Few-Mode Fiber Transmission System Based on Probability Shaping and Interleaved Encoding

Tong Wu; Feng Tian; Leijing Yang

doi:10.3788/AOS202242.0706006

Acta Optica Sinica, Volume. 42, Issue 7, 0706006(2022)

Few-Mode Fiber Transmission System Based on Probability Shaping and Interleaved Encoding

Tong Wu, Feng Tian^*, and Leijing Yang

School of Electronic Engineering, State Key Laboratory of Information Photonics and Optical Communication, Beijing Key Laboratory of Space-Round Interconnection and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China

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Figures & Tables(9)

Fig. 1. Experimental block diagram of few-mode fiber transmission system

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Fig. 2. Schematic of interleaved encoding

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Fig. 3. Mode field diagrams for six modes. (a) LP₀₁; (b) LP_11a; (c) LP_11b; (d) LP_21a; (e) LP_21b; (f) LP₀₂

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Fig. 4. Schematic of displacement and rotation of optical fiber segment. (a) Optical fiber segments; (b) displacement and rotation of cross section of optical fiber

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Fig. 5. Simulation diagram of few-mode fiber transmission system

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Fig. 6. Variation curve of bit error rate of different modes with optical signal-to-noise ratio. (a) Uniform distribution signal; (b) MB distribution signal

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Fig. 7. Influence of probabilistic shaping and interleaved coding on bit error rate. (a) Variation curves of bit error rate of LP_11a mode and LP₀₂ mode in MB distribution signal and first signal channel of test signal with OSNR; (b) variation curves of 6-channel error rate of uniform distributed signal, MB distributed signal, and test signal with OSNR of 18 dB

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Fig. 8. Variation curves of bit error rate of LP_11a mode of uniform distributed signal and first signal channel of test signal with distance of optical fiber when OSNR is 21 dB

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Table 1. Element of K_ij

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Table 1. Element of K_ij

Parameter	Expression
K₁₁	exp(-b²/4ξ²)
K₁₂	$\frac{\sqrt[]{2}}{2}$ · $\frac{y_{0}}{ξ}$ ·K₁₁
K₁₃	$\frac{\sqrt[]{2}}{2}$ · $\frac{x_{0}}{ξ}$ ·K₁₁
K₁₄	$\frac{1}{4 ξ^{2}}$ ·sin 2θ·K₁₁
K₁₅	$\frac{1}{4 ξ^{2}}$ ·cos 2θ·K₁₁
K₁₆	- $\frac{b^{2}}{4 ξ^{2}}$ ·K₁₁
K₂₁	- $\frac{\sqrt[]{2} b}{2 ξ}$ ·sin(φ₀-θ)·K₁₁
K₂₂	$\frac{1}{ξ^{2}}$ · $[ξ^{2} \cos φ_{0} + \frac{b \cdot y_{0}}{2} \sin (φ_{0} - θ)]$ ·K₁₁
K₂₃	$\frac{1}{ξ^{2}}$ · $[- ξ^{2} \sin φ_{0} + \frac{b \cdot x_{0}}{2} \sin (φ_{0} - θ)]$ ·K₁₁
K₂₄	$\frac{\sqrt[]{2}}{ξ^{3}}$ · $[\frac{ξ^{2} b}{2} \cos (φ_{0} + θ) + \frac{b x_{0} y_{0}}{4} \sin (φ_{0} - θ)]$ ·K₁₁
K₂₅	$\frac{\sqrt[]{2}}{ξ^{3}}$ · $[- \frac{ξ^{2} b}{2} \sin (φ_{0} + θ) + \frac{b^{3}}{2} \cos 2 θ \sin (φ_{0} - θ)]$ ·K₁₁
K₂₆	K₂₁- $\frac{\sqrt[]{2}}{ξ^{3}}$ · $\frac{b^{3}}{8}$ sin(φ₀-θ)·K₁₁
K₃₁	- $\frac{\sqrt[]{2} b}{2 ξ}$ cos(φ₀-θ)·K₁₁
K₃₂	$\frac{1}{ξ^{2}} [ξ^{2} \sin φ_{0} - \frac{b y_{0}}{2} \cos (φ_{0} - θ)]$ K₁₁
K₃₃	$\frac{1}{ξ^{2}} [ξ^{2} \cos φ_{0} - \frac{b x_{0}}{2} \cos (φ_{0} - θ)]$ K₁₁
K₃₄	$\frac{\sqrt[]{2}}{ξ^{3}} [\frac{ξ^{2} b}{2} \sin (φ_{0} + θ) - \frac{b^{3}}{8} \sin 2 θ \cos (φ_{0} - θ)]$ K₁₁
K₃₅	$\frac{\sqrt[]{2}}{ξ^{3}} [\frac{ξ^{2} b}{2} \sin (φ_{0} - θ) - \frac{b^{3}}{8} \cos 2 θ \cos (φ_{0} - θ)]$ K₁₁
K₃₆	K₃₁+ $\frac{\sqrt[]{2} b^{3}}{8 ξ^{3}}$ cos(φ₀-θ)K₁₁
K₄₁	$\frac{b^{2}}{4 ξ^{2}}$ sin(2θ-2φ₀)K₁₁
K₄₂	$\frac{\sqrt[]{2}}{ξ^{3}} [\frac{y_{0} b^{2}}{8} \sin (2 θ - 2 φ_{0}) - \frac{ξ^{2} b}{2} \cos (2 φ_{0} - θ)]$ K₁₁
K₄₃	$\frac{\sqrt[]{2}}{ξ^{3}} [\frac{x_{0} b^{2}}{8} \sin (2 θ + 2 φ_{0}) + \frac{ξ^{2} b}{2} \sin (2 φ_{0} - θ)]$ K₁₁
K₄₄	$\frac{1}{ξ^{4}} [ξ^{4} \cos 2 φ_{0} - \frac{ξ^{2} b^{2}}{2} \cos 2 φ_{0} + \frac{b^{4}}{16} \sin 2 θ \sin (2 θ - 2 φ_{0})]$ K₁₁
K₄₅	$\frac{1}{ξ^{4}} [- ξ^{4} \sin 2 φ_{0} + \frac{ξ^{2} b^{2}}{2} \sin 2 φ_{0} +$ $\frac{b^{4}}{16} \cos 2 θ \sin (2 θ - 2 φ_{0})]$ K₁₁
K₄₆	K₄₁- $\frac{1}{ξ^{4}} [\frac{ξ^{2} b^{2}}{2} \sin (2 φ_{0} - 2 θ) + \frac{b^{4}}{16} \sin (2 θ - 2 φ_{0})]$ K₁₁
K₅₁	$\frac{b^{2}}{4 ξ^{2}}$ cos(2φ₀-2θ)K₁₁
K₅₂	$\frac{\sqrt[]{2}}{ξ^{3}} [\frac{ξ^{2} b}{2} \sin (θ - 2 φ_{0}) + \frac{y_{0} b^{2}}{8} \cos (2 φ_{0} - 2 θ)]$ K₁₁
K₅₃	$\frac{\sqrt[]{2}}{ξ^{3}} [- \frac{ξ^{2} b}{2} \cos (θ - 2 φ_{0}) + \frac{y_{0} b^{2}}{8} \cos (2 φ_{0} - 2 θ)]$ K₁₁
K₅₄	$\frac{1}{ξ^{4}} [ξ^{4} \sin 2 φ_{0} - \frac{ξ^{2} b^{2}}{2} \sin 2 φ_{0} + \frac{x_{0} y_{0} b^{2}}{8} \cos (2 φ_{0} - 2 θ)]$ K₁₁
K₅₅	$\frac{1}{ξ^{4}} [ξ^{4} \cos 2 φ_{0} - \frac{ξ^{2} b^{2}}{2} \cos 2 φ_{0} + \frac{b^{4}}{16} \cos (2 φ_{0} - 2 θ)]$ K₁₁
K₅₆	K₅₁- $\frac{1}{ξ^{4}} [\frac{b^{4}}{16} \cos (2 φ_{0} - 2 θ) - \frac{ξ^{2} b^{2}}{4} \cos (2 φ_{0} - 2 θ)]$ K₁₁
K₆₁	K₁₁- $\frac{1}{ξ^{2}} (ξ^{2} + \frac{b^{2}}{4})$ K₁₁
K₆₂	K₁₂- $\frac{\sqrt[]{2} x_{0} b^{2}}{8 ξ^{3}}$ K₁₁
K₆₃	K₁₃- $\frac{\sqrt[]{2} y_{0} b^{2}}{8 ξ^{3}}$ K₁₁
K₆₄	K₁₄- $\frac{1}{ξ^{4}} [\frac{b^{4}}{16} \sin 2 θ - \frac{ξ^{2} b^{2}}{4} \sin 2 θ]$ K₁₁
K₆₅	K₁₅- $\frac{1}{ξ^{4}} [\frac{b^{4}}{16} \cos 2 θ - \frac{ξ^{2} b^{2}}{4} \cos 2 θ]$ K₁₁
K₆₆	K₁₆- $\frac{1}{ξ^{4}} (- ξ^{4} + \frac{ξ^{2} b^{2}}{4} - \frac{b^{4}}{16})$ K₁₁

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Tong Wu, Feng Tian, Leijing Yang. Few-Mode Fiber Transmission System Based on Probability Shaping and Interleaved Encoding[J]. Acta Optica Sinica, 2022, 42(7): 0706006

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