Abstract
Distributed storage systems are composed by many unreliable storage nodes over a network. A data file is redundantly stored in multiple storage nodes to provide high reliability. Recently erasure codes with Maximum Distance Separable (MDS) property are gradually employed in distributed storage systems to reduce the cost of reliably storing large amounts of data. Regenerating codes are a class of erasure codes which can achieve the optimal trade-off between the storage capacity and the bandwidth needed to repair a failed node. However, one of the critical drawbacks of existing MDS erasure codes in general is the high coding and repair complexities, since the coding and repair processes involve expensive multiplication operations in a finite field. Binary Addition and Shift Implementable Cyclic-convolutional (BASIC) codes, which is a coding framework of linear codes with a binary cyclic code as the alphabet, were proposed recently with lower computational complexity by replacing a finite field multiplication by a cyclic-shift operation. This paper provides an overview of the existing results of BASIC codes, and proposes several interesting open problems about BASIC codes.
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