1. Introduction

Optical networks that carry more than 90% of global data traffic are currently developing towards to ultra-high-speed, ultra-large capacity, and ultra-long distance. As the structure of the next-generation optical network becomes more complex and diverse, eavesdropping or interception will become a serious problem for security. It is easy for Eve to monitor fiber-optic cables through bending, splitting, scattering, etc [1]. Therefore, it is necessary to explore advanced encryption methods to ensure the security of high-speed optical fiber transmission systems. In recent years, various advanced encryption methods have been proposed, including quantum key distribution (QKD) [2], quantum secure direct communication (QSDC) [3], optical chaotic encryption [4], quantum noise stream cipher (QNSC) [5], etc. Among these methods, QKD combined with one-time-pad (OTP) is considered to be the only known way to achieve absolute security. However, OTP requires that the length of plaintext must be the same as the length of the key, so the transmission rate of the system is limited by the key rate (e.g. kbit/s) [6]. On the other hand, in the QKD system, photons carrying key information are prepared at the single-photon level and will be mostly scattered and absorbed by the transmission channel. Meanwhile, in order to ensure quantum security, photons cannot pass through classical optical amplification, thus the loss is the main reason to limit its transmission distance [7]. Unlike QKD which mainly completes the negotiation of keys, QSDC has ability to estimate the secrecy capacity of a realistic quantum channel and transmit information in a channel with eavesdropping. Unfortunately, QSDC also requires photons at the single-photon level and there is also considerable loss in the transmission process. The transmission rate and distance of QSDC are limited to few kbit/s and 100 km. As for optical chaotic encryption, it applies the nonlinear dynamics of physical components to generate an optical chaotic carrier for information encryption in a classical channel. The highest record of the reported optical chaotic encryption is about tens of Gbit/s over 100 km. However, it is very difficult to achieve synchronization between the transmitter and the receiver in a high-speed and long-distance system [8]. Meanwhile, in order to generate large bandwidth chaotic sources, dedicated devices and transmission links are required. QNSC realizes secure transmission in the classical channel through digital encryption and noise masking. Digital encryption can be realized through the Y-00 protocol [9]. After digital encryption, the plaintext of low-order modulation format (e.g. 16QAM) can be mapped to an ultra-dense high-order (e.g. 65536QAM) ciphertext. When the optical power reaches the mesoscopic level, the ultra-dense high-order ciphertext is affected by the coherent state quantum (shot) noise [10]. At the same time, amplified spontaneous emission (ASE) noise introduced by an Erbium-doped fiber amplifier (EDFA) plays a positive role in preventing Eve from identifying the correct judgment threshold. Therefore, the quantum noise and ASE noise will mask the ciphertext together. As we mentioned, QNSC does not need to use additional devices and its transmission link is compatible with the current high-speed optical communication systems. Therefore, QNSC has great advantages in realizing high-speed and long-haul secure optical communications.

In recent years, three QNSC encryption schemes have been proposed, including the intensity modulation (IM)/QNSC [11–13], the phase modulation (PM)/QNSC [14–16], and the QAM/QNSC [6,17–19]. Combined with the low cost and simple construction of intensity modulation and direct detection (IMDD) technology, IM/QNSC scheme has been experimentally verified in a 100-Gbit/s IMDD transmission system over 100-km standard single-mode fiber (SSMF) [13]. Although PSK/QNSC scheme can easily achieve long-distance transmission [14–16], the transmission rate is only limited to tens of Gbit/s. But so far, these two schemes have not been able to take into account both high-speed and long-distance at the same time. In 2014, M. Nakazawa et al. employed amplitude and phase encryption of the light beam simultaneously to present a QAM/QNSC scheme. Currently, the QAM/QNSC scheme has been proven in various high-speed (≥100-Gbit/s) long-distance (≥100-km) transmission systems by combining with polarization division multiplexing (PDM) and coherent detection.

In 2016, G. Böcherer et al. proposed a probabilistic shaping (PS) method based on a constant composition distribution matcher (CCDM) [20]. A large number of simulation and experimental results show that the probabilistic shaping modulation formats have a significant improvement in the achievable transmission rate and distance compared with the traditional modulation formats applied at optical fiber transmission systems [21–23]. In this paper, we introduce probabilistic shaping to the QAM/QNSC secure transmission systems for further improving transmission performance. In the transmitter, we first generate a PS-16QAM signal by CCDM. Then based on Y-00 protocol, the basis symbols are encoded and converted from the original low-order modulation format PS-16 (2²× 2²) QAM to the ultra-dense high-order PS-65536 (2⁸× 2⁸) QAM. The experimental results show that the 201.6Gbit/s PDM-PS-65536QAM/QNSC system can achieve 520 km transmission under 7% hard-decision forward error correction (HD-FEC) threshold (BER = 3.8 × 10⁻³) and 1200 km under 20% soft-decision (SD) FEC threshold (BER = 2.4 × 10⁻²), respectively. To the best of our knowledge, the experimental results achieve the largest rate-distance product record for the QAM/QNSC secure transmission systems, as indicated in Fig. 1. Note that the encrypted ultra-dense high-order signal in this work is PS-65536 (2⁸× 2⁸) QAM limited by the arbitrary waveform generator resolution (Keysight M8195A with 8 bits resolution). As the resolution increases to n-bit, the QNSC system can generate PS-2ⁿ× 2ⁿ QAM signals to further improve the security.

 

Fig. 1. Transmission distances and single-channel line rates of QNSC transmission experiments in recent years.

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2. Principle

Figure 2 shows the generation process of ultra-dense high-order PS-QAM signal based on the Y-00 protocol. In the QNSC scheme, the seed key is often shared in advance between the transmitter (Alice) and the legal receiver (Bob). At present, there are a lot of solutions to realize key distribution such as algorithm-based key distribution, classical physical key distribution and QKD. Alice uses the seed key to drive two pseudorandom number generators (PRNGs) for generating two key streams. One is to encrypt the plaintext bits, and the other is used as bit basis states to randomize the location of constellation points. After bit encryption, the ciphertext bits are first divided into I and Q bits, and entered into the CCDM module, which can achieve probabilistic shaping operation. After that, the amplitude distribution of PS-PAM4 (2 bits per symbol) of I and Q can constitute the PS-16QAM (4 bits per symbol). In order to simplify the Y-00 encryption and decryption, the symbol spacing of PS-PAM4 is redefined in the generation process. For example, if our goal is to generate ultra-dense high-order PS-2^(m + 2)× 2^(m + 2)QAM (2^(m + 2) bits per symbol) where m is the number of basis state, the amplitudes of I and Q components (PS-PAM-2^m + 2) are defined in the interval [-2^m + 2+ 1,2^m + 2-1]. Thus, the original amplitude [0, 1, 2, 3] of I and Q components (PS-PAM4) need to be redefined as [-2^m + 2+ 0 × 2^m + 1+ 1, -2^m + 2+ 1 × 2^m + 1+ 1, -2^m + 2+ 2 × 2^m + 1+ 1, -2^m + 2+ 3 × 2^m + 1+ 1], where the redefined minimum amplitude level is equal to that of PS-PAM-2^m + 2. Meanwhile, since each amplitude level of PS-PAM4 can be encrypted by 2 m basis states, the distance between two amplitude levels is 2^m + 1 after redefinition.

 

Fig. 2. The generation process of ultra-dense high-order PS-QAM.

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Subsequently, the bit basis states (B_b-I, B_b-Q) from PRNG_2 are converted into the basis symbol (B_s-I, B_s-Q) through binary-decimal mapping operation. Therefore, when the redefined PS-16QAM (I_data, Q_data) is encrypted by different basis states, the ciphertext (D_I, D_Q) can be obtained by adding (2×B_s-I, 2×B_s-Q) to (I_data, Q_data). With the random change of the basis states in each time slot, the original low-order modulation format can be encrypted into the ultra-dense high-order PS-2^(m + 2)× 2^(m + 2)QAM. For example, we consider converting a PS-16QAM constellation to a PS-1024QAM encrypted constellation. In this case, the bit number of basis state m is 3. The amplitude of the I and Q component (PS-PAM4) of the original PS-16QAM need to first redefine as [-31, -15,1,17]. Here, we consider using basis state (B_b-I, B_b-Q) = (010, 001) to encrypt the plaintext (I_data, Q_data) = (17, -15). After binary-decimal mapping, (B_b-I, B_b-Q) can be mapped into (B_s-I, B_s-Q) as (2, 1) so that the ciphertext (21, -13) can be obtained.

At the receiver side, the received ciphertext can be expressed as (D_I+ N_I, D_Q+ N_Q) where N_I and N_Q represent the influence of the quantum (shot) noise and ASE noise on I and Q components, respectively. The constellation of the received signal before Y-00 decryption is depicted in Fig. 3(a). For the legal receiver, Bob can get the same two sets of key streams as Alice. Therefore, Bob can use the basis symbol (B_s-I, B_s-Q) to decrypt the received ciphertext and obtain the plaintext (I_data+ N_I, Q_data+ N_Q) affected by noise. The constellation of the received signal after Y-00 decryption is depicted in Fig. 3(b).

 

Fig. 3. Constellations of received signal without (a) and with (b) Y-00 decryption.

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3. Experimental setup and results

The experimental setup for Y-00 QNSC optical fiber transmission system is shown in Fig. 4. In the digital signal processing (DSP) of transmitter, Alice generates the PS-16QAM signal by CCDM module and completes digital encryption through the Y-00 protocol. We insert one pilot symbol every 15 ciphertext symbols in the data sequence for estimating the laser phase noise. The overhead of pilot symbols is 6.25%. The light from a ∼3kHz narrow linewidth laser at ∼1550.1 nm is modulated by an integrated LiNbO3 I/Q modulator with 25 GHz bandwidth driven by two digital-to-analog converters (DACs) operating at 64GSa/s with 25 GHz analog bandwidth. After photoelectric modulation, the uniform 65536QAM (carrying 16QAM/QNSC) and four types (e.g. H = 3.4, 3.5, 3.6, 3.7) PS-65536QAM (carrying PS-16QAM/QNSC) optical signals can be obtained. Here, H is the information entropy. Note that the DAC (Keysight M8195A) has a nominal resolution of 8 bits, which gives a maximum of 2⁸ = 256 levels per quadrature. The PS-65536 (2⁸× 2⁸) QAM constellation by itself requires 256 levels, leaving no extra bit for Nyquist pulse shaping [6,24]. After signal modulation, a PDM emulator, which is composed of two polarization controllers (PCs), two variable optical attenuators (VOAs) and an optical delay line, is applied to obtain 199.8Gbit/s (27GBaud × 3.7 × 2), 201.6Gbit/s (28GBaud × 3.6 × 2), 199.5Gbit/s (28.5GBaud × 3.5 × 2), 204Gbit/s (30GBaud × 3.4 × 2) PDM-PS-65536QAM, and 200Gbit/s (25GBaud × 4 × 2) PDM-65536QAM. The optical power P_out is maintained at -10dBm which is a typical power level after an optical modulator [6]. The transmission link is composed of multi-spans SSMF whose dispersion parameter, attenuation, and nonlinear coefficient are D = 16.9-ps/nm/km, α=0.2-dB/km, γ=1.27-km⁻¹·W⁻¹, respectively. Fiber loss of each span is compensated using an EDFA with a noise figure of ∼5 dB. In our transmission system, optical polarization tracking is used to realize polarization demultiplexing, while the data-aided method can also realize the polarization demultiplexing operation in such systems. An optical band-pass filter (OBPF) in the link is used to filter out the out-of-band ASE noise. At the receiver terminal, the transmission signal and the LO are combined at the 90° polarization-and-phase diversity hybrid, and then photo-detected by the balanced photo-detector (BPD). The output electrical signals are sampled at 80GSamples/s by a real-time digital oscilloscope with 33 GHz electrical bandwidth. Finally, the digital signals are processed in the off-line digital signal processing module including IQ imbalance compensation, low-pass filter, chromatic dispersion compensation, timing equalization, carrier phase recovery, Y-00 decryption and BER calculation. For carrier phase recovery operation, Bob extracts the pilot and estimates the phase noise of pilots by the Viterbi-Viterbi algorithm [25].

 

Fig. 4. The experimental seup for Y-00 QNSC optical fiber transmission system.

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In Fig. 5(a), the BER curves of different information entropy (H = 3.4, 3.5, 3.6, 3.7, 4) signals under different signal-to-noise rate (SNR) conditions are calculated in the AWGN channel. The symbol rates of these signals in simulation are consistent with the experiment setup. Since the polarization multiplexing operation is not considered in simulation, the bit rate of these signals is half of the experiment. As shown in Fig. 5(a), without the influence of band-limited effect, the lower the information entropy is, the better the tolerance of noise is. Furthermore, we further calculate the BER curves of all five modulation format signals under the back-to-back experiment system, where the ASE module is applied to change the OSNR value which can be measured by the optical spectrum analyzer (OSA). As depicted in Fig. 5(b), the experiment results show that all PS signals have lower BER than the uniform signal at nearly the same bit rate. When H is set at 3.4 and 3.5, the BER performance is worse than that of H = 3.6 and H = 3.7. We consider that the limited bandwidth of the electrical components may be the main factor. When H is set at 3.6, the experiment system can obtain the best performance so that we choose the 201.6Gbit/s (28GBaud × 3.6 × 2) PDM-PS-65536QAM signals for experimental transmission.

 

Fig. 5. The BER curves under (a) the AWGN and (b) the back-to-back experiment system.

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In addition, we further analyze the probabilistic shaping gain under different launching powers. As shown in Fig. 6, the optimal launching power is located at around 1dBm. When the launching power increases beyond 1dBm, the influence of the nonlinear impairment (i.e. self-phase modulation) will be more serious, which leads to the performance gain of probabilistic shaping to decrease. Meanwhile, it further causes the BER performance of the probability shaping signals to be gradually close to that of uniform signals. This is mainly because probabilistic shaping has increased standard moments, which results in stronger nonlinear interference (NLI) than uniform signal in highly nonlinear regime [21]. Thus, the gain brought by probabilistic shaping will decrease with the launching power increasing. The constellations before and after decryption under 400 km transmission are inserted in Fig. 7(a) and (b). We further measure the BER performance under different transmission distances in Fig. 7(c), where the launching power is 1dBm. The experimental results show that our PS/QNSC scheme can achieve 520 km and 1200 km transmission under 7%HD-FEC and 20%SD-FEC thresholds, while the distance of uniform scheme is 240 km and 620 km, respectively. The improvement of ∼280 km and ∼580 km can be obtained by using the PS/QNSC scheme under 7%HD-FEC and 20%SD-FEC.

 

Fig. 6. The BER curves for Bob with different launching powers over 400 km transmission.

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Fig. 7. Experimental results of Y-00 QNSC system: the constellations (a) before and (b) after decryption under 400 km transmission; (c) the BER curves for Bob with different transmission distances.

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It is necessary to discuss the security of the PS-QAM/QNSC system. As shown in Fig. 4, we assume that Eve has access to the two best places (point A and point B) for tapping: i) point A, after data modulation and before the first EDFA, where the signal is mainly affected by quantum noise and the ASE noise is the smallest; and ii) point B, after the first EDFA where the OSNR is highest but the signal is corrupted by ASE noise. A ciphertext signal can be masked by noise when the modulation format is high enough. As shown in Fig. 8, the adjacent distance between two symbols decreases as the modulation level of ciphertext signal increases. When the adjacent distance is significantly low, noise can easily cover a large number of symbols.

 

Fig. 8. Noise-masked constellations of QAM/QNSC.

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The number of masked signals (NMS) of noise and the detection failure probability (DFP) are considered as two security evaluation criteria which have been applied in the reported QNSC schemes [13]. The NMS ${\Gamma _{\textrm{PS} - \textrm{UD - QAM}}}$ of ultra-dense high-order ciphertext can be defined as

For the encrypted PS-65536QAM signal, we have 256 encrypted I and Q levels normalized to ±1. Hence, the normalized decision level ${\Delta _{\textrm{PS} - \textrm{UD - QAM}}}$ of ultra-dense high-order ciphertext is defined by ${\Delta _{\textrm{PS} - \textrm{UD - QAM}}} = {2 / {(256 - 1)}}$. The average noise distribution ${\bar{\sigma }_{\textrm{PS - 16QAM}}}$ around the symbols for the decrypted PS-16QAM, which is defined as

After Y-00 decryption, the constellation of the plaintext affected by noise is depicted in Fig. 9(a), where N_I and N_Q represent the influence of the quantum (shot) noise and ASE noise on I and Q components. We take the 1^th constellation point as an example to calculate the noise variance $\sigma _{I,n}^2$ and $\sigma _{Q,n}^2$, and the other 15 constellation points are calculated accordingly. As shown in Fig. 9(a), the standard deviation $\sigma _{I,1}^{} = 0.1116$ and $\sigma _{Q,1}^{} = 0.1116$ can be obtained from the constellation of the plaintext affected by noise, thus ${\bar{\sigma }_{\textrm{PS - 16QAM}}} = 0.1115$ according to Eq.(2). Meanwhile, the NMS is 808 based on Eq.(1), while the DFP is 1-1/NMS = 0.9988. Note that these results are measured at point B with the received power of -6dBm.

 

Fig. 9. (a) The constellation after Y-00 decryption; the noise distribution of (b) I and (c) Q of the constellation.

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In order to analyze the masking performance of shot noise more clearly, we test the NMS and DFP of noise at point A where the signal is mainly affected by quantum noise and the ASE noise is the smallest. As depicted in Fig. 10(a), the NMS of noise in point A is about 830 when the output power of transmitter (considered as the received power of Eve) is -10dBm. Meanwhile, the detection failure probability is about 0.9988. If only a part of the optical power is tapped, then the masking number increases. The practical factor will significantly reduce the probability in real situations, and high practical security with irreducible security bounds based on shot noise can be achieved. Subsequently, the NMS and DFP of noise at point B (after the EDFA where the OSNR is highest but the signal is corrupted by ASE noise) under different received powers are calculated in Fig. 11. Since shot noise and ASE noise are employed to mask the ciphertext, the NMS and DFP are respectively about 840 and 0.99881 when the received power is -10dBm. Due to the influence of ASE noise, the NMS and DFP of point B will be higher than that of point A under the same received power. As the received power increases, ASE noise will play a major role so that the NMS and DFP decreased. Significantly, when the received power is 0dBm, the NMS and DFP are still at a high level about 720 and 0.9986. Thus, point B where ASE noise is the main noise is also considered safe. With the increase of transmission distance, the number of EDFAs is increasing so that the influence of ASE noise is more serious, which can ensure the security of the long-distance transmission system.

 

Fig. 10. (a) NMS and (b) DFP with different received powers of Eve at point A.

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Fig. 11. (a) NMS and (b) DFP with different received powers of Eve at point B.

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4. Conclusions

In this paper, we presented a PS-QAM/QNSC secure transmission scheme which uses the Y-00 protocol to convert the low-order modulation to ultra-dense high-order modulation, and then employs the physical randomness of noise to ensure high security of the encryption system. Since the DAC resolution is limited only with 8-bit, PS-2⁸× 2⁸QAM signal is generated in our experiments. As the resolution increased to n-bit, PS-2ⁿ× 2ⁿ QAM signal can be generated and the Y-00 QNSC system can achieve better security. The proposed scheme has been demonstrated in a PDM-PS-65536QAM system carrying a 201.6Gbit/s (28GBaud × 3.6 × 2) PDM-PS-16QAM signal transmitted over 520 km (7% HD-FEC threshold) and 1200 km (20% SD-FEC threshold) SSMF. After accounting for the FEC and pilot overhead, the net rate can reach 178Gbit/s (201.6Gbit/s/(1 + 7%FEC + 6.25%polit)) and 160Gbit/s (201.6Gbit/s/(1 + 20%FEC + 6.25%polit)) under 7% and 20% FEC threshold, respectively. To the best of our knowledge, the experimental results achieve the largest rate-distance product record for the QAM/QNSC secure transmission systems. We believe that the proposed PS-QAM/QNSC secure transmission scheme can be integrated into existing high-speed long-distance optical fiber communication systems.