In this paper, the maximal length of maximal distance separable (MDS) codes is studied, and a new upper bound formula of the maximal length of MDS codes is obtained. Especially, the exact values of the maximal length ...In this paper, the maximal length of maximal distance separable (MDS) codes is studied, and a new upper bound formula of the maximal length of MDS codes is obtained. Especially, the exact values of the maximal length of MDS codes in some parameters are given.展开更多
Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>...Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).展开更多
It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundan...It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability. Under this criterion, an maximum distance separable（MDS） code has optimal redundancy. In this paper, we address a new class of MDS array codes for tolerating triple node failures by extending the row di- agonal parity（RDP） code, named the RDDP（row double diagonal parity） code. The RDDP code takes advantages of good perform- ances of the RDP code with balanced I/0. A specific triple-erasure decoding algorithm to reduce decoding complexity is depicted by geometric graph, and it is easily implemented by software and hardware. The theoretical analysis shows that the comprehensive properties of the RDDP code are optimal, such as encoding and decoding efficiency, update efficiency and I/0 balance performance.展开更多
This paper presents a novel method, called TSHOVER, for tolerating up to triple disk failures in RAID/DRAID architectures or others reliable storage systems. TSHOVER is two-dimensional code, which employs horizontal c...This paper presents a novel method, called TSHOVER, for tolerating up to triple disk failures in RAID/DRAID architectures or others reliable storage systems. TSHOVER is two-dimensional code, which employs horizontal code and vertical code at the same time with simple exclusive-OR (XOR) computations. This paper shows the new step ascending concepts used in encoding, and it has the capability of realizing fault tolerance. TSHOVER has better data recovery ability to those disk network storage systems with relatively more dynamic changes in the number of disks. Compared with RS and STAR code, TSHOVER has better encoding performance. When updating a data strip, only 6 XOR operations are needed. Both experimental results and theoretical analyses show that TSHOVER has better performance and higher efficiency than other algorithms.展开更多
文摘In this paper, the maximal length of maximal distance separable (MDS) codes is studied, and a new upper bound formula of the maximal length of MDS codes is obtained. Especially, the exact values of the maximal length of MDS codes in some parameters are given.
文摘Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).
基金Supported by the National Natural Science Foundation of China(60873216)the Key Project of Sichuan Provincial Department of Education(12ZA223)
文摘It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability. Under this criterion, an maximum distance separable（MDS） code has optimal redundancy. In this paper, we address a new class of MDS array codes for tolerating triple node failures by extending the row di- agonal parity（RDP） code, named the RDDP（row double diagonal parity） code. The RDDP code takes advantages of good perform- ances of the RDP code with balanced I/0. A specific triple-erasure decoding algorithm to reduce decoding complexity is depicted by geometric graph, and it is easily implemented by software and hardware. The theoretical analysis shows that the comprehensive properties of the RDDP code are optimal, such as encoding and decoding efficiency, update efficiency and I/0 balance performance.
基金the National Natural Science Foundation of China (No. 60403043)
文摘This paper presents a novel method, called TSHOVER, for tolerating up to triple disk failures in RAID/DRAID architectures or others reliable storage systems. TSHOVER is two-dimensional code, which employs horizontal code and vertical code at the same time with simple exclusive-OR (XOR) computations. This paper shows the new step ascending concepts used in encoding, and it has the capability of realizing fault tolerance. TSHOVER has better data recovery ability to those disk network storage systems with relatively more dynamic changes in the number of disks. Compared with RS and STAR code, TSHOVER has better encoding performance. When updating a data strip, only 6 XOR operations are needed. Both experimental results and theoretical analyses show that TSHOVER has better performance and higher efficiency than other algorithms.
