Constructing Liberation Codes Using Latin Squares

Abstract

In recent years, multi-erasure correcting coding systems have become more pervasive. RAID6 is an important 2-erasure correcting code specification. But there is no consensus on the best concrete RAID6 coding scheme. Plank developed a brand new class of RAID6 codes called the Liberation codes that achieves good encoding, updating and decoding performance. In this paper, we present a chained decoding algorithm for the Liberation codes. Its performance is comparable with the bit matrix scheduling algorithm developed by Plank, but is more intuitive and reveals the essence better. In the process, we present a new class of Liberation codes called the Latin Liberation codes. These codes are based on column-hamiltonian Latin squares, hence the name. They are superior to the Liberation codes in parameter flexibility and structure flexibility. Finally, we analyze the performance of several XOR-based RAID6 codes and give some suggestion on their application.