Efficient Sub-Codeword Key Equation Solver for Generalized Integrated Interleaved BCH Decoder

Abstract

Generalized integrated interleaved (GII) error-correcting codes nest sub-codewords to form codewords of more powerful codes. They can achieve hyper-speed decoding with good error correction capability. For GII codes built on BCH codes, the first decoding stage is to decode individual BCH sub-words. This stage largely determines the throughput and dominates the area of the overall decoder. Unlike that in traditional BCH decoding, longer polynomials need to be kept in the key-equation solver (KES) step of the first stage in order to continue the KES step in the second-stage nested decoding of GII codes. To take advantage of the very fast storage class memories (SCMs), GII codes with 3-error-correcting BCH sub-codewords can be utilized. This brief proposes a low-complexity and high-speed design for the KES of 3-error-correcting BCH sub-word decoding. Formulas are developed to compute the KES results directly instead of utilizing the traditional iterative process. More importantly, through analyzing the properties of the involved variables, the coefficients are scaled and reformulated to substantially reduce the complexity. Detailed hardware implementation architectures are also developed in this brief. Our design achieves three times throughput with 20.2% smaller area than the best prior design for a code over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$GF(2^{10})$ </tex-math></inline-formula> .