Quasi-cyclic Minimum Storage Regenerating Codes for Distributed Data Compression

Nowadays, it is possible to optimize the storage size of large files in distributed environments, maintaining the same availability level in the system. Although replication (backups) is the most used option, it is possible to make use of erasure coding in order to significantly compress the storage size [1]. However, using erasure coding, more information needs to be transmitted than when using replication, in order to replace a node which has failed. This is called the code repair problem. The amount of transmitted information can be an important issue when the file size is very large. If network coding is used in conjunction with erasure codes, the transmitted information can be reduced by compressing the sent data in the regeneration phase. This solution minimizes the code repair problem and consists of the use of regenerating codes introduced by Dimakis et al. [2]. Nevertheless, using network coding, computational resources for any node in the system are required, since linear operations must be carried out and systems of equations must be solved in the nodes. This requirement is too strong for many simple storage devices [3]. In this paper a new family of Minimum Storage Regenerating codes is proposed. These codes not only compress the storage size using erasure coding and achieve optimality for the amount of transmitted information when d = k + 1, but also demand few computational requirements. Therefore, they could be used for simple hard discs without computational resources.