Generalized Integrated Interleaving Codes

Tang and Koetter proposed generalized integrated interleaving Reed-Solomon codes in which each code of the second layer belongs to different subcode of the first layer code, based on the rationale that the strongest code is used to correct the most corrupted component word while the weakest code corrects the least corrupted component word. The authors also presented a decoding algorithm which is sophisticated due to handling miscorrection of the interleave self-decoding, and cumbersome due to large amount of repetitive operations. In this paper, we first demonstrate that it is essential to neglect the first layer miscorrection for their practical applications. We then devise an efficient decoding algorithm by ignoring the first layer miscorrection and by intelligently reusing preceding results during each iteration of decoding attempt. Neglecting the first-layer miscorrection also enables to explicitly and neatly formulate the decoding failure probability. We further construct an efficient systematic encoding algorithm, which had been open. We also propose a novel generalized integrated interleaving scheme for binary BCH codes, prove a lower bound on the minimum distance, and derive a similar encoding and decoding algorithm as that of Reed-Solomon codes.