Hisashi Futaki

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. Recently, LDPC codes have attracted much attention. The performance of LDPC codes is very close to the Shannon limit, with practical decoding complexity. We proposed LDPC coded OFDM (LDPC-COFDM) systems with BPSK and showed that the LDPC codes are effective in improving the bit error rate (BER) of OFDM in multipath environments (see Futaki, H. and Ohtsuki, T., IEEE VTC2001 fall, vol.1, p.82-6, 2001). LDPC codes can be decoded using a probability propagation algorithm known as the sum-product algorithm or belief propagation. To clarify iterative decoding properties in LDPC-COFDM systems, we first investigate the distribution of the number of iterations where the decoding algorithm stops. In mobile communications, multilevel modulation is preferred for high bandwidth efficiency. However, it has not been clarified how to apply LDPC codes to OFDM systems with multilevel modulation. We propose a decoding algorithm for the LDPC-COFDM systems with M-PSK. By simulation, we show that LDPC-COFDM systems achieve good error rate performance with a small number of iterations on both AWGN and frequency-selective fading channels. We confirm that the algorithm for LDPC-COFDM systems with M-PSK work correctly.

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 a multipath fading environment that causes intersymbol interference (ISI). There are many error-correcting codes applied to OFDM, convolutional codes, Reed-Solomon codes, turbo codes, and so on. Low-density parity-check (LDPC) codes have attracted much attention particularly in the field of coding theory. LDPC codes were proposed by Gallager (1962) and the performance is very close to the Shannon limit with practical decoding complexity like turbo codes. We propose LDPC coded OFDM (LDPC-COFDM) systems to improve the bit error rate (BER) of OFDM. We show that the BER of the LDPC-COFDM is worse than that of the TCOFDM on an AWGN channel, while that of the LDPC-COFDM is better than that of the turbo-coded OFDM (TCOFDM) on a frequency-selective fading channel.

LDPC-based space-time transmit diversity schemes with multiple transmit antennas

Space-time transmit diversity (STTD) and space-time block coding (STBC) are the 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, it has been shown that when the block length is relatively 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 paper, we propose a concatenation scheme of LDPC codes and STBC with multiple transmit antennas. We refer to it as the LDPC-STBC. We evaluate the frame error rate (FER) of the LDPC-STBC with multiple transmit antennas in a flat Rayleigh fading channel by the computer simulation. We show that the FER of the LDPC-STBC is worse than that of the turbo-STBC in a quasi-static Rayleigh fading channel, while that of the LDPC-STBC is better than that of the turbo-STBC in a flat Rayleigh fading channel. Furthermore, we show that the FER of the LDPC-STBC without channel interleaver (CI) is better than that of the turbo-STBC with CI in a fast fading channel.

Low-density parity-check (LDPC) coded MIMO systems with iterative turbo decoding

Transmit diversity schemes have been studied for high spectral-efficiency and high bit-rate transmission, such as multi-input multi-output (MIMO) systems. In the MIMO system, forward error correction coding is essential for high quality communications. Recently, low-density parity-check (LDPC) codes have attracted much attention as good error correcting codes like turbo codes. LDPC codes have been applied to MIMO systems, where we refer to the system as the MIMO-LDPC. In this paper, we propose a new MIMO-LDPC system with iterative turbo decoding (MIMO-LDPC-TD) using two LDPC encoders and two LDPC decoders to improve the performance of the MIMO-LDPC. Since each decoder in the MIMO-LDPC-TD is smaller than that in the MIMO-LDPC, the decoding complexity at each decoder in the MIMO-LDPC-TD is less than that in the MIMO-LDPC. We also compare the performance of the MIMO-LDPC with that of the turbo coded MIMO systems (MIMO-turbo) on flat Rayleigh fading channels. We show that the MIMO-LDPC-TD can achieve the good error rate performance with reduced decoding complexity at each decoder on it flat Rayleigh fading channel, particularly on a slow fading channel. We also show that the MIMO-LDPC can achieve the better error rate performance than the MIMO-turbo on a fast Rayleigh fading channel.

Low-density parity-check (LDPC) coded OFDM systems with M-PSK

Orthogonal frequency division multiplexing (OFDM) is a very attractive technique to achieve the high-bit-rate transmission required for future mobile communications. To improve the error rate performance of OFDM, forward error correction coding is essential. Recently, low-density parity-check (LDPC) codes, which can achieve the near Shannon limit performance, have attracted much attention. We proposed the LDPC coded OFDM (LDPC-COFDM) systems to improve the error rate performance of OFDM. We showed that LDPC codes are effective to improve the error rate performance of OFDM on a frequency-selective fading channel. In mobile communications high bandwidth efficiency is required, and thus multilevel modulation is preferred. We also proposed the decoding algorithm for the LDPC-COFDM systems with MPSK on an AWGN channel. In this paper, we evaluate the error rate performance of the LDPC-COFDM systems with M-PSK using the Gray and the natural mappings on an AWGN channel, and that of the systems with M-PSK using the Gray mapping on a flat Rayleigh fading channel. We show that the LDPC-COFDM systems with M-PSK using the Gray mapping have better error rate performance than the systems using the natural mapping on an AWGN channel. We also show that the LDPC-COFDM systems with QPSK is more effective than the other systems on a flat Rayleigh fading channel.