Pre-calculated Equation-based Decoding in Failure-tolerant Distributed Storage

Data distribution together with erasure-tolerant codes allow to store data reliably, even with failed or temporarily disconnected storage resources. The encoding algorithm, i.e. the calculation of the codewords is expressed by XOR equations. Even decoding is the execution of a failurespecific set of equations that are build code-specifically and with knowledge of the failure situation. A new concept for a storage system is to provide encoding equations and decoding equations in advance, as a full description of the code which eliminates the calculations to obtain therecovery strategy. This concept includes that also decoding equations have to be provided in advance, for many different failure situations. This results in a large number of equations and may require a considerable amount of memory, but still a moderate amount - which can be traded for the gained flexibility and simplicity. In this paper we analyze the storage consumption of such a preprocessed decoding equation set. Furthermore, a data structure to access the required equations is proposed. It is shown that codes can be translated into equation sets that are used as parameter set by a storage system.