In multiple-input multiple-output (MIMO) wireless systems, the receiver must extract each transmitted signal from received signals. Iterative signal detection with belief propagation (BP) can improve the error rate performance, by increasing the number of detection and decoding iterations in MIMO systems. This number of iterations is, however, limited in actual systems because each additional iteration increases latency, receiver size, and so on. This paper proposes a convergence acceleration technique that can achieve better error rate performance with fewer iterations than the conventional iterative signal detection. Since the Log-Likelihood Ratio (LLR) of one bit propagates to all other bits with BP, improving some LLRs improves overall decoder performance. In our proposal, all the coded bits are divided into groups and only one group is detected in each iterative signal detection whereas in the conventional approach, each iterative signal detection run processes all coded bits, simultaneously. Our proposal increases the frequency of initial LLR update by increasing the number of iterative signal detections and decreasing the number of coded bits that the receiver detects in one iterative signal detection. Computer simulations show that our proposal achieves better error rate performance with fewer detection and decoding iterations than the conventional approach.

Irregular Low-Density Parity-Check (LDPC) codes generally achieve better performance than regular LDPC codes at low Eb/N0 values. They have, however, higher error floors than regular LDPC codes. With respect to the construction of the irregular LDPC code, it can achieve the trade-off between the performance degradation of low Eb/N0 region and lowering error floor. It is known that a decoding algorithm can achieve very good performance if it combines the Ordered Statistic Decoding (OSD) algorithm and the Log Likelihood Ratio-Belief Propagation (LLR-BP) decoding algorithm. Unfortunately, all the codewords obtained by the OSD algorithm satisfy the parity check equation of the LDPC code. While we can not use the parity check equation of the LDPC code to stop the decoding process, the wrong codeword that satisfies the parity check equation raises the error floor. Once a codeword that satisfies the parity check equation is generated by the LLR-BP decoding algorithm, we regard that codeword as the final estimate and halt decoding; the OSD algorithm is not performed. In this paper, we propose a new encoding/decoding scheme to lower the error floor created by irregular LDPC codes. The proposed encoding scheme encodes information bits by Cyclic Redundancy Check (CRC) and LDPC code. The proposed decoding scheme, which consists of the LLR-BP decoding, CRC check, and OSD decoding, detects errors in the codewords obtained by the LLR-BP decoding algorithm and the OSD decoding algorithm using the parity check equations of LDPC codes and CRC. Computer simulations show that the proposed encoding/decoding scheme can lower the error floor of irregular LDPC codes.

Multiple-Input Multiple-Output (MIMO) wireless systems offer both high data rates and high capacity. Since different signals are transmitted by different antennas simultaneously, interference occurs between the transmitted signals. Each receive antenna receives all the signals transmitted by each transmit antenna simultaneously. The receiver has to detect each signal from the multiplexed signal. A Minimum Mean Square Error (MMSE) algorithm is used for spatial filtering. MMSE filtering can realize low complexity signal detection, but the signal output by MMSE filtering suffers from interference by the other signals. MMSE-SIC combines MMSE filtering and Soft Interference Cancellation (SIC) with soft replicas and can achieve good Bit Error Rate (BER) performance. If an irregular LDPC code or a turbo code is used, the reliability and BER of the information bits output by the decoder are likely to be higher and better than the parity bits. In MMSE-SIC, bits with poor reliability lower the accuracy of soft replica estimation. When the soft replica is inaccurate, the gain obtained by SIC is small. M-ary Phase Shift Keying (PSK) and M-ary Quadrature Amplitude Modulation (QAM) also achieve high data rates. Larger constellations such as 8 PSK and 16 QAM transfer more bits per symbol, and the number of bits per symbol impacts the accuracy of SIC. Unfortunately, increasing the number of bits per symbol is likely to lower the accuracy of soft replica estimation. In this paper, we evaluate three mapping schemes for MMSE-SIC with an LDPC code and a turbo code with the goal of effectively increasing the SIC gain. The first scheme is information reliable mapping. In this scheme, information bits are assigned to strongly protected bits. In the second scheme, parity reliable mapping, parity bits are assigned to strongly protected bits. The last one is random mapping. Computer simulations show that in MMSE-SIC with an irregular LDPC code and a turbo code, information reliable mapping offers the highest SIC gain. We also show that in MMSE-SIC with the regular LDPC code, the gains offered by the mapping schemes are very small.

Irregular LDPC codes can achieve better error rate performance than regular LDPC codes. However, irregular LDPC codes have higher error floors than regular LDPC codes. The Ordered Statistic Decoding (OSD) algorithm achieves approximate Maximum Likelihood (ML) decoding. ML decoding is effective to lower error floors. However, the OSD estimates satisfy the parity check equation of the LDPC code even the estimates are wrong. Hybrid decoder combining LLR-BP decoding algorithm and the OSD algorithm cannot also lower error floors, because wrong estimates also satisfy the LDPC parity check equation. We proposed the concatenated code constructed with an inner irregular LDPC code and an outer Cyclic Redundancy Check (CRC). Owing to CRC, we can detect wrong codewords from OSD estimates. Our CRC-LDPC code with hybrid decoder can lower error floors in an AWGN channel. In wireless communications, we cannot neglect the effects of the channel. The OSD algorithm needs the ordering of each bit based on the reliability. The Channel State Information (CSI) is used for deciding reliability of each bit. In this paper, we evaluate the Block Error Rate (BLER) of the CRC-LDPC code with hybrid decoder in a fast fading channel with perfect and imperfect CSIs where 'imperfect CSI' means that the distribution of channel and those statistical average of the fading amplitudes are known at the receiver. By computer simulation, we show that the CRC-LDPC code with hybrid decoder can lower error floors than the conventional LDPC code with hybrid decoder in the fast fading channel with perfect and imperfect CSIs. We also show that combining error detection with the OSD algorithm is effective not only for lowering the error floor but also for reducing computational complexity of the OSD algorithm.

In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high Eb/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.