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arXiv 2404.04477cs.ITmath.IT
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有限块长光纤 MIMO 信道的基本极限

Fundamental Limits of Optical Fiber MIMO Channels With Finite Blocklength

Xin Zhang, Dongfang Xu, Shenghui Song, Mérouane Debbah

AI总结:

本文针对有限块长光纤多芯/多模 Jacobi MIMO 信道,利用信息密度中心极限定理推导最优平均错误概率上下界,并通过数值验证其逼近 LDPC 码性能。

摘要:

多输入多输出(MIMO)技术被视为提升光纤通信吞吐量和可靠性的一种有前景方法。然而,文献中尚不存在有限块长(FBL)光纤 MIMO 系统基本极限的结果。本文研究 FBL 区域内光纤多芯/多模系统的基本极限,此时编码速率是容量的 O(1/√(ML)) 阶扰动,其中 M 和 L 分别表示发射信道数和块长。考虑 Jacobi MIMO 信道——该信道被提出用于建模光纤系统中近乎无损的传播和串扰——我们推导了最优错误概率的上界和下界。为此,我们首先在发射信道数、接收信道数、可用信道数和块长以相同速度趋于无穷的渐近区域中,建立了信息密度的中心极限定理。随后,该结果被用于推导在所关注速率下最优平均错误概率的上界和下界。所得理论结果揭示了 FBL 下 Jacobi MIMO 信道的有趣物理洞见。第一,当可用信道数趋于无穷时,为 Jacobi 信道推导的界退化为 Rayleigh 信道的界。第二,高信噪比(SNR)近似表明,更多的可用信道数会导致更大的错误概率。数值结果验证了理论结果的准确性,并表明所推导的界比中断概率更接近实际 LDPC 码的性能。

英文摘要:

The multiple-input and multiple-output (MIMO) technique is regarded as a promising approach to boost the throughput and reliability of optical fiber communications. However, the fundamental limits of optical fiber MIMO systems with finite block-length (FBL) are not available in the literature. This paper studies the fundamental limits of optical fiber multicore/multimode systems in the FBL regime when the coding rate is a perturbation within $\mathcal{O}(\frac{1}{\sqrt{ML}})$ of the capacity, where M and L represent the number of transmit channels and blocklength, respectively. Considering the Jacobi MIMO channel, which was proposed to model the nearly lossless propagation and the crosstalks in optical fiber systems, we derive the upper and lower bounds for the optimal error probability. For that purpose, we first set up the central limit theorem for the information density in the asymptotic regime where the number of transmit, receive, available channels and the blocklength go to infinity at the same pace. The result is then utilized to derive the upper and lower bounds for the optimal average error probability with the concerned rate. The derived theoretical results reveal interesting physical insights for Jacobi MIMO channels with FBL. First, the derived bounds for Jacobi channels degenerate to those for Rayleigh channels when the number of available channels approaches infinity. Second, the high signal-to-noise (SNR) approximation indicates that a larger number of available channels results in a larger error probability. Numerical results validate the accuracy of the theoretical results and show that the derived bounds are closer to the performance of practical LDPC codes than outage probability.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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