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Reed-Solomon (RS) codes can be found in many digital communication and storage systems. Recently, significant advancements have been made on algebraic soft-decision decoding (ASD) of RS codes. Among the ASD algorithms with practical multiplicity assignment scheme, the bit-level generalized minimum distance (BGMD) decoding algorithm can achieve similar or higher coding gain with lower complexity. Interpolation is one of the major steps in ASD algorithms. The newly proposed Lee-O'Sullivan (LO) interpolation algorithm is computationally simple, and thus can potentially lead to practical high-speed and small-area hardware implementation of the interpolation step. In this paper, a novel interpolation architecture for the BGMD decoder based on the LO algorithm is proposed. By exploiting the characteristics of the LO algorithm and the multiplicity assignment scheme in the BGMD decoder, the proposed interpolation architecture for a (255, 239) RS code can achieve 15% higher efficiency in terms of speed over area ratio than prior efforts.