On the Maximally Recoverable Property for Multi-Protection Group Codes

In this paper, we study the maximally recoverable (MR) property for multi-protection group (MPG) codes. MPG codes with MR property achieve the best erasure recoverability given configurations, where a configuration represents the structural relationship between data and parity symbols. We present construction and decoding algorithms for MPG codes with MR property. We show that both recoverability and minimum decoding overhead of any MPG code with MR property depend only on the configuration, where decoding overhead is defined as the additional number of symbols to access, in order to decode the lost data symbols.