We explicitly characterize sufficient conditions on the selection of L to make the codes maximum distance separable (MDS). Compared with EVENODD codes and RDP codes, the largest k that can be supported by the new codes is nearly doubled, and the asymptotic encoding complexity of the new codes is same, that is, asymptotically approaches r XORs per original data bit with increasing L and k. Moreover, for prime L,$r = 2$and$k = 2L-3$, the new code exactly achieves the optimal encoding complexity. For the case$r = 4$, the largest k that can be supported by the new codes is larger than the recently proposed so-called Variants of Extended Shortened Independent-Parity (V-ESIP) systematic array code in a number of code dimension selections, and meanwhile, the obtained explicit conditions on L to guarantee the MDS property of the new codes also apply to classical EVENODD codes and RDP codes, but are more general than well known explicit ones in the literature. The decoding process of the new array codes is also discussed. In particular, the$r\times r$block inverse matrix involved in decoding is explicitly characterized, which applies to all MDS array codes generalized from RDP or EVENODD codes in the literature.

MDS array codes have been extensively studied due to their applications in storage systems. In this paper, we first propose a novel method of constructing MDS array codes by deleting one row and one column from the circulant matrices associated to some polynomials. Several new classes of MDS array codes with flexible parameters are constructed. In particular, we give a new algebraic presentation of the Blaum-Roth codes with sparser parity-check matrices. We also obtain a family of MDS array codes over finite fields with even characteristics whose parity-check matrices have the lowest density. Furthermore, based on these new MDS array codes, we give a general construction of optimal locally repairable array codes (LRACs) achieving the Singleton-type bound. Additionally, we obtain some new optimal LRACs of long lengths. Finally, we present a scheduled algorithm for syndrome computations of binary optimal LRACs with redundancy 4, which can tolerate three failures. The number of XORs per data bit required in our algorithm approaches 2 as the length approaches infinity, which is the same as the MDS codes tolerating three failures. However, the number of nodes required during the repair of a failed node in our optimal LRACs is only about half of that in MDS array codes.

In this short paper, we will provide a new explicit construction of binary MDS array codes with triple parities from their parity-check matrices, which contains array codes with array number 8 (8 bits=1 byte). In addition, to demonstrate the applicability of our MDS array codes, we present an effective decoding method aimed at the erased errors. Furthermore, a fast encoding algorithm of our extended MDS array codes is also explored, whose computational complexity is 2 XORs per bit when their code lengths approach infinity.

Given a prime L, we present a new construction of (L−1)-dimensional (k+r,k) systematic array codes with r ≤ 4, and concretely characterize sufficient conditions on the selection of L to guarantee the codes’ MDS property. The largest possible k that can be supported by the new MDS array codes is 2L−4, nearly twice as large as that supported by classical MDS array codes such as EVENODD codes and RDP codes. Moreover, the number of XORs per original data bit required in encoding of the new codes asymptotically approaches r with increasing k and L, same as EVENODD codes and RDP codes. In addition, for the case r = 4, the explicit conditions on L we obtain to guarantee the new codes’ MDS property can also be used to guarantee the MDS property of EVENODD codes and RDP codes, but are more general than the well known ones in the literature.

From the perspective of parity-check matrices, we present new constructions of$q$-ary maximum distance separable (MDS) array codes with multiple parities. Applying these constructions, some new types of MDS array codes with array numbers$m-\tau $can be derived, where${\mathrm{ gcd}}(m,q)=1$. Moreover, an explicit construction of binary MDS array codes is also presented. Compared to the existing MDS array codes, one important characteristic of these codes is that their available code lengths are much longer, which is suitable for large-scale storage systems. In some particular cases, the maximum code lengths of these codes and their extension can be up to$2^{m-\tau }$and$2^{m-\tau }+1$(or$2^{m-\tau }+2$), respectively. Moreover, to demonstrate the applicability of our constructed MDS array codes, we present an effective generic decoding method for the erased errors. In particular, when there are no more than three erasures occurring, a scheduled algorithm for the syndrome computation of our explicit construction is further proposed, whose computational complexity is asymptotically optimal. Furthermore, this algorithm can be directly applied to the encoding procedure of their extended form. The simulation shows that our new MDS array codes have better encoding and decoding performances than the corresponding extended RS codes coupled with different algorithms.

In this paper, we firstly present a new construction of binary maximum distance separable (MDS) array codes, from which some types of new MDS array codes of minimum distance 4 with array dimension (p−1)×(ℓ+2) can be deduced. Based on the construction, binary locally repairable array codes (LRACs) of minimum distance 4 are also explored, whose array dimension is (p−1)×2ℓ and column locality is ℓ − 1. Particularly, when 2 is a primitive root module p, a scheduled algorithm for syndrome computation of the LRACs is proposed, which converges to 2 XORs per data bit when ℓ approaches infinity.

Memory maximum-distance-separable (mMDS) sliding window codes are a type of erasure codes with high erasure-correction capability and low decoding delay. In this paper, we study two types of systematic mMDS sliding window codes over erasure channels, i.e., scalar codes defined over a finite field GF(2L), and vector codes defined over a vector space GF(2)L. We first devise an efficient heuristic algorithm to produce an mMDS sliding window scalar code over relatively small GF(2L). Then, we investigate a special class of mMDS sliding window vector codes whose encoding/decoding are achieved by basic circular-shift and bit-wise XOR operations, and propose a general method to generate such mMDS vector codes. Our complexity analysis shows that the proposed vector codes yield much lower encoding/decoding complexity than the scalar codes. The theoretical and numerical results also demonstrate that mMDS sliding window codes dominate MDS block codes in terms of decoding delay and erasure-correction capability.

The vehicle-to-grid (V2G) technique, which enables the bidirectional power exchange between electric vehicles (EVs) and power grid, becomes promising in current smart grid research. In this paper, a game theoretic model is proposed to study the interaction among EVs in a V2G system with V2G technique incorporated. This V2G game is a game with imperfect information in which each EV does not any private information of other EVs. To find the Nash equilibrium of this game, a machine learning-based algorithm is proposed based on fictitious self-play. Our simulation results show that the proposed algorithm can approximately converge to the Nash equilibrium of the game under imperfect information. This demonstrates the efficacy of the proposed algorithm in solving the V2G game. A pre-training approach is also proposed to accelerate the convergence of the algorithm by using the historical data from the interactions of EVs in the game.

The vehicle-to-grid (V2G) technique, which utilizes electric vehicles (EVs) to provide ancillary services for power grid, becomes promising in current smart grid research. In this paper, a game theoretic approach is proposed to motivate EVs to provide frequency regulation services for power grid. The interaction between the EV aggregator and EVs is formulated as a Stackelberg game. We find that the Stackelberg game admits a unique equilibrium solution, and the existence and uniqueness of the Nash equilibrium are validated. Algorithms have been devised for finding the Nash equilibrium of the game. Our simulation results show that the proposed game theoretic V2G scheduling approach can motivate EVs to schedule their charging/discharging activities so as to smooth out the power fluctuations from the grid while maximizing their own utilities. This demonstrates the effectiveness of the use of the V2G game in providing regulation service to the grid.

In recent years, the vehicle-to-grid (V2G) system, which utilizes electric vehicles (EVs) to provide ancillary services for power grid, draws a lot of interests in smart grid research community. When considering a large number of EVs distributed in different geographical locations, how to coordinate these EVs to provide ancillary services becomes a critical issue. In this paper, a generic hierarchical framework for V2G system to provide frequency regulation services is proposed to address this issue. A practical multi-level online V2G algorithm is proposed for the hierarchical V2G scheduling and it requires no forecasting information for regulation signals.We test our proposed algorithm in the simulation of a four- level hierarchical V2G system. The results show that the proposed algorithm has advantages over the existing methods on smoothing out the real- time power fluctuations.

The renewables will constitute an important part of the future smart grid. As a result, the growing portion of renewable generation in the power grid will bring challenges to the operations of the power grid because of the fluctuation and intermittency properties of renewables. In order to make the operations of power grid stable and reliable, the power outputs from renewable energy sources must be smoothed. In this paper, we propose a scheme inspired from the idea of the leaky bucket mechanism for smoothing the power output from a renewable energy system. In our proposed method, the settings of energy storage size and power output level have significant effects on the system performance and thus needs to be determined. An optimization framework is thus proposed for storage and power output planning of the renewable energy system. To operate our proposed scheme practically, a load-adaptive power smoothing algorithm is devised aiming to match the power output level with the actual load in the grid. Our simulation studies show that the proposed algorithm can reduce the operation cost comparing to other algorithms and maintain high renewable energy utilization.