Low-density parity-check codes: Highway to channel capacity

Low-density parity-check (LDPC) codes are not only capacity-approaching, but also greatly suitable for high-throughput implementation. Thus, they are the most popular codes for high-speed data transmission in the past two decades. Thanks to the low-density property of their parity-check matrices, the optimal maximum a posteriori probability decoding of LDPC codes can be approximated by message-passing decoding with linear complexity and highly parallel nature. Then, it reveals that the approximation has to carry on Tanner graphs without short cycles and small trapping sets. Last, it demonstrates that well-designed LDPC codes with the aid of computer simulation and asymptotic analysis tools are able to approach the channel capacity. Moreover, quasi-cyclic (QC) structure is introduced to significantly facilitate their high-throughput implementation. In fact, compared to the other capacity-approaching codes, QC-LDPC codes can provide better area-efficiency and energy-efficiency. As a result, they are widely applied in numerous communication systems, e.g., Landsat satellites, Chang'e Chinese Lunar mission, 5G mobile communications and so on. What's more, its extension to non-binary Galois fields has been adopted as the channel coding scheme for BeiDou navigation satellite system.