Scaled Nested Key Equation Solver for Generalized Integrated Interleaved Decoder

Generalized integrated interleaved (GII) codes nest short Reed-Solomon or BCH sub-codewords to form codewords of higher error-correction capability. They enable hyper-speed decoding and efficient failure recovery in distributed storage. Although the nested decoding can continue from the key equation solver (KES) result of the sub-codeword decoding, its discrepancy coefficient computation leads to long critical path. A recent nested KES architecture reduced the critical path to the same as that of the KES for sub-codeword decoding. Nevertheless, the nested KES has large area. This brief proposes a novel scaled nested KES algorithm and architecture to reduce the area requirement. Scaled versions of the polynomials are utilized to enable the sharing of product terms and the nested KES algorithm is reformulated to efficiently incorporate the scaling without changing the decoding output. As a result, the number of expensive finite field multipliers is significantly reduced. For an example code over
$GF(2^{8})$
that corrects up to 28 errors, from architectural analysis, the proposed architecture achieves 17% area reduction with only one more gate in the critical path.