A 124-Gb/s Decoder for Generalized Integrated Interleaved Codes

Generalized integrated interleaved (GII) codes have attracted much attention in distributed storage systems since they can reduce the overall redundancy by creating redundancy shared by the interleaves. The Berlekamp-Massey (BM) algorithm makes the GII decoding efficient by reusing the preceding results at each decoding stage. However, it also forms the speed bottleneck of GII decoders. The reformulated inversionless Berlekamp-Massey (riBM) algorithm is well known for its short critical path, but it is not generally suitable for GII decoding since its polynomials are difficult to be reused directly. In this paper, we address this issue by reinitializing the polynomials and propose a riBM-based GII decoding algorithm. In our simulations, slight performance degradation induced by the first-layer miscorrection is observed in the high signal-to-noise ratio (SNR) region. Hence, a subtle method is introduced to handle the miscorrected interleaves. Furthermore, the hardware architecture of the proposed decoding algorithm is developed and a high throughput decoder for the given example GII code is implemented. The synthesis results under TSMC 28-nm technology show that the decoder can achieve a throughput of up to 124 Gb/s. Moreover, the decoder has been implemented into a field-programmable gate array (FPGA) to validate its error-correction performance.