Systematic Encoder of Generalized Three-Layer Integrated Interleaved Codes

To reduce the network traffic overhead and latency associated with failure recovery in distributed storage, it is essential to adopt locally recoverable (LRC) erasure codes. Among available LRC codes, the generalized integrated interleaved (GII) codes that nest individual interleaves to generate shared parities achieve good tradeoffs on locality, redundancy, and complexity. To further improve the locality, a construction of three-layer GII codes has been developed recently. This paper proposes an efficient systematic encoding scheme for three-layer GII codes. Due to the fundamentally different structure in the nesting matrix, the design of three-layer GII encoders face new issues that do not exist in prior two-layer encoders. The parities from both layers of nesting need to be accommodated in the interleaves. The parity allocation and the procedure of the interleave encoding are jointly considered to ensure the generation of target codewords. Additionally, a reduced-complexity implementation architecture of the proposed encoding scheme is presented in this paper.