Spatially coupled LDPC-BCH codes in quantum secure direct communications

Abstract

Quantum secure direct communication systems are limited by high erasure probabilities and low receiving probabilities due to the high light source losses in the optical elements and optical fibers. A channel mitigation method based on spatially coupled LDPC-BCH codes is presented here to ensure reliable information transformations in quantum secure direct communication systems to resolve the problems of low-rate and Shannon limit-approaching code designs. Spatially coupled LDPC-BCH codes are constructed by coupling multiple identical block LDPC-BCH codes with edge spreading. The extrinsic information transfer functions of the spatially coupled LDPC-BCH code are analyzed to derive the decoding thresholds for the code ensembles. Simulations show that the spatially coupled LDPC-BCH codes have decoding thresholds closer to the Shannon limit with lower bit error rates than block LDPC-BCH codes. The spatially coupled LDPC-BCH code channel mitigation scheme has a transmitting efficiency of 0.001 and a bit error rate less than 10 −6 when the channel receiving probability is set at 0.4%. 摘要 受光源、光器件和光纤损耗影响, 量子安全直接通信系统的信息传输面临删除概率极大、接收概率极低的难题。为保证量子安全直接通信系统信息传输的可靠性, 该文提出了基于空间耦合LDPC-BCH码的信道补偿方案, 解决了极低码率码字构造和逼近Shannon限实用码字设计2方面的问题。将多个相同的分组LDPC-BCH码通过边连接的方式耦合起来构造得到了空间耦合LDPC-BCH码。建立了空间耦合LDPC-BCH码集的外信息转移函数, 并基于外信息转移函数分析了码集的译码门限值。仿真结果表明：与分组LDPC-BCH码相比, 空间耦合LDPC-BCH码的译码门限更接近Shannon限, 误比特率更低。在信道接收概率为0.4%时, 采用传输效率为0.001的空间耦合LDPC-BCH码信道补偿方案, 系统误比特率低于10 -6 。