Reliability Analysis for Full-2 Code

Recently, with the fast development of storage system, 2-erasure coding schemes were widely used in industrial society. To meet different requirements, many kinds of 2-erasure coding schemes were presented, such as Reed-Solomon codes, binary linear codes, parity array codes, and so on. Full-2 code is a 2-erasure binary linear code. It is a non-MDS code, but achieves optimal encoding, decoding, and updating performance. Moreover, its fault tolerance is beyond 2, i.e. ¿2-erasure¿ is the huge undervaluation of its fault tolerance. It is hard to evaluate the precise reliability of full-2 code. The reason is that the reliability model is complex and the proportion of recoverable k-erasures (k > 2) to total k-erasures is difficult to calculate. In this paper, we present a combinatorial method to analyze the precise reliability of full-2 code. The reliability of full-2 based storage systems is also evaluated.