In this paper, the application of non-binary low-density parity-check (NBLDPC) codes to MIMO systems which employ hundreds of antennas at both the transmitter and the receiver has been proposed. Together with the well-known low-complexity MMSE detection, the moderate length NBLDPC codes can operate closer to the MIMO capacity, e.g., capacity-gap about 3.5 dB (the best known gap is more than 7 dB). To further reduce the complexity of MMSE detection, a novel soft output detection that can provide an excellent coded performance in low SNR region with 99% complexity reduction is also proposed. The asymptotic performance is analysed by using the Monte Carlo density evolution. It is found that the NBLDPC codes can operate within 1.6 dB from the MIMO capacity. Furthermore, the merit of using the NBLDPC codes in large MIMO systems with the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems is also pointed out.
Recently, it has been proved that both MMSE and MF detectors are near optimal detection for large scale MIMO systems, e.g., MIMO systems with hundreds of antennas. In order to attain near capacity region with reasonable complexity, lowcomplexity detector with soft-output generation is necessary for coded large MIMO systems. We show in this paper that the nonbinary LDPC codes and well-known soft-output MMSE detector can be utilized to significantly reduce the gap to capacity. We also propose a novel soft-output MF-based detector for the non-binary LDPC coded large MIMO systems. With this proposed detector, capacity approaching performance, i.e., the gap to capacity of 1.6 dB, can be achieved with ultra low-complexity detection, e.g., just 0.28% of MMSE detection. Moreover, use of the proposed scheme in large MIMO systems is found to be robust to the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems.
High rate irregular QC-LDPC codes based on circulant permutation matrices, for efficient encoder implementation, are proposed in this article. The structure of the code is an approximate lower triangular matrix. In addition, we present two novel efficient encoding techniques for generating redundant bits. The complexity of the encoder implementation depends on the number of parity bits of the code for the one-stage encoding and the length of the code for the two-stage encoding. The advantage of both encoding techniques is that few XOR-gates are used in the encoder implementation. Simulation results on partial response channels also show that the BER performance of the proposed code has gain over other QC-LDPC codes
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