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.

Implementation and security analysis of practical quantum secure direct communication

Rapid development of supercomputers and the prospect of quantum computers are posing increasingly serious threats to the security of communication.Using the principles of quantum mechanics,quantum communication offers provable security of communication and is a promising solution to counter such threats.Quantum secure direct communication(QSDC)is one important branch of quantum communication.In contrast to other branches of quantum communication,it transmits secret information directly.Recently,remarkable progress has been made in proof-of-principle experimental demonstrations of QSDC.However,it remains a technical feat to bring QSDC into a practical application.Here,we report the implementation of a practical quantum secure communication system.The security is analyzed in the Wyner wiretap channel theory.The system uses a coding scheme of concatenation of lowdensity parity-check(LDPC)codes and works in a regime with a realistic environment of high noise and high loss.The present system operates with a repetition rate of 1 MHz at a distance of 1.5 kilometers.The secure communication rate is 50 bps,sufficient to effectively send text messages and reasonably sized files of images and sounds.