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Nonbinary low-density parity-check (NB-LDPC) codes constructed over GF(q) (q >; 2) can achieve higher coding gain than binary LDPC codes when the code length is moderate. A complete partial-parallel decoder architecture based on the Min-max algorithm is proposed for quasi-cyclic NB-LDPC codes in this paper. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm <; q messages are kept on each edge of the associated Tanner graph. The computation units and the scheduling of the computations are optimized in the context of layered decoding to reduce the area requirement and increase the speed. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity and latency analysis, our design is much more efficient than any previous design. Our proposed decoder for a (744, 653) code over GF(25) has also been synthesized on a Xilinx Virtex-2 Pro FPGA device. It can achieve a throughput of 9.30 Mbps when 15 decoding iterations are carried out.