Digital All-Optical Physical-Layer Network Coding

Network coding (NC) has recently attracted intense research focus for its potential to provide network throughput enhancements, security and reduced network congestions, improving in this way the overall network performance without requiring additional resources. In this chapter, the all-optical physical-layer network coding (AOPNC) technique is presented, focusing on digital encoding schemes that are based on optical XOR logical gates. It is also discussed how digital AOPNC can be implemented between subcarrier-modulated (SCM) optical signals in radio-over-fiber (RoF) networks, circumventing the enhanced complexity arising by the use of SCM signals and the asynchrony that might exist between the data arriving at the encoding unit. AOPNC demonstrations are described for simple on/off keyed (OOK)-SCM data signals, as well as for more sophisticated higher-order phase modulation formats aiming to further improve spectrum efficiency and transmission capacity.


Introduction
The explosive data traffic growth in combination with the increasing use of smart mobile devices has created the need for high-throughput wireless access networks at Gb/s scale [1,2]. In this context, radio-over-fiber (RoF) networks have recently stepped in as a promising solution to satisfy this demand by seamlessly converging the ubiquity and mobility of the "last-meter" wireless networks with the high capacity of backhaul optical networks [3,4]. Up to now, there are several RoF signal generation and modulation schemes [5,6] as well as advanced functionalities 10 GHz SC. For validation purposes, the optical encoding operation is further evaluated by deploying a second MZI-XOR gate to decode the signal and retrieve the original information.
To extend the use of this concept in more sophisticated modulation formats and in mm-wave communications [6,7,27], a digital AOPNC scheme for 60 GHz SCM DQPSK signals was also investigated with physical-layer simulations for a bit rate equal to 4Gb/s. The all-optical encoder, residing in the central office (CO), consists of a delay interferometer (DI) stage for the DQPSK-to-OOK conversion, a stage of SOA-MZI-based OOK-XOR gates followed by the SOA-MZI-based phase regenerator [28,29] that forms the phase-encoded signal. A remote 60 GHz oscillator wavelength feeder is also incorporated in the NC unit to generate an additional wavelength spaced by 60 GHz to the encoded signal wavelength for allowing up-conversion through the beating at the receiver site [30]. An electrical XOR decoder was used in the simulations, emulating the decoding operation that would normally be performed at the wireless users' site, assuming wireless transmission by the RAU to the wireless user.
The rest of the chapter is organized as follows: Section 2 presents the proposed AOPNC-RoFbased conceptual scheme; Section 3 includes the setup and the results for the coding between two OOK-SCM signals; Section 4 presents the AOPNC setup and results for the DQPSK-SCM signals. Finally, conclusions are addressed in Section 5. Figure 1 illustrates the proposed AOPNC-based RoF network, comprising the NC unit at the CO and the two wireless end users communicated with the respective RAUs, which in turn are connected with the CO via a fiber. Users A and B transmit their packets to the RAUs, where they are converted to SCM optical streams through the modulation of the laser diodes (LDs), coupled together and forwarded to the CO through the optical media. The physical layer all-optical XOR-encoding operation is performed on the fly at the CO and the resultant signal is broadcasted back to both RAUs, de-multiplexed from the uplink traffic and converted from optical-to-electrical (o/e) by means of a photodiode (PD). The electrical encoded signal is transmitted from each RAU to the respective wireless user in  order to be decoded. Each user recovers the bit sequence originating from the other user by performing a second XOR function between its own locally stored data and the received NC-encoded data. In this way, the AOPNC technique implemented at the CO is capable of encoding information coming from users located in different cells, which is not feasible with current wireless NC schemes. Figure 2(a) depicts the frame scheduling in an RoF network where no network coding is employed, as well as the frame scheduling in an RoF-NC-based communication scheme. In both cases, it is considered that for the uplink, RAU-A and B transmit data packets modulated on the wavelengths λ1 and λ2, respectively, while for the downlink traffic, the CO uses λ3. When network coding is not employed, RAUs transmit Data A and B to the CO during the first timeslot, while the CO receives both packets and forwards packet from user A to B and packet from user B to A, using two successive timeslots. When network coding is applied in an RoF network, then the CO encodes and broadcasts the NC-encoded packet to both users in a single timeslot, occupied only two timeslots for the uplink and downlink traffic. This concept exploits the pre-amble and post-amble of the frames [31] for packet order resolving in case of non-synchronized packets. Figure 2(b) shows the encoding and decoding operation when packets from user A and B reach the encoding unit at the CO bit level synchronized or with a time delay equal to Δt (asynchronous operation). In the case of synchronous operation, data from user A and B are digitally encoded by means of a SOA-MZI XOR gate and broadcasted to both users. Each user recovers the packet of the other user by performing a second bitwise XOR operation between the received encoded signal and its own data. Considering that the end users are wireless clients that may reside at different distances from their respective RAUs resulting even to sub-bit time mismatch between the two packets reaching the CO, it is critical for the AOPNC scheme to operate also for asynchronous data.

Concept overview
As shown in Figure 2(b), during asynchronous operation, a sub-bit optical pulse with duration equal to Δt is generated in the encoding packet. However, the final decoded packets from the second XOR operation can still be correctly recovered by both end users through a second XOR operation, without any data loss.

Digital all-optical physical-layer network coding for OOK-SC signals
3.1. Experimental setup Figure 3 shows the experimental configuration, exploiting two SOA-MZI gates, the first for the encoding process at the CO and the second for decoding XOR operation that in a realistic RoF is performed at the end user. The continuous wave (CW) signals at λ1 = 1549.8 nm, λ2 = 1553.1 nm and λ3 = 1553.6 nm were emitted by three tunable LDs (TLDs), multiplexed by an array waveguide grating (AWG) and modulated by an electro-absorption modulator (EAM) by a 10 GHz electrical clock signal for the SC generation. The output of the EAM was amplified by an erbium-doped fiber amplifier (EDFA) and de-multiplexed by means of an AWG. Signals λ1 and λ2 were further OOK modulated by two LiNbO 3 modulators, which were driven by a programmable pattern generator (PPG) loaded with 2.5 Gb/s NRZ 2 7 -1 pseudo random bit sequence (PRBS), so as to form the SCM-OOK uplink data A and B signals. These uplink signals were transmitted through spools of single-mode fibers (SMF) with lengths of 3.9 km and 4 km, emulating the uplink connections between the RAUs and CO. An optical delay line (ODL) was employed at the branch carrying the data B stream, in order to enable bit-level synchronization during synchronous operation and insert time offsets at the asynchronous operation. Stream λ3 was not modulated with data in order to emulate the SC produced at the CO and used for the downlink traffic. Variable optical attenuators (VOAs) and polarization controllers (PCs) were also employed for power regulation and polarization adjustments, respectively.
The data streams (λ1, λ2) were injected into the control ports A and D, while λ3-SC was applied at the port C of the SOA-MZI XOR gate 1. The input power levels were measured, 800 μW(−1 dBm) for λ1, λ2 and 400 μW(−4 dBm) for λ3. The SOA-MZI was biased in such a way so that port G acts as the switching port. Hence, when only one of the two data is present, a π shift between the two SOA-MZI branch signal constituents is obtained by cross-phase modulation (XPM) and λ3 emerges with a logical "1" at the output port G. Otherwise, when both data signals are equally present, then λ3 bears a logical "0", confirming the implementation of an all-optical XOR gate by means of an SOA-MZI. The output port of the first XOR encoding gate was filtered and launched into port D of the second SOA-MZI XOR gate, which  acts as a decoder. A part of data A was connected with port A for decoding data B, while a CW signal launches port C (λ4 = 1548.4 nm). Equivalently, when data A is decoded, data B is connected to port A of the second SOA-MZI. The input power levels were measured, −1 dBm for the control signals λ1, λ3 and − 4 dBm for λ4. SMF and ODL were used for pattern and bit-level synchronization. The output of the XOR2 gate was filtered by a 0.65 nm filter and monitored by an optical sampling oscilloscope (OSC).
The SOA-MZIs featured two 1600 μm long hybrid-integrated SOAs, both operating at a moderate current value of 180 mA. The SOA gain recovery value at driving conditions was 180 ps for both SOA-MZI XOR gates, significantly longer than the 100 ps period of the SC signal. In this way, the SOA-MZI response of both XOR gates is turned into a low-pass filtering [26], neglecting the high-speed sub-carrier of the optical control data A and B signals but correctly processing their data envelopes. Figure 4 presents the experimental results obtained for the synchronous encoding and decoding operations between two 2.5 Gb/s data streams. Figure 4(a) and (b) shows the input time traces of data A and B, respectively, while the XOR stream at the output of the first SOA-MZI is shown in Figure 4(c). The encoded stream features a logical "1" bit value when data A and B correspond to different bit values, while it is equal to "0" when the two data have the same logical bit value. Figure 4(d) and (e) illustrates the decoded data A and B at the output of the second SOA-MZI, after the XOR operation between the encoded signal and either the data B or data A, respectively. It should be noted that the decoded streams featured sub-bit dips between successive "1"s, resulting from the XOR operation when logical "1"s are generated by the transition from differential phase +π between the SOA-MZI branches to −π. However, the initial data patterns were retrieved successfully, confirming the successful decoded process at 2.5 Gb/s. Figure 4(f) and (g) depicts the eye diagrams of the input OOK-SCM data A and B, respectively. Figure 4(h) shows the eye diagram of the XOR-encoded signal at the output of the first SOA-MZI, exhibiting an extinction ratio (ER) of 9.6 dB and an amplitude modulation (AM) of 0.5 dB. Figure 4(i) and (j) illustrates the eye diagrams of the decoded data A and B, respectively, exiting the second SOA-MZI XOR gate. Both eye diagrams exhibit an ER equal to 8.2 dB and an AM equal to 1.2 dB.

Experimental results for synchronous operation
The successful encoding and decoding operations were also verified with the aid of bit error rate (BER) measurements. Figure 4(k) shows the BER curves carried out at various stages of the system. The BER curves reveal error-free operations for both decoded data signals, having a power penalty equal to 3.2 dB when compared with the initial OOK data signals at BER = 10 −9 . This power penalty is partially attributed to the SC modulation of data A and B, which introduces a power penalty of 2 dB. BER curves for the encoded XOR stream exiting the first SOA-MZI were also carried out for two cases: when the SCM-OOK DATA are directly inserted to the encoder without the use of extra fiber and when fiber spools of 3.9 km and 4 km are inserted between the OOK-SC data A and B and the first XOR gate in order to emulate the uplink connection. The power penalty between these two BER curves (with and without fiber) is negligible. By comparing the XOR curves with the OOK SCM data, the power penalty at 10 −9 is approximately 0.7 dB.

Experimental results for asynchronous operation
Possible asynchrony between the two data streams reaching the encoding unit was also examined by introducing various sub-bit temporal delays at data B, as may potentially be introduced by mobile wireless users. shows the decoded data A and B after the second XOR operation between the encoded pattern and the initial data pattern of data B or A, respectively. In this operation, both data A and B were successfully retrieved, with decoded data B having a delay equal to the time offset. The highlighted insets magnify the traces in a specific part of the stream where the asynchrony can be observed and the XOR signal appears to have "parasitic" pulses equal to the respective time offsets.
The successful asynchronous operation was also evaluated with BER measurements, by inserting various relative delays between the two data and measuring the error rate for the downconverted decoded signal.  DI1-u and DI2-v arms is set to 45 and −45° so as to recover the u-and v-constituents of data A and B, respectively. The u and v components correspond to the PRBS sequences before the differential encoding to I and Q bits as it is explained by Vorreau et al. [28].
The upper output port of each DI is connected with an AWG that de-multiplexes Data A and B signals, while the output of the DI's lower port is filtered by a band pass filter (BPF) with a center frequency equal to λ2 that keeps the OOK-SCM ¯¯ DataB and ignores the OOK-SCM data A. The OOK-converted streams are inserted into the control ports of the OOK-XOR gates based on SOA-MZIs and a continues wave λt (temp)=1555nm was inserted in their probe port. The data A-u and B-u are injected into the first SOA-MZI so as the OOK-XORu signal to be generated at the output switching port. The data A and ¯¯ DataB u -constituents are applied at the second SOA-MZI forming the OOK − ¯ XORu at the output of the switching port. Similarly, the OOK-XORv and OOK − ¯ XORv are obtained at the output ports of the third and fourth MZIs, respectively. All the OOK encoded signals are then filtered and driven to the phase regeneration stage where the amplitude-to-phase conversion is performed by means of two SOA-MZIs. Particularly, the OOK-XORu and OOK − ¯ XORu are inserted into the control port of the fifth SOA-MZI and a continues wave in λ3=1557.36 nm was launched in the probe input port. The relative phase in the SOA arms was controlled by a high-level bit either in the OOK-XORu or the OOK − ¯ XORu arm, forming in this way the phase-encoded signal between data A-u and B-u components [28,29]. Equivalently, the OOK-XORv and OOK − ¯ XORv streams are injected in the control arms of the lower SOA-MZI, forming the phase-and wavelength (λ3)converted XORv signal. The phase-formatted XORu and XORv output streams are filtered and recombined with a relative phase shift (PS) of 90° so as to form the four-level (4-L) phaseformatted XOR signal. Finally, the phase regenerator output at λ3 is coupled with a coherent CW at λ3+60GHz generated by the remote 60GHz oscillator (OSC) wavelength feeder [31]. The phase-formatted XOR signal is sent via SMFs of 4 km to the RAU receiver (Rx) where it  was converted to RF data by utilizing the beating at the PD [31]. The output is filtered by a BPF centered at 60 GHz and transmitted through an assumed wireless link to the user's Rx, where the electrical decoding is performed. Figure 7(a) presents the user's Tx which produces the DQPSK-SCM data signal. Each user's Tx comprises a PPG loaded with a 4 Gb/s NRZ 2 7 -1 PRBS, so as to form the electrical data.
A serial-to-parallel distributor is fed with the output stream of the PPG and synchronously splits it into the two output streams (u and v), each having a data rate of 2Gb/s, resulting in a total bit rate equal to 4 Gb/s. The DQPSK differential encoding unit converts the u-and v-constituents into the respective I and Q signals, which then are inserted into the electrical phase modulators (PMs) to modulate the 60 GHz signal coming from a local oscillator (LO). RF signals coming from the LO have a relative phase difference of 90°, so as the DQPSK-RF signal to be generated after the combination of the phase-formatted I and Q streams. constituents, while user B decodes the data A u and v streams. The synchronization of the NC encoding signals and the user's data is achieved by the use of a time delay (Δτ).
The simulations were carried out with the VPI photonics software suite [32], using as input the response of a custom-made SOA-MZI model [33] that matches the experimental measured response of a 1600-μm long hybrid-integrated SOA. The input power levels that were used were −1 dBm for the control signals and −4 dBm for the probe light, for all OOK SOA-MZIs. Both SOAs of the OOK-XOR and OOK − ¯ XOR MZI gates were driven by current values of 250 mA and had a recovery time of 100 ps, significantly longer than the 16.67 ps period of the 60 GHz SC. The SOAs of the phase regeneration XOR gates are driven by a 300 mA DC current and had an 80 ps recovery time. Figure 8 shows the time traces, eye diagrams and spectra obtained at various stages of the network coding-based 2 Gbaud RoF link during synchronous operation. The indicative patterns used for the simulation results are "1011111001" and "1010100110" for the u-and v-components of data A, while "1011010110" and "0100001100" were used for the data Bu and Bv components, respectively. Figure 8(a) and (b) shows the OOK-XORu and OOK-XORv time traces exiting the SOA-MZI-1 and SOA-MZI-3, respectively. Pulses are observed in the XOR streams, when data A and B constituents have different logical bit representations, while the power level is equal to 0 when data A and B exhibit the same logical value. The intensity and phase traces of the NC-phase-formatted stream at the output of the regenerator are shown in Figure 8(c). The intensity envelope reveals a constant "high" power level, with small duration sub-bit dips generated by the transition of the differential phase between the SOA-MZI-5 and SOA-MZI-6 branches from +90° to −90°. The phase time trace presents the NC phase-encoded resultant signal, whose optical phase φ can take one of the four values: [−135, 135,−45 and 45°], corresponding to the logical bit pairs: "XORu, XORv"= ["00", "01", "10" and "11"], respectively. The grey markers highlight the encoding scheme, where the absence of the OOK-XORu and -XORv pulses is imprinted as −135°, the XORv pulses as 135°, the XORu pulses as −45° and the existence of both XORu, XORv pulses as 45°. Figure 8(d) and (e) depicts the electrical OOK down-converted XORu and XORv streams at the output of the low-pass filter (LPF) in the end-user receiver. These traces confirm the successful conversion of the four-level phase-formatted XOR signal to two binary NRZ-OOK XORu and XORv streams.

Simulated results for asynchronous operation
In this section, the asynchronous operation was evaluated for different sub-bit time offsets between the two data signals. Figure 9 includes the time traces and eye diagrams of the asynchronous encoding and decoding operation for a time offset of 0.5 of the symbol time duration (250ps). Figure 9(a) shows the OOK-XORu stream, generated after the XOR operation between the data Au and the delayed by 250 ps data Bu constituents at the output of the SOA-MZI-1, while Figure 9(b) illustrates the OOK-XORv signal exiting the SOA-MZI-3. As it is highlighted by the grey markers, the data asynchrony generates sub-bit pulses and dips at the encoded streams, which are said to be "interrupted". Figure 9(c) illustrates the intensity and phase traces of the four-level phase-formatted XOR signal exiting the regeneration stage after the recombination of the binary phase-XORu and phase-XORv signals. The intensity trace exhibits a constant power envelope with small duration sub-bit dips generated from the transitions of the differential phase from +90° to −90° between the SOA-MZI-5 and/or SOA-MZI-6 branches. The phase trace shows the four different phase levels of the encoded signal, exhibiting sub-bit phase pulses and dips with a duration equal to 250 ps. Figure 9(d) and (e) depicts the XOR-u and XOR-v signals that were at the same time OOK-and down-converted by multiplying the received XOR streams with the respective in-phase 60 GHz signals generated by the LO at stage E.

Figure 9(f)-(j)
shows the eye diagrams of the asynchronous encoding process. Particularly, Figure 9(f) and (g) illustrates the eye diagrams of OOK-XOR-u and XOR-v streams for a temporal offset equal to 0.5, exhibiting an ER of 11.7 dB, an AM of 1.1 dB, a PO of 1.4 dB and a jitter of 25 ps. As shown, an intersection is observed at both eye diagrams after a time delay equal to 250 ps from the beginning of the pulse. This intersection that has a jitter equal to 21 ps is formed by both sub-bit pulse falls and risings during the asynchronous XOR operation. Figure 9(h) illustrates the intensity and phase eye diagrams of the NC-phase-encoding signal at the output of the regenerator. An intensity envelope with an AM of 1.8 dB and PO of 2.1 dB is shown, exhibiting sub-bit dips when the relative phase of SOA-MZI-5 and/or SOA-MZI-6 is changed from 90 to −90° and vice versa. The respective phase eye diagram shows the four different phase levels of the encoded signal, revealing a small phase fluctuation equal to 1.5°. The electrical eye diagrams of the down-converted OOK-XORu and XORv signals at the users' Rx are depicted in Figure 9(i) and (j), revealing an ER, AM, PO and a jitter equal to 9, 0.7, 0.9 dB and 32 ps, respectively.

Figure 9(k)-(r)
shows the time traces and eye diagrams of the asynchronous decoding operation. Figure 9(k) and (l) depicts the decoded data Bu and Au components after the digital XOR operation between the encoded pattern of XORu and the initial pattern either of data Au or data Bu at the users A and B Rx, respectively. Similarly, Figure 9(m) and (n) illustrates the decoded data Bv and Av at the user A and B receivers, respectively. In that operation, it is shown that despite the interruptions which appear as "parasitic" pulses or dips at the NC-encoded signals, both the components of data A and B were at the end correctly recovered with the decoded data B components having a delay equal to the time offset. Figure 9(o) and (p) depicts the eye diagrams of the decoded data Bu and Au, respectively, both exhibiting an ER of 8.7 dB, an AM of 1.1 dB and jitter of 40 ps, with short duration dips and spikes appearing after time delay equal to 250 ps from the beginning of the symbol. Similarly, Figure 9(q) and (r) shows the eye diagrams of the decoded data Bv and Av, reporting similar eye characteristics (ER=8.7 dB and AM=1.1 dB, jitter=40 ps).
The asynchronous decoding operation was evaluated by carrying out BER measurements. Figure 10(a) shows the BER measurements versus the received RF power, for the decoded Au and Bu streams, when the time offset between the two data is equal to 0.25, 0.5 and 0.75 of the symbol duration. All BER curves show error-free operations at 10 −9 . The BER curves reveal similar performance between synchronous and asynchronous operation, owing to the dips and spikes that were present at the edge of the pulse during synchronous operation being shifted within the duration of the pulses, however, without affecting the other pulse characteristics, such as ER, AM, PO, jitter and noise. Similarly, Figure 10(b) depicts the BER curves of the decoded Av and Bv streams for time offsets equal to 0τ symbol , 0.25τ symbol , 0.5τ symbol and 0.75τ symbol , showing error-free operations with negligible power penalty between the different BER curves. It is evident that the performance of the proposed AOPNC scheme remains similar even in the case of asynchronous packets reaching the network coder.

Conclusion
In this chapter, the concept of digital all-optical physical-layer network coding (AOPNC) was presented, targeting the future high-throughput radio-over-fiber (RoF) networks. In this scheme, the bitwise network coding (NC) is performed on the fly at the central office (CO) and the resultant packet is broadcasted at the wireless users, where the decoding takes place. The applicability of the AOPNC scheme between OOK-sub-carrier-modulated (SCM) data signals was confirmed by an experimental demonstration, employing a 10 GHz SC and an all-optical XOR gate as the digital NC encoder. An AOPNC scheme capable of performing the digital encoding and decoding between DQPSK-SCM data signals was also described. In this scheme the scenario of all optical encoding for 60 GHz SC used in mm-wave communications, followed by electrical decoding at the end users, was evaluated via physical-layer simulations. It should be noted that the described all-optical network Coding concept may in principle be applied also in RoF systems using DPSK-SCM and dual polarization (DP)-DQPSK-SCM modulation formats.