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Space-time transmit diversity (STTD) and space-time block codes (STBC) are the attractive techniques for high bit-rate and high capacity transmission. Recently, low-density parity-check (LDPC) codes have attracted much attention as good error correcting codes achieving the near Shannon limit. Concatenation schemes of LDPC codes and STBC (LDPC-STBC), and turbo codes and STBC (turbo-STBC) have been proposed. The performance of the LDPC-STBC is better than that of the turbo-STBC on a flat Rayleigh fading channel. The performance of LDPC code can be analyzed by density evolution (DE). In this paper we analyze the performance of the LDPC-STBC by using DE. Also, we optimize the irregular LDPC codes for the LDPC-STBC by using DE. Furthermore, we evaluate the error rate performance of the optimized irregular LDPC codes and the regular LDPC codes for the LDPC-STBC. From the numerical and simulation results, we show that the LDPC-STBC with the irregular LDPC codes achieves better error rate performance than the LDPC-STBC with the regular LDPC codes.