Quasi-cyclic Minimum Bandwidth Regenerating Codes

In a distributed storage environment the data file is not placed in just one but in more than one devices which are connected through a network. There are many examples such as RAID systems and Internet storage applications. When data needs to be stored, there is usually one issue it needs to be faced: the availability of such data. Basically, this data needs to be persistent over time and resistant against failures in the storage devices. The solution to the availability problem consists of adding redundancy, but it is possible to add redundancy by using different schemes. The most trivial and common one is the replication scheme (data backups). It is also possible to use classical erasure coding to minimize the amount of stored data in a distributed environment [9]. However, the use of an erasure coding scheme introduces what it is known as the code repair problem and which is related to the amount of downloaded data (bandwidth) needed to replace a failed node. Regenerating codes were introduced in [2] to minimize the code repair problem. The main idea is to make the most of both erasure coding [4] and network coding [1], to minimize the amount of stored data and the bandwidth used, respectively. Although regenerating codes are an excellent solution for both problems, they have a drawback inherited from the use of network coding, since nodes must be able to do linear combinations over a finite field. This operation has a complexity of O(n) and forces nodes to be provided with computational resources. In this paper, we present a new family of Minimum Bandwidth Regenerating codes which do not need any computational resources and which are based on quasi-cyclic codes.