Decoding algorithms for low-density parity-check codes with multilevel modulations

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 [1]. 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 [1] 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 [1], where the decoding complexity of the proposed BP algorithm is less than that of the algorithm in [1]. We also show that the proposed BP-based algorithms can achieve the good trade-off between the complexity and the error rate performance.