Modified GII-BCH Codes for Low-Complexity and Low-Latency Encoders

Abstract

Generalized integrated interleaved Bose–Chaudhuri–Hocquenghem (GII-BCH) codes show great potentials in some storage applications, such as flash memory programming, since they need less redundancy than the simple interleaved BCH codes for a target reliability. The coefficient vectors that are precomputed from the conversion matrix play a very important role in the GII-BCH encoding and also characterize its hardware architecture. However, they require a large amount of computations, including matrix inversions and multiplications both modulo polynomials. In addition, the GII-BCH encoders also suffer from high complexity and latency. In this letter, we modify the original conversion matrix and directly obtain the coefficient vectors without sacrificing error-correction performance. The modified coefficient vectors are much simpler than the original ones due to their independence on the error-correction capabilities. Furthermore, encoder architectures for the original and the modified GII-BCH codes are developed and compared. It is shown that the encoders for the modified GII-BCH codes perform significantly better than those for the original ones in both hardware complexity and latency.