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A class of quasi-systematic block-circulant LDPC (QSBC-LDPC) Codes is proposed. The parity-check matrix of a QSBC-LDPC code is a sparse block-circulant matrix with a quasi-systematic structure. Due to the special structure of the parity-check matrix, only limited memories, XOR computations and cyclic-shifting operations are needed in the recursive encoding process of the QSBC-LDPC codes. Simulations show that the QSBC-LDPC codes provide remarkable performance improvement with low encoding complexity.