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Journal of Tsinghua University(Science and Technology)

Spatially coupled LDPC-BCH codes in quantum secure direct communications

Wang Ping, Zhen Sun, Liuguo Yin, Jianhua Lü

Published Sep 15, 2019• 2 citations
Publisher

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 。

DOI
10.16511/j.cnki.qhdxxb.2019.21.025

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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 。
Spatially coupled low-density parity-check block codes (SC-LDPC-BCs) are a class of LDPC codes in which certain ensembles achieve capacity under iterative belief propagation decoding. Prior work has considered these codes mostly from a protograph perspective. Following this viewpoint, our work presents new protographs for the design of protograph-based SC-LDPC-BCs. A reciprocal channel approximation (RCA) analysis of the terminated protographs yields the asymptotic performance limits of the ensembles in terms of their iterative decoding thresholds. Our protographs possess the properties of linear minimum distance growth rate and excellent thresholds. We consider the following channels in our work: binary-input additive white Gaussian noise channel (BI-AWGNC), binary erasure channel (BEC), and binary symmetric channel (BSC). Our work focuses on obtaining good designs, with two classes of ensembles being asymptotically regular, for all the three channels while minimizing rate loss.
In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an FPGA-based decoder where we show that very low error rates can be achieved and that conventional block-based LDPC codes can be outperformed. In the second part of the paper, we focus on the combination of spatially coupled LDPC codes with different demodulators and detectors, important for future systems with adaptive modulation and for varying channel characteristics. We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.
We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCHCCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 1e-5 is achieved at Eb/N0 = -1.465 dB, which is only 0.125 dB from the ultimate Shannon limit.
Absorbing sets are known to be the primary factor in the error-floor performance of low-density parity-check (LDPC) codes with message passing decoders over the additive white Gaussian noise (AWGN) channel. Besides showing excellent waterfall performance, spatially coupled LDPC (SC-LDPC) codes that are constructed by an edge spreading technique are known to have fewer cycles and absorbing sets than their block code counterparts, and therefore to exhibit better error-floor performance. Based on our previously obtained results for quantized LDPC block decoders, we derive lower bounds on the performance of quantized SC-LDPC decoders, including both a flooding schedule decoder and a sliding window decoder. Numerical simulation results confirm the accuracy of the obtained bounds and show that, for quantized decoders, properly designed SC-LDPC codes have better error-floor performance than their underlying LDPC block codes.
We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCH-CCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 10−5is achieved atEb/N0=−1.465E_{b}/N_{0} = -1.465Eb​/N0​=−1.465dB, which is only 0.125 dB from the ultimate Shannon limit.
Quantum secure direct communication (QSDC) is capable of direct confidential communications over a quantum channel, which is achieved by dispensing with the key agreement channel of the well-known quantum key distribution (QKD). However, to make QSDC a practical reality, we have to mitigate its reliance on quantum memory, its immediate communication interruption caused by eavesdropping and its low transmission reliability due to the heavy qubit losses. Hence a new QSDC protocol is proposed based on a sophisticated coded single-photon DL04 QSDC protocol to tackle the open challenges. In particular, quantum memory is dispensed with and a high-accuracy secrecy capacity estimate is derived for this protocol by conceiving dynamic joint encryption and error-control (JEEC) coding. We demonstrate that this quantum-memory-free DL04 QSDC (QMF-DL04 QSDC) protocol inches closer to the quantum channel's capacity and significantly improves the original DL04 QSDC's robustness. Moreover, a rate-compatible low-rate JEEC coding scheme is designed for the proposed framework, and the JEEC code advocated is shown to approach the secrecy capacity, despite tolerating an extremely high loss of qubits in the time-varying wiretap channel. Our simulations and experimental results demonstrate that the QMF-DL04 QSDC scheme significantly increases both the secure information rate and the communication distance of the original DL04 protocol.