Generalized Integrated Interleaved Codes
Generalized integrated interleaved codes refer to two-level Reed-Solomon codes such that each code of the nested layer belongs to different subcode of the first layer code. In this paper, we first devise an efficient decoding algorithm by ignoring first-layer miscorrection and by intelligently reusing preceding results during each iteration of a decoding attempt. Neglecting first-layer miscorrection also enables to explicitly and neatly formulate the decoding failure probability. We next derive an erasure correcting algorithm for Redundant Arrays of Independent Disks (RAID) systems. We further construct an algebraic systematic encoding algorithm, which had been open. Analogously, we propose a novel generalized integrated interleaving scheme over binary Bose-Chaudhuri-Hocquenghem (BCH) codes, reveal a lower bound on the minimum distance, and derive a similar encoding and decoding algorithm as those of Reed-Solomon codes.