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Optics Letters

High-security probabilistic shaping method via chaotic tagging

Qingwei Wang, Bo Liu, Jianxin Ren, Yaya Mao, Shuaidong Chen, xiumin song, Xiangyu Wu, JiYuan Wang, zining pan, Xian Lu, Mingqian Liu

Published Apr 17, 2026• 0 citations
Publisher

Abstract

This paper proposes a high-security probabilistic shaping 16-7QAM mapping method via constellation-level chaotic tagging. A novel, to the best of our knowledge, constellation-level chaotic tagging rule is devised that re-maps the original 16 signal points, each encoded by 4 bits, onto predefined 3-bit modulation symbols. Simultaneously, a Lorenz chaotic system is employed to generate a chaotic sequence, from which a 2-bit tag corresponding to each 3-bit modulation symbol is extracted to form the constellation-level chaotic tag. Subsequently, each signal point is combined with a 2-bit tag generated by a Lorenz chaotic system to form the final output consisting of 7 signal points. Experimental validation over a seven-core fiber transmission system shows that, at a bit error rate of 3.8 × 10 −3 , the proposed probabilistic shaping 16-7QAM constellation achieves a 0.49 dB improvement in receiver sensitivity compared with conventional 16-QAM. Moreover, the encryption scheme has almost no impact on the transmission performance of the probabilistic shaping signal itself. Additionally, the key space of the scheme reaches 10 105 , effectively ensuring physical layer security. The proposed method exhibits robust performance and strong security, enhancing both the transmission performance and security of the system.

DOI
10.1364/ol.588892

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This paper proposes a high-security probabilistic shaping 16-7QAM mapping method via constellation-level chaotic tagging. A novel, to the best of our knowledge, constellation-level chaotic tagging rule is devised that re-maps the original 16 signal points, each encoded by 4 bits, onto predefined 3-bit modulation symbols. Simultaneously, a Lorenz chaotic system is employed to generate a chaotic sequence, from which a 2-bit tag corresponding to each 3-bit modulation symbol is extracted to form the constellation-level chaotic tag. Subsequently, each signal point is combined with a 2-bit tag generated by a Lorenz chaotic system to form the final output consisting of 7 signal points. Experimental validation over a seven-core fiber transmission system shows that, at a bit error rate of 3.8 × 10 −3 , the proposed probabilistic shaping 16-7QAM constellation achieves a 0.49 dB improvement in receiver sensitivity compared with conventional 16-QAM. Moreover, the encryption scheme has almost no impact on the transmission performance of the probabilistic shaping signal itself. Additionally, the key space of the scheme reaches 10 105 , effectively ensuring physical layer security. The proposed method exhibits robust performance and strong security, enhancing both the transmission performance and security of the system.
A lossless key-accompanying transmission method based on noise-masked three-dimensional (3D) index mapping over four-core fiber is proposed. This scheme utilizes a four-dimensional (4D) chaotic model to mask the bits of the original data and orthogonal frequency division multiplexing (OFDM) symbols. Its initial value key is transformed into binary bits, and the error-free transmission of the key is ensured by periodic key repetition. And the masking of the key is achieved by introducing noise bits. In the process of constellation mapping, the 16 constellation points are divided into inner constellations and outer constellations. The traceless loading of the key is achieved by controlling the mapping rule using noisy key bits. A 115-kilometer four-core fiber transmission experiment of the noise-masked 3D index mapping method was successfully verified. The experimental results show that the difference between different cores of the four-core fiber is no more than 0.35 dB. There is almost no signal-noise ratio (SNR) penalty before and after signal encryption. The difference in sensitivity at the receiver is only 0.05 dB, which proves that this scheme can achieve lossless key transmission. As this scheme adopts the method of key repetition, it can ensure the correct demodulation of the key and the precise index of the constellation B. Compared with the traditional 16 quadrature amplitude modulation (QAM) signal, a sensitivity gain of 0.75 dB can be achieved. As for the illegal receiver, due to the lack of correct keys and encryption methods, the accuracy rate of key extraction is 0%, and the bit error rate (BER) remains at around 0.5. Even if the key index position is displaced by one bit, the BER will soar above 0.48. And through five repetitions, 100% correct recovery of the key at the legitimate receiver can be guaranteed. This scheme has excellent transmission effect and security, and can effectively guarantee the performance of the next-generation communication system.
We propose a chaotic spatial symbol transforming encryption method for enhancing the physical layer security in fiber-optic systems based on space-division multiplexed (SDM) transmission. The designed 3-D chaotic sequences are used to scramble the real and imaginary part of quadrature amplitude modulation (QAM) symbols, permute the symbol-to-space mapping, and control iteration times between the two processes. The encrypted transmission of 200 Gb/s per mode polarization-division-multiplexed 16QAM signals has been simulated over 1000-km two-mode fiber. The results show that the eavesdropper cannot recover the original information with a part of the security keys or a part of the transmitted signals when the iteration times are beyond 5. We found the error spreading phenomenon can be combined with the mode-dependent loss (MDL) to realize the system security enhancement. When eavesdroppers coupled signals out from SDM waveguide by bending-induced fiber tapping, they need reduce the bend radius to receive more spatial leak modes. The bending-induced fiber tapping inherently causes MDL. Although the error spreading phenomenon leads to bit-error-rate increasing by 1.3 dB than conventional 16QAM transmission, it will be a promising solution to overcome the weakness that the huge amount of data can be compromised by taping out the portion of the signal in single-mode transmission.
This paper proposes an odd-order quantum noise-like stream cipher scheme based on joint index modulation (JIM) constellation shaping. By utilizing subcarrier index modulation and dual-mode index techniques, additional information is transmitted through the combination distribution of silent subcarrier positions and constellation modes associated with subcarriers. An odd-order 9QAM signal is constructed, and by optimizing the index rule, constellation shaping is achieved while transmitting more information, increasing the distribution of constellation points within the signal. A 4D hyper-chaotic system is employed to implement multi-dimensional disturbances, including bitwise XOR of the original signal, subcarriers, symbols, and elevate the constellation order. Furthermore, the scheme performs upsampling on the chaotic system's initial values and actively introduces noise bits, which are appended to the initial signal as a basis state to enable key-accompanying transmission. Ultimately, the constellation-shaped 9QAM signal is escalated to a 576QAM signal with constellation shaping features. Experimental results demonstrate the successful transmission of a 2.94 Gb/s quantum noise stream signal over a 25 km single-mode fiber intensity modulation direct detection (IMDD) system. The experimental results show that the proposed JIM-576QAM1 signal provides a 0.7 dB gain at Forward error correction (FEC) = 3.8 × 10 −3 compared to random distribution of the two constellation modes. The proposed scheme maintains a bit error rate (BER) of 0 for key transmission, and abruptly increases to 0.5 in the event of misalignment, indicating a high sensitivity and accuracy of the system with respect to the key. At varying received optical power, the number of masked signal power remain consistent at 20480, and the detection failure probability stays around 1, demonstrating the stability and security of the proposed quantum noise stream encryption scheme. With a key space as large as 10 149 , the scheme can effectively counter brute-force attacks from unauthorized receivers. The proposed scheme exhibits high reliability and security, making it a promising candidate for future optical access applications.
In this article, we propose a high-security transmission scheme of power division 3-D carrier-less amplitude and phase (PD-3D-CAP) based on polling-permutation encryption and noise masking key distribution. By implementing the 6D Lorenz digital chaotic system, we scramble the 3D-CAP signal, effectively enhancing the security performance of the system. In our scheme, the proposed noise-masking key distribution can be considered noise-like and transmitted along with the chaotic encrypted signal in the channel. It is important to note that our mechanism also enables uninterrupted authentication and decryption at the receiver to handle continuous key updates. We experimentally demonstrate the transmission of a 12.67 Gb/s 3D-CAP signal over a 2 km 7-core fiber using the proposed scheme. The scheme allows for simultaneous key transmission without a significant increase in the bit error rate. Additionally, we compare the performance of the PD-3D-CAP scheme to that of the PD-2D-CAP scheme, and observe a sensitivity gain of 0.4 dB with the proposed PD-3D-CAP scheme.
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