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Reed-Solomon (RS) codes have very broad applications in digital communication and storage systems. The developed algebraic soft-decision decoding (ASD) algorithms of RS codes can achieve substantial coding gain with polynomial complexity. Among the ASD algorithms with practical multiplicity assignment schemes, the bit-level generalized minimum distance (BGMD) decoding algorithm can achieve similar or higher coding gain with lower complexity. ASD algorithms consist of two major steps: the interpolation and the factorization. In this paper, novel architectures for both steps are proposed for the BGMD decoder. The interpolation architecture is based on the newly proposed Lee-O'Sullivan (LO) algorithm. 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 25% higher efficiency in terms of speed/area ratio than prior efforts. Root computation over finite fields and polynomial updating are the two main steps of the factorization. A low-latency and prediction-free scheme is introduced in this paper for the root computation in the BGMD decoder. In addition, novel coefficient storage schemes and parallel processing architectures are developed to reduce the latency of the polynomial updating. The proposed factorization architecture is 126% more efficient than the previous direct root computation factorization architecture.