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Reed-Solomon (RS) codes are one of the most extensively used error control codes in digital communication and storage systems. Recently, significant advancements have been made on algebraic soft-decision decoding (ASD) of RS codes. These algorithms can achieve substantial coding gain with polynomial complexity. One major step of ASD is the interpolation. Various techniques have been proposed to reduce the complexity of this step. Further speedup of this step is limited by the inherent serial nature of the interpolation algorithm. In this paper, taking the bit-level generalized minimum distance (BGMD) ASD as an example, we propose a novel technique to combine the computations from multiple interpolation iterations. Compared to the single interpolation iteration architecture for a (255, 239) RS code, the combined architecture can achieve 2.7 times throughput with only 2% area overhead in high signal-to-noise ratio scenarios.