The Advanced Decoding Schemes for Low-density Parity-check Codes

In this thesis, a new code construction method and two enhanced decoding schemes for low-density parity-check (LDPC) codes were proposed to improve their error performance. In the first part of the thesis, we develop a new construction method of binary spatially-coupled (SC) LDPC codes for storage applications based on Euclidean geometry (EG) and a two-dimensional edge-spreading process. We show that the error performance of the constructed EG-SC LDPC codes is superior to that of their EG LDPC code counterparts, and there is no error floor compared to the protograph SC LDPC codes and regular LDPC codes. To achieve a high error correction capability, we further propose a reliability-based windowed decoding (RBWD) scheme for the SC LDPC codes based on a partial message reservation method and a partial syndrome check stopping rule. It is shown that the RBWD scheme significantly improves the error floor performance compared to the sliding window decoder with the conventional WBF algorithm. We investigate the decoding of the LDPC codes adopted in the fifth generation (5G) mobile networks. We propose a two-dimensional scale-corrected min-sum algorithm based on partial self-correction and message amplification, which results in the error performance near the sum-product algorithm (SPA). Then we present an enhanced quasi-maximum likelihood (EQML) decoding method to further improve the error performance for 5G short LDPC codes. The proposed decoding method performs node selection with multiple rounds of decoding tests. We also present a partial pruning stopping rule to reduce the decoding complexity and derive a lower bound on the error performance. We show that the EQML decoding method outperforms the SPA with the same decoding complexity and approaches the Polyanskiy-Poor-Verdú bound within 0.4 dB. We also design a decoding scheme based on the approximate message passing (AMP) algorithm for the 5G LDPC codes. We propose a decoding model, which aims to recover the error vector from the output of the decoder. When the initial decoding attempt fails, the AMP detector estimates the reliability of the channel outputs and flips the signs of unreliable channel outputs to create the new input sequence for one more decoding test. We show that the proposed AMP-aided decoding scheme achieves a 0.1 dB gain over the counterpart of one-time decoding for various block lengths and low code rates and the obtain about 0.05 dB gain for the EQML decoding