We study the optimal design of heterogeneous Coded Elastic Computing (CEC) where machines have varying computation speeds and storage. CEC introduced by Yang et al. in 2018 is a framework that mitigates impact elastic events, can join leave at arbitrary times. In CEC, data distributed among using Maximum Distance Separable (MDS) code such subsets perform desired computations. However, state-of-...

The excellent reliability provided by RAID Level 5 data organization has been seen to be insuucient for future mass storage systems. We analyze the multi-dimensional disk array in search of the necessary improved reliability. The paper begins by introducing multi-dimensional disk array data organization schemes based on maximum distance separable error correcting codes and incorporating both st...

Diffusion layers are critical components of symmetric ciphers. MDS matrices are diffusion layers of maximal branch number which have been used in various symmetric ciphers. In this article, we examine decomposition of cyclic matrices from mathematical viewpoint and based on that, we present new cyclic MDS matrices. From the aspect of implementation, the proposed matrices have lower implementati...

In this paper we consider the fundamental question of optimizing finite field multiplications with one fixed element. Surprisingly, this question did not receive much attention previously. We investigate which field representation, that is which choice of basis, allows for an optimal implementation. Here, the efficiency of the multiplication is measured in terms of the number of XOR operations ...

Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy but also achieve 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 suff...

Locally repairable codes, or locally recoverable codes (LRC for short) are designed application in distributed and cloud storage systems. Similar to the classical block there is an important bound called Singleton-type codes. In this paper, optimal code refers a achieving bound. Like MDS (maximum distance separable) have some very nice combinatorial structures. Since introduction of people put ...

Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.

Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made two-layer encoding scheme which concatenates an outer maximum-distanceseparable (MDS) code and an inner repetition code. In this paper, we generalize the applicatio...

Efficient Soft Decoding Techniques for Reed-Solomon Codes Farnaz Shayegh, PhD. Concordia University, 2010 The main focus of this thesis is on finding efficient decoding methods for ReedSolomon (RS) codes, i.e., algorithms with acceptable performance and affordable complexity. Three classes of decoders are considered including sphere decoding, belief propagation decoding and interpolation-based ...