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Designers are increasingly relying on field-programmable gate array (FPGA)-based emulation to evaluate the performance of low-density parity-check (LDPC) codes empirically down to bit-error rates of 10-12 and below. This requires decoding architectures that can take advantage of the unique characteristics of a modern FPGA to maximize the decoding throughput. This paper presents two specific optimizations called vectorization and folding to take advantage of the configurable data-width and depth of embedded memory in an FPGA to improve the throughput of a decoder for quasi-cyclic LDPC codes. With folding it is shown that quasi-cyclic LDPC codes with a very large number of circulants can be implemented on FPGAs with a small number of embedded memory blocks. A synthesis tool called QCSyn is described, which takes the H matrix of a quasi-cyclic LDPC code and the resource characteristics of an FPGA and automatically synthesizes a vector or folded architecture that maximizes the decoding throughput for the code on the given FPGA by selecting the appropriate degree of folding and/or vectorization. This helps not only in reducing the design time to create a decoder but also in quickly retargeting the implementation to a different (perhaps new) FPGA or a different emulation board.