Recently, low-density parity-check (LDPC) codes have attracted much attention. LDPC codes can achieve the near Shannon limit performance like turbo codes. For the LDPC codes, the reduced complexity decoding algorithms referred to as uniformly most powerful (UMP) BP- and normalized BP-based algorithms were proposed for BPSK on an additive white Gaussian noise (AWGN) channel. The conventional BP and BP-based algorithms can be applied to BPSK modulation. For high bit-rate transmission, multilevel modulation is preferred. Thus, the BP algorithm for multilevel modulations is proposed in . In this paper, we propose the BP algorithm with reduced complexity for multilevel modulations, where the first likelihood of the proposed BP algorithm is modified to adjust multilevel modulations. We compare the error rate performance of the proposed algorithm with that of the conventional algorithm on AWGN and flat Rayleigh fading channels. We also propose the UMP BP- and normalized BP-based algorithms for multilevel modulations on AWGN and flat Rayleigh fading channels. We show that the error rate performance of the proposed BP algorithm is almost identical to that of the algorithm in, where the decoding complexity of the proposed BP algorithm is less than that of the algorithm in. We also show that the proposed BP-based algorithms can achieve the good trade-off between the complexity and the error rate performance.

In this letter, we propose the Low-Density Parity-Check (LDPC) coded Orthogonal Frequency Division Multiplexing (OFDM) systems to improve the error rate performance of OFDM. We also evaluate the iterative decoding performance on both an AWGN and a frequency-selective fading channels. We show that when the energy per information bit to the noise power spectral density ratio Eb/N0 is not small, the LDPC coded OFDM (LDPC-COFDM) systems have the good error rate performance with a small number of iterations. We also show that when the Eb/N0 is small, the BER of the LDPC-COFDM systems is worse than that of the Turbo coded OFDM (TCOFDM) systems, while when the Eb/N0 is not small, the BER of the LDPC-COFDM systems is better with a small number of iterations.

Space-time transmit diversity (STTD) and space-time block coding (STBC) are attractive techniques for high bit-rate and high capacity transmission. The concatenation scheme of turbo codes and STBC (Turbo-STBC) was proposed and it has been shown that the Turbo-STBC can achieve the good error rate performance. Recently, low-density parity-check (LDPC) codes have attracted much attention as the good error correcting codes achieving the near Shannon limit performance like turbo codes. The decoding algorithm of LDPC codes has less complexity than that of turbo codes. Furthermore, when the block length is large, the error rate performance of the LDPC codes is better than that of the turbo codes with almost identical code rate and block length. In this letter, we propose a concatenation scheme of LDPC codes and STBC. We refer to it as the LDPC-STBC. We evaluate the error rate performance of the LDPC-STBC by the computer simulation and show that the error rate performance of the LDPC-STBC is almost identical to or better than that of the Turbo-STBC in a flat Rayleigh fading channel.