Performance of low-density parity-check (LDPC) coded OFDM systems

Orthogonal Frequency Division Multiplexing (OFDM) is a very attractive technique for high-bit-rate data transmission in multipath environments. Many error-correcting codes have been applied to OFDM, convolutional codes, Reed-Solomon codes, Turbo codes, and so on. Recently, low-density parity-check (LDPC) codes have attracted much attention particularly in the field of coding theory. LDPC codes were proposed by Gallager in 1962 and the performance is very close to the Shannon limit with practical decoding complexity like Turbo codes. We proposed the LDPC coded OFDM (LDPC-COFDM) systems with BPSK and showed that the LDPC codes are effective to improve the bit error rate (BER) of OFDM in multipath environments [1]. LDPC codes can be decoded by using a probability propagation algorithm known as the sum-product algorithm or belief propagation. When the LDPC codes are used for the OFDM systems, the properties of the iterative decoding, such as the distribution of the number of iterations where the decoding algorithm stops, have not been clarified. In mobile communications, a high bandwidth efficiency is required, and thus the multilevel modulation is preferred. However, it has not been clarified how we can apply LDPC codes to the OFDM systems with multilevel modulation. In this paper, first we investigate the distribution of the number of iterations where the decoding algorithm stops in the LDPC-COFDM systems. Moreover, we propose the decoding algorithm for the LDPC-COFDM systems with M-PSK. From the simulation, we show that the LDPC-COFDM systems achieve good error rate performance with a small number of iterations on both an AWGN and a frequency-selective fading channels. We confirm that the algorithm for the LDPC-COFDM systems with M-PSK work correctly.