## Abstract

We propose and experimentally demonstrate a proof-of-concept of a programmable optical transceiver that enables simultaneous optimization of multiple programmable parameters (modulation format, symbol rate, power allocation, and FEC) for satisfying throughput, signal quality, and latency requirements. The proposed optical transceiver also accommodates multiple sub-channels that can transport different optical signals with different requirements. Multi-degree-of-freedom of the parameters often leads to difficulty in finding the optimum combination among the parameters due to an explosion of the number of combinations. The proposed optical transceiver reduces the number of combinations and finds feasible sets of programmable parameters by using constraints of the parameters combined with a precise analytical model. For precise BER prediction with the specified set of parameters, we model the sub-channel BER as a function of OSNR, modulation formats, symbol rates, and power difference between sub-channels. Next, we formulate simple constraints of the parameters and combine the constraints with the analytical model to seek feasible sets of programmable parameters. Finally, we experimentally demonstrate the end-to-end operation of the proposed optical transceiver with offline manner including low-density parity-check (LDPC) FEC encoding and decoding under a specific use case with latency-sensitive application and 40-km transmission.

© 2017 Optical Society of America

## 1. Introduction

Advanced digital signal processing (DSP) including forward error collection (FEC) [1–4] enables high capacity fiber-optic transmission systems [5] when it is combined with coherent reception. In addition to the high capacity, the low latency on fiber-optic transmission systems is attracting attention in fields related to short reach and high capacity transmission, as it would be applicable for next-generation datacenter interconnection (DCI) among geographically distributed data centers in metro areas [6–8]. In this context, latency on digital coherent transceivers including the processing delay of FEC can be considerable part of the total latency in the physical layer. For example, optical signal transmission at the wavelength of 1550 nm over the standard single mode fiber (SSMF) of 25 km leads to a delay of approximately 122 μs [9]. In contrast, the delay generated on FEC decoding can range from 15 to 150 μs [9]. The latency of 25.5 μs with a G975.1-I.3 concatenated BCH decoder (throughput: 81.9 Gbit/s) from post-layout simulation in 90-nm complementary metal-oxide-semiconductor (CMOS) technology has been reported [10]. Thus, it seems that latency generated in the physical layer can be minimized by optimizing the algorithm of DSP including the FEC of digital coherent transceivers.

Flexible optical transceivers, which are optical transceivers with programmable parameters, show promise as a straightforward solution to control the parameters of DSP [11–19] and FEC [20–22]. However, such flexible optical transceivers have been mainly investigated in terms of the trade-off between reachability and throughput, not between throughput and latency.

In [23], we proposed a flexible optical transceiver that enables simultaneous optimization of multiple parameters (modulation format, symbol rate, power allocation, and FEC) for satisfying multiple requirements including throughput and latency. We call it the application-oriented programmable optical transceiver (AoPot). We demonstrated that the AoPot can remedy its coarse granularity of selectable modulation format by using the SNR tuning of each Nyquist-FDM sub-channel through different optical power allocations.

In this paper, we further extend the discussion in [23] with a multiple-parameter controller that consists of a precise analytical model and parameter constraints. First, we formulate the equations of constraints that must be satisfied for given requirements, namely, throughput, signal quality, and latency. Next, we established an analytical model including setup imperfection and determined the characterization of the implemented AoPot with dual polarization (DP) 4 quadrature amplitude modulation (QAM), 16QAM, and 64QAM formats. The analytical model can also predict correct BERs even with different power allocations between sub-channels. By combining the analytical model and the formulated constraints, we experimentally demonstrate the end-to-end operation of the AoPot under a specific use case with latency-sensitive application and 40-km transmission. In this demonstration, all transmitted bits were decoded by a low-density parity-check (LDPC) FEC decoder to determine required SNR for specified signal quality after FEC.

In section 2 of this paper, we present the concept and basic mechanics of the proposed AoPot including the constraints of the parameters and the analytical model. Section 3 describes the experimental setup and DSP algorithm of the AoPot. In section 4, we demonstrate the AoPot operation on the implemented optical transceiver by combining the analytical model and the constraints. We conclude in section 5 with a brief summary.

## 2. Concept of AoPot

#### 2.1 Overview of AoPot

First, we give an overview of the AoPot, as shown in Fig. 1. Unlike the existing flexible optical transceivers, the AoPot controls multiple programmable parameters of DSP and FEC to satisfy multiple given requirements simultaneously. The AoPot consists of two parts: an optical transceiver and an AoPot controller. The optical transceiver is implemented by optical/electrical components and DSP with the programmable parameters. The AoPot controller optimizes the programmable parameters of the optical transceiver by using the predicted performance of the optical transceiver with each set of the programmable parameters.

Specifically, a set of requirements for *i*-th application (*T _{i}, Q_{i}, L_{i}*) for

*i*= 1…

*N*(

*N*is the number of sub-channels) are given from the network controller to the AoPot controller.

*T*,

_{i}*Q*, and

_{i}*L*are throughput, required Q-factor after FEC at receiver side, and latency in the physical layer of the

_{i}*i*-th application, respectively. By means of the constraints checker in Fig. 1, sets of feasible parameters of the AoPot (modulation format, symbol rate, etc.) are selected in such a way that the sets of (

*T*) from all possible combinations of the programmable parameters of the AoPot are satisfied. The practical form of the constraints will be discussed in section 2.2. The constraints checker also uses calibration information of the optical transceiver to modify the analytical model (see section 2.2 for details). The constraints checker finds sets of feasible solutions that satisfy the given requirements in a space of the programmable parameters.

_{i}, Q_{i}, L_{i}If there are multiple feasible sets of the programmable parameters after the constraints checker has been conducted, objectives given by the network controller will be used to guide the optimization of the parameters. The objectives, such as “minimizing latency” or “maximizing throughput”, are realized in the solution selector.

Once a set of parameters is selected, the set of programmable parameters (modulation format, symbol rate, etc.) is deployed on the optical transceiver by the setting deployer. By using multiple sub-channels, the AoPot controller virtually divides the total resources of the optical transceiver into small portions and re-aggregates them [24,25]. The optical transceiver, which consists of a laser diode (LD), digital to analog converter (DAC), analog to digital converter (ADC), photo diode (PD), optical hybrid, and dual polarization (DP)-IQ modulator (IQM), is shown in Fig. 1. The AoPot controller can access all programmable parameters in the optical transceiver. The setting deployer sends the set of programmable parameters to the optical transceiver through the hardware abstraction layer. The optical transceiver can be implemented on commercial off-the-shelf optical/electrical hardware without any additional optical/electrical components except for moderate additional functionality in the DSP. Thus, the AoPot can enjoy a potential cost advantage in the hardware implementation.

#### 2.2 Constraints of the programmable parameters on AoPot

The increased controllability of DSP and FEC parameters in AoPot naturally comes with extra complexity of the programmable parameter management. In this section, we present formulations of the constraints between the requirements and the programmable parameters in the AoPot so that infeasible combinations of the parameters can be discarded. A set of feasible parameters satisfies Eqs. (1)–(3) for *i* = 1*…N*:

In Eq. (1), *s _{i}*,

*m*, and

_{i}*r*denote symbol rate, number of constellation points, and code rate of the

_{i}*i*-th sub-channel signal, respectively. A symbol

*m*represents the constellation size, e.g., 4 for QPSK and 64 for 64QAM. We assumed polarization multiplexing in Eq. (1). The parameter

_{i}*s*is restricted by

_{i}*i*= 1

*…N*, where

*R*is the total symbol rate. The

_{s}*m*, and

_{i}, s_{i}*r*are selected from a set of constellation sizes

_{i}*{m*symbol rates

^{(1)}…m^{(Nformt)}},*{s*and code rates

^{(1)}…s^{(Nsr)}}*{r*, where

^{(1)}…r^{(Ncr)}}*N*and

_{format}, N_{sr},*N*are number of selectable modulation formats, symbol rates, and code rates, respectively.

_{cr}In Eq. (2), we assumed a block code for FEC. *u _{i}* is the processing delay of decoding for one iteration in FEC decoder assigned for the

*i*-th sub-channel. Total processing delay by FEC decoding of the

*i*-th sub-channel is given by the product of

*u*and the number of FEC decoding iterations

_{i}*n*is determined by code rate

_{i}. u_{i}*r*symbol rate

_{i},*s*constellation size

_{i},*m*and FEC algorithm

_{i},*c*, which is a symbol representing different FEC algorithms.

_{i}*T*and

_{i}^{DSP}*T*are delay by DSP without FEC decoder and fiber transmission of the

_{i}^{Trans}*i*-th sub-channel, respectively.

In Eq. (3), *ε _{i}* is the occupied ratio for the

*i*-th sub-channel over total optical power

*P*addressed by a single AoPot. Optical power of the

*i*-th sub-channel

*p*is given by

_{i}*i*= 1

*…N. Δ*is the designed budget for penalty due to nonlinearity of fiber transmission and other imperfections. A function

*f*(·) in Eq. (3) denotes a function of

*s*,

_{i}*m*,

_{i}**= {**

*ε**ε*

_{1}…

*ε*

_{N}}, and OSNR to derive pre-FEC Q-factor of the

*i*-th sub-channel. A function

*g*(·) is a converting function from post-FEC Q-factor to pre-FEC Q-factor with the FEC decoder specified by

*c*,

_{i}*r*, and

_{i}*n*. Specifically, the function

_{i}*f*(·) can be calculated from the pre-FEC BER and the relationship between Q-factor and BER for

*i*= 1…

*N*:

*a*(

*m*) is the average number of nearest neighbors in the symbol constellation,

_{i}*d*(

*m*) is the minimum distance between two symbols, erfc(·) is the complementary error function, and

_{i}*B*is the bandwidth of ASE noise (12.5 GHz in this paper), for

_{n}*i*= 1…

*N*. A set of parameters (

*a*(

*m*),

_{i}*d*(

*m*)) = (2, 2), (3, 2/5(10)

_{i}^{0.5}), and (3.5, 2/7(7)

^{0.5}) were used for

*m*= 4, 16, and 64, respectively.

_{i}Generally, there are deviations between theory and actual measured results, especially in higher order modulation formats such as 64QAM. We therefore discuss and describe a practical formulation of pre-FEC BER estimation that includes these deviations due to limitations of the implemented transceiver. It is essential to establish an analytical model that includes setup limitations for finer control of the AoPot. In order to characterize the limitations, two parameters, *k* and *η*, are introduced in Eq. (7) with *i* = 1…*N* [26]:

*k*indicates the degree of imperfection of matching between receiver and transmitter, which induces a shifting of the BER curve. The parameter

*η*leads to an error floor at the high OSNR region, for example, due to cross-talk between adjacent sub-channels and component imperfection.

A function *g*(·) in Eq. (3) denotes a conversion function from required post-FEC Q-factor *Q _{i}* to pre-FEC Q-factor under condition with

*c*,

_{i}*r*,

_{i}*m*, and

_{i}*n*. Specifically, the function between pre- and post-FEC Q-factor can be obtained from FEC encoding and decoding simulation under additive white Gaussian noise (AWGN). Finally, all symbols used in Eqs. (1)–(8) are summarized in Table 1.

_{i}## 3. Experimental setup

The experimental setup, which consists of the AoPot controller and the optical transceiver, is shown in Fig. 2(a). The AoPot controller was implemented by Python and computed feasible sets of programmable parameters by the following procedure:

- 1. Find sets of feasible parameters {
*s*,_{i}*m*,_{i,}n_{i}*ε*} (_{ι}*i*= 1…N) by using the constraints of Eqs. (1), (2), and (3). - 2. If there are no feasible parameter sets in procedure 1, the given requirements are excessive for the current system.
- 3. If multiple feasible parameter sets are obtained, select a solution to maximize the given objectives.

As an example, we assumed a maximization of Q-margin from FEC threshold as the objective in this experiment to simplify discussion.

The optical transceiver consists of the transceiver hardware and AoPot DSP. At the transmitter, an external cavity laser (~25 kHz linewidth) was used as a light source for the channel at 193.3 THz. An indium phosphide (InP)-based dual polarization (DP) IQ-modulator was driven by the drive signals generated by four-channels DACs with a sample rate of 64 GSample/s, a physical resolution of 8 bits. The modulated signal was launched into a pure silica core fiber (PSCF, *Loss* = 0.163 dB/km, *A _{eff}* = 135 μm

^{2}, and

*D*= 20.9 ps/nm/km) and erbium-doped fiber amplifiers (EDFA). The fiber length was 40 km and fiber input power was set to 0 dBm.

At the receiver, the received OSNR was varied by additional noise loading after transmission. The local oscillator had a linewidth of ~25 kHz and was superimposed with the signal in a polarization-diversity optical hybrid. The outputs of the hybrid were connected to four balanced photo-diodes. The resulting signals were digitized by four ADCs with a sample rate of 40 GS/s and a bandwidth of 16 GHz. The digital samples corresponding to more than 4 million symbols were processed offline to ensure a sufficient error count for all tested BERs.

Block diagrams of DSP at both the transmitter- and receiver-side are shown in Fig. 2(a). In order to implement the AoPot concept on DSP, we introduced two techniques: (1) CW pilot-assisted carrier phase recovery (CPR) and frequency offset compensation (FOC) [27] to support any modulation formats and symbol rates of each sub-channel on the same DSP architecture, and (2) Nyquist filtered frequency division multiplexing (Nyquist-FDM) [28] for multitenancy of application-by-application sub-channels with different requirements.

For the CW pilot-assisted CPR and FOC, two CW pilots with different frequencies are inserted at the outermost sides on either of two polarizations. The CW-pilot to signal power ratio is set to –16 dB. To avoid cross-talk between sub-channel and CW-pilot, a *Pilot_GB* of 200 MHz was inserted. In between two CW pilots, we set multiple sub-channel signals denoted by no. *i* (optical bandwidth of signal no. *i* is denoted *s _{i}*) assisted by using a Nyquist-FDM technique, namely, digital spectral shaping, to reduce the spectral width combined with digital frequency offset of the sub-channel signals. The Nyquist-FDM was utilized with a roll-off factor of 0.01. A

*Data_GB*(guard-band between sub-channels) of 100 MHz was inserted to reduce cross-talk. Before the Nyquist FDM block, a power allocation block was inserted in order to address the diverse SNR margin among sub-channels with different modulation formats and FECs (see Fig. 2(b) for the schematic power spectrum). The power allocation block arbitrates SNR over all sub-channels while satisfying all requirements such as latency and throughput by adapting the allocated optical power of each sub-channel.

At the receiver side, the inserted CW pilots were separated in the digital domain and then used for FOC and CPR by utilizing the extracted phase information from the pilot. The pilots also enable rough polarization de-multiplexing at the receiver side. After these CW pilot-based DSPs, an adaptive equalizer implemented by 101-tap minimum mean square error (MMSE)-based butterfly-structured finite impulse response (FIR) filters was used for fine equalization of each sub-channel.

A log likelihood ratio (LLR) block calculated a posteriori probabilities from signals after AEQ of each sub-channel. The digital video broadcasting satellite second-generation (DVB-S.2) [29] -based LDPC code (length of 16,200 bits including 21.6% overhead) was implemented and used with various iterations from 1 to 15. The decoding parameters were tuned to satisfy requirements such as latency and received BER. For example, when an application requires reducing latency in the physical layer (for latency-sensitive application), a small number of iterations of the FEC decoder was selected to minimize processing delay.

## 4. Results and discussion

#### 4.1 Characterization of AoPot

In this section, we characterize the BER performance of the implemented AoPot described in section 3 to determine the parameters *k* and *η* in Eq. (8) in the two sub-channels case. The total bandwidth of the AoPot (16 GHz) was equally divided into two 8-GBd sub-channels. The modulation formats of dual polarization *m*-th quadrature amplitude modulation (DP-*m*QAM, *m* = 4, 16, and 64) was used.

First, we studied a case where each sub-channel has equal optical power for different combinations of modulation formats. The modulation format of sub-channel no. 1 was fixed to DP-4QAM and that of sub-channel no. 2 was varied from DP-16QAM to 64QAM (see Fig. 3(a)). Measured constellations of each modulation format at the OSNR of 31 dB are shown in Fig. 3(b). These constellations suggest that all signals ranging from 4QAM to 64QAM were successfully demodulated by using the DSP architecture described in section 3.

Figure 4 shows the experimentally measured BERs as a function of OSNR for each modulation format and sub-channel. Note that OSNR in this paper is defined by total signal power including CW-pilots and all sub-channels. Colored dashed lines in Fig. 4 show BERs predicted by Eq. (7) with *ε _{i}* = 0.5. The experimentally measured BERs deviated from the theoretical predictions by Eq. (7). These deviations can be explained by the limitations of the experimental setup. For example, the limited number of ADC/DAC bits affected the BER performance and lead to an error floor. Thus, we determined the values of

*k*and

*η*in Eq. (8) by best-fitting. By using the measured BERs with DP-4QAM, 16QAM, and 64QAM, we found the optimum value of parameters

*k*and

*η*to be

*k*= 0.917 and

*η*= 0.00248. Colored solid lines in Fig. 4 show BERs predicted by Eq. (8) with the determined

*k*and

*η*. These lines show excellent agreement between the predicted curve and the experiment results over all modulation formats.

Next, we experimentally confirmed the versatility of the determined *k* and *η* with optical power difference between sub-channels. An optical signal consisting of two 8-GBd DP-16QAM sub-channels was used for this evaluation. Measured optical spectra with several power differences between sub-channels are shown in Fig. 5 (resolution: 150 MHz). The CW pilot tone can be measured in these spectra. Figure 6 shows measured BERs as a function of OSNR with optical power differences between sub-channels ranging from 0 to 6 dB. The solid and dashed lines in Fig. 6 show the case of BERs calculated by Eq. (8) with the parameters *k* and *η* determined without power difference. That means the curves in Fig. 6 are not fitting curves. Figure 6 shows that Eq. (8) can estimate correct BERs even with power differences between sub-channels, thus demonstrating the effectiveness of the analytical model of the AoPot based on Eq. (8) for pre-FEC BER prediction of each sub-channel.

Next, we characterized the relationship between the input Q-factor and the output BER of LDPC FEC for 16QAM modulation format implemented in the AoPot at back-to-back. The optical signal used for this verification consisted of two 8-GBd DP-16QAM sub-channels without optical power difference. Note that the performance of FEC is dependent on the modulation format. We measured the post-FEC BER of sub-channel no. 1 as a function of the pre-FEC Q-factor calculated from the pre-FEC BER of sub-channel no. 1 with several numbers of decoding iterations and show the results in Fig. 7. Colored dashed lines show simulation results under additive white Gaussian noise (AWGN) and plot points show experimentally measured results. The difference of pre-FEC Q-factor was around 3.9 dB at the post-FEC BER of 10^{−5} over the number of iterations from 1 to 15. The inset of Fig. 7 shows the required pre-FEC Q-factors for achieving the post-FEC BER of 3.4 × 10^{−5} (i.e., Q = 12 dB) as a function of the number of iterations for the LDPC FEC decoder. When the number of decoding iterations increased, the required pre-FEC Q-factor decreased, but that was saturated around *N _{iter}* = 15.

#### 4.2 Demonstration of control on AoPot

Next, we used the analytical model established in the previous section to experimentally demonstrate a use case of the AoPot operation for satisfying the multiple requirements of various applications. We applied two applications for the AoPot: (i) a standard one and (ii) a latency-sensitive one. Applications (i) and (ii) were launched on sub-channels no. 1 and 2 of the AoPot, respectively. Equipment-related parameters were assumed to be *u _{i}* = 1.5 μs,

*T*= 9 μs, and

_{i}^{DSP}*T*= 200 μs for

_{i}^{Trans}*i*= 1, 2. Received OSNR was set to 17 dB. The same values of

*k*and

*η*determined in section 4.1 were used to include the limitation of the transceiver setup. System parameter

*Δ*was set to 0.5 dB. FEC algorithm

*c*(

_{i}*i*= 1, 2) was fixed to the LDPC FEC code based on the standard of DVB-S.2 with the fixed code rate

*r*(

_{i}*i*= 1, 2) of 37/45. The selectable values were restricted on the parameters of

*s*∈ {0.1, 0.2,…0.9} × 16 GHz,

_{i}*m*

_{i}∈{4, 16, 64}, 10 log

_{10}(

*ε*) ∈ {–6, –5,5, –5.0 … + 5.0, + 5.5, + 6}, and

_{1}/ε_{2}*n*

_{i}∈ {1, 2,…15}.

Under these assumptions, the AoPot controller aimed to find a feasible set of parameters {*s _{i}*,

*m*,

_{i}*ε*,

_{i}*n*} for sub-channels no. 1 and 2. Considering first an extremely simple case with the requirements of the

_{i}*i*-th sub-channel with

*T*= 100 Gbps, there was no candidate for a feasible parameter set because the maximum total throughput of the implemented AoPot is 158 Gbps, which is less than

_{1}= T_{2}*T*+

_{1}*T*. In contrast, we could find feasible parameter sets with the moderate requirements of (

_{2}*T*) = (50 Gbps, 12 dB, 240 μs) and (

_{1}, Q_{1}, L_{1}*T*) = (50 Gbps, 12 dB, 211 μs). The constraints checker can reduce the 455,625 combinations of {

_{2}, Q_{2}, L_{2}*s*,

_{i}*m*,

_{i}*ε*,

_{i}*n*} (

_{i}*i*= 1, 2) to 15 feasible parameter sets by applying Eq. (1), (2), and (3) in this use case. We can set the objectives to maximizing the minimum Q-margin over all sub-channels. After the solution selector, we had the solutions {

*s*,

_{1}*m*,

_{1}*ε*,

_{1}*n*} = {8e9, 16, 0.69, 1} and {

_{1}*s*,

_{2}*m*,

_{2}*ε*,

_{2}*n*} = {8e9, 16, 0.31, 15} for launching signals onto the AoPot. The both constraints checker and solution selector were processed by Python on a standard personal computer (Intel Core i5 processor and 10 GB RAM) within 40 msec.

_{2}In the following section, we experimentally verify the obtained parameter set from the AoPot controller by using the implemented AoPot transceiver. Figure 9 shows a feasible parameter space for (*T _{1}, Q_{1}, L_{1}*) = (50 Gbps, 12 dB, 240 μs) and (

*T*) = (50 Gbps, 12 dB, 211 μs) with {

_{2}, Q_{2}, L_{2}*s*,

_{1}*m*,

_{1}*n*} = {8e9, 16, 1} and {

_{1}*s*,

_{2}*m*,

_{2}*n*} = {8e9, 16, 15}. Residual parameter 10 log

_{2}_{10}(

*ε*) was varied from 0 to 6 dB. Vertical axis shows the Q-margin from the FEC threshold of each sub-channel. Colored solid lines and plots in Fig. 8 show the results obtained from the analytical model and the experiment, respectively. Filled and open plots were measured from experiments at back-to-back and after transmission, respectively. Considering the design margin

_{1}/ε_{2}*Δ*= 0.5 dB, an area that satisfies the requirements on both sub-channels no. 1 and 2 shows a feasible parameter area. Figure 8 shows that a parameter (

*ε*) corresponding to around 3.5 dB (i.e.

_{1}/ε_{2}*ε*≈0.69 and

_{1}*ε*≈ 0.31) would maximize the Q-margin for satisfying all required constraints.

_{2}Finally, we directly measured post-FEC BER with the parameter set of {*s _{1}*,

*m*,

_{1}*ε*,

_{1}*n*,

_{1,}s_{2}*m*,

_{2}*ε*,

_{2}*n*} = {8e9, 16, 0.69, 1, 8e9, 16, 0.31, 15} that was specified by the AoPot controller. Here, the requirements

_{2}*T*and

_{i}*L*were automatically satisfied by the chosen modulation format, symbol rate, code rate, and iteration number of FEC. The requirement

_{i}*Q*= 12 dB is satisfied with post-FEC BER < 3.4 × 10

_{i}^{−5}. Figure 9(a) and (b) shows the measured post-FEC BER of each sub-channel as a function of the received OSNR. With the power difference calculated in the AoPot controller (

*ε*= 0.69

_{1}*= 0.31), we found successful reception of both sub-channels no. 1 and 2 with OSNR < 17 dB. Note that the required OSNR of both sub-channels was almost the same even with different FEC performances of each sub-channel in this case thanks to the analytical model that predicted correct BER curves even with power differences. To highlight the effect of parameter optimization on*

_{,}ε_{2}*ε*, we added the BER of each sub-channel without power difference (

_{i}*ε*=

_{1}*ε*= 0.5) in Fig. 9(a) and (b). In cases without power difference, each sub-channel had different required OSNRs to satisfy the required

_{2}*Q*due to the different performance of the assigned LDPC FEC with different number of iteration for decoding. This indicates that the operator should assign a higher OSNR for a given link to realize simultaneous reception of both sub-channels. In other words, excess OSNR was provided for sub-channel no. 1 in the case without power difference. In contrast, when we assigned the specified power difference by the AoPot controller, each sub-channel had almost the same required OSNR for achieving the given requirement

_{i}*Q*We can thus operate the AoPot with a lower received OSNR by transferring the excess OSNR from sub-channel no. 1 to 2. Additionally, as Fig. 9(b) shows, our proposed scheme can be operated under a short reach transmission condition corresponding to a 40-km reach with the fiber input power of 0 dBm/channel.

_{i}.## 5. Summary

We have proposed a programmable optical transceiver that enables simultaneous optimization of multiple programmable parameters (modulation format, symbol rate, power allocation, and FEC) for satisfying throughput, signal quality, and latency requirements. The proposed optical transceiver also accommodates multiple sub-channels that transport different signals with different requirements. An analytical model to predict the correct pre-FEC BER was demonstrated with different modulation formats (DP-4QAM, 16QAM, and 64-QAM) and various power differences between sub-channels up to 6 dB. The constraints of the DSP and FEC parameters were derived to find feasible sets of the programmable parameters before optical signal deployment. As a proof-of-concept, we have experimentally demonstrated the end-to-end operation of the proposed optical transceiver with offline manner including low-density parity-check (LDPC) FEC encoding and decoding under a specific use case assuming latency-sensitive application on a DP-16QAM signal after 40-km transmission.

## Acknowledgments

We thank Mr. Kiichi Sugitani for implementing the FEC code and Mr. Hiroki Amaike for his experimental support. Further, we are grateful for inspiring discussions with Dr. Zhenning Tao and Dr. Liang Dou.

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