Abstract
Generalized integrated interleaved (GII) codes nest sub-codewords, also called interleaves, to generate parities shared by the interleaves. They achieve better tradeoffs compared to other locally recoverable erasure codes and are good candidates for hyper-speed data storage and communications. By nesting the interleaves in a hierarchical manner, the recent three-layer GII codes further improve the decoding locality. However, due to the fundamentally different structure and larger size of the nesting matrix, three-layer GII decoding faces many issues that do not exist previously. In this paper, constraints on the relative correction capabilities of the nested codes are defined to achieve the target correction goal. The bottleneck on syndrome conversion matrix inversion is eliminated by transforming the conversion matrices and syndrome vectors. The overall decoding process is optimized to increase correction capability and reduce complexity.
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