\section*{Acknowledgemets}
This work was supported by the European Research Council (ERC Starting Grant 'EnTeraPIC', number 280145), by the Alfried Krupp von Bohlen und Halbach Foundation, by Helmholtz International Research School for Teratronics (HIRST), by the Initiative and Networking Fund of the Helmholtz Association, by the Center for Functional Nanostructures (CFN) of the Deutsche Forschungsgemeinschaft (DFG) (project A 4.8), by the DFG Major Research Instrumentation Programme, by the Karlsruhe Nano-Micro Facility (KNMF), by the Karlsruhe School of Optics \& Photonics (KSOP), by the Swiss National Science Foundation (NCCR Nano-Tera, NTF MCOMB), by a Marie Curie IAPP Action and by the DARPA program QuASAR. Samples have been fabricated at the EPFL Center for Micro- and Nanotechnology (CMI).

\section*{Methods}

\subsection*{Experimental setup and ring resonator design.} 
The pump for Kerr comb generation is generated by an external-cavity laser (New Focus Velocity Model TLB-6728), a polarization controller (PC) and an erbium-doped fibre amplifier (EDFA) providing an output power of up to 37~dBm, see Fig.~\ref{Fig2}. The coupling loss between the lensed fibre and the Si$_3$N$_4$ chip amounts to approximately 3~dB per facet. In the data transmission experiments we pump a resonance near 1549.4~nm. The tunable fibre Bragg grating (FBG~1) at the output of the device suppresses the remaining pump signal by approximately 20~dB. The ring resonator consists of nearly stoichiometric Si$_3$N$_4$ grown in multiple layers with intermediate annealing steps \citep{levy2010}. The strip waveguides are patterned with electron beam lithography and transferred to the substrate by reactive ion etching with SF$_6$/CH$_4$ chemistry. The waveguides are then embedded into a SiO$_2$ cladding using low-pressure chemical vapour deposition (LPCVD). The waveguides are 2~\micro m wide and 750~nm high, and the sidewalls are inclined by 12$^\circ$ with respect to the vertical direction (Fig.~\ref{Fig2}, Inset 1). 

The high-temperature growth technique used to fabricate the 750~nm thick layers of stoichiometric Si$_3$N$_4$ requires annealing at 1200$^\circ$C. This makes it difficult to fabricate SiN resonators in the framework of standard CMOS processes. One option to overcome these limitations is to use dedicated fabrication processes and multi-chip integration as illustrated in Fig.~\ref{Fig1}. Alternatively, it is possible is to deposit Si$_3$N$_4$ at 400$^\circ$C and to use UV thermal processing (UVTP) at lower temperatures to reduce the defect density. Both techniques are subject to ongoing research.

In the first data transmission experiment, the resonator exhibits a free spectral range (FSR) of 17~GHz, and a loaded Q-factor of $8\times10^5$. Kerr combs are generated using an on-chip pump power of approximately 33~dBm. For the second experiment, we fabricated a resonator with a FSR of 25~GHz, which exhibits an increased Q-factor of $2\times10^{6}$. The comb is generated with approximately 29~dBm of on-chip pump power, and the measured line spacing deviates by less than 6~MHz from the designed 25~GHz. We expect that microresonators with further improved Q-factors will enable generation of broadband frequency combs with hundreds of lines that cover optical bandwidths of hundreds of nanometers - a multiple of what can be achieved with state-of-the-art distributed-feedback WDM laser arrays in InGaAsP technology. Note that in the envisaged system illustrated in Fig.~\ref{Fig1}, the use of FBG for pump light suppression will become superfluous: If the frequency comb is extracted by a second waveguide coupled to the ring resonator, direct through-coupling of strong cw pump light is not possible, and FBG notch filters are not needed.

\subsection*{Generation of low phase-noise Kerr combs.}
To obtain low phase-noise Kerr combs, the pump parameters are adjusted in two steps using the setup depicted in Fig.~\ref{Fig2}: First, the pump wavelength is periodically scanned across the resonance at a frequency of approximately 100~Hz while staying within the stop band of FBG~2 and continuously measuring the power conversion to the spectral region outside the stop band. During these scans the polarization of the pump signal is slowly varied to maximize the conversion. Maintaining this polarization, the detuning of the pump signal with respect to the resonance wavelength is then carefully adjusted until the initially broad RF spectrum (Fig.~\ref{Fig2}, Inset 3) exhibits a single narrow peak (Fig.~\ref{Fig2}, Inset 4). Note that the frequency axes of Insets 3 and 4 have different scales. The power spectrum of Inset 3 was recorded with a resolution bandwidth (RBW) of 10~kHz whereas Inset 4 was recorded with a RBW of 30~kHz. For an on-chip pump power of approximately 33~dBm the essential part of the optical comb spectrum is depicted in Inset 5 of Fig.~\ref{Fig2}. From this partial spectrum we selected the lines for our data transmission experiments. Spectra of the comb used for the second experiment can be found in the SI. 

The on-chip pump power needed for Kerr comb generation in the first and in the second experiment, still amounts to 33~dBm and 29~dBm, respectively. However, there is considerable room for future improvements - Kerr combs have been demonstrated with a threshold power as low as 50~\micro W in silica toroids \citep{haye2007}. In general, the threshold for Kerr comb generation scales inversely quadratic with the Q-factor of the resonator \citep{kippenberg2004a}. A 10-fold Q-factor improvement would lead to a reduction of the pump power by a factor of 100 and the 2~Watt pump laser could be replaced by 20~mW pump laser diode.

\subsection*{Feedback stabilization of a Kerr comb. }
To maintain low-phase noise comb states during an extended data transmission experiment, it is important to keep the pump conditions as constant as possible. In the first experiment, we found that the on-chip pump power is a crucial parameter and must be kept constant to approximately $\pm$5~\% to maintain thermal locking of the cavity resonance to the pump wavelength \citep{carmon2004}. The second experiment relies on stable comb generation for extended studies of data transmission performance. This is achieved by an independent control loop based on commercially available hardware (Melles Griot NanoTrak) that keeps the lensed fibres in the optimum coupling position. In addition, we implemented a second control loop using a commercially available PID controller (TEM Messtechnik LaseLock), which takes the power in the comb lines as feedback signal and controls the pump laser detuning such that thermal drifts of the resonator are followed by slight adaptation of the pump wavelength, see SI for a more detailed discussion. The combination of these two control loops enables stable Kerr comb operation over several hours without human interaction.

\begin{figure*}
\includegraphics[width=1\textwidth]{Fig5_comb_stable_setup.png}

\caption{\textbf{Generation and stabilization of a Kerr frequency comb in the second transmission experiment. a,} The experimental setup is similar to the one used in the first experiment, see Fig.~\ref{Fig2}. Due to an improved Q-factor, the pump power could be reduced which allows filtering of the ASE noise originating from the pump EDFA using a 2~nm band pass filter (BPF). The resonator (inset 1) exhibits a FSR of 25~GHz and a loaded Q-factor of $2\times10^{6}$. Using an on-chip power of 29~dBm, we pump a resonance near 1549.4~nm. The pump parameters are manually adjusted using the scheme described in the Methods Section. The insets on the right-hand side show the RF (top) and optical (mid and bottom) spectra of the resulting comb. For a stable comb output, we control the wavelength of the pump laser. As a feedback signal, we use the comb power $P_{comb}$ measured behind FBG~1. \textbf{b,} $P_{comb}$ (left axis, orange) and the total power $P_{tot}$ measured at the output of the chip (right axis, black) as a function of the detuning $\delta\lambda$ from the cold cavity resonance. The circle indicates the operation point of the control loop, which corresponds to the manually adjusted low phase-noise comb state. The control loop is activated after the pump parameters have been optimized. \textbf{c,} Feedback and wavelength control signal for a time frame of three hours. The pump wavelength follows the thermal drifts of the resonance, which leads to perfectly stable comb output power.}
\label{Fig5}
\end{figure*}



\subsection*{Signal impairment analysis. } 
In the first experiment, the optical carrier-to-noise-density ratio (OCN$_0$R) is limited by the ASE noise originating from the pump amplifier. To determine the OCN$_0$R, we need to estimate the noise power density right at the frequency of the respective comb line. This is done by averaging the spectral power densities obtained in the middle between two comb lines. The spectral power densities were measured with an optical spectrum analyser (Ando AQ 6317B) in a 0.01~nm bandwidth and renormalized to a bandwidth of 1~Hz.



\begin{figure*}
\includegraphics[width=1\textwidth]{Fig6_data_setup.png}

\caption{\textbf{Data transmission setup.} A tunable delay interferometer (DI) is used to separate the incoming frequency comb into carriers that belong to odd and even channels. The two sets of channels are then separately modulated at a symbol rate of 14~GBd using QPSK or 16QAM signals and Nyquist sinc-pulses. The two data streams are merged and fed into a polarization multiplexer (PolMUX), comprising a half-wave plate (HWP), a delay line and a polarization beam splitter (PBS). The PolMUX splits the optical signal in two parts, delays one of them to form two uncorrelated data streams, and recombines them on two orthogonal polarization states of the standard single-mode transmission fibre (SSMF). The receiver comprises an erbium-doped fibre amplifier (EDFA), an optical band-pass filter (BPF), and an optical modulation analyzer (OMA) with a tunable laser serving as a local oscillator (LO). Digital signal processing in the baseband is used to separate the WDM channels and to demultiplex the polarizations. Insets: \textbf{1,} Spectra of the unmodulated carriers after separation by the DI. Even channels are represented by the magenta solid line, odd channels by the red dotted line. The extinction ratio is better than 20~dB for all channels; \textbf{2,} Optical spectrum at the input of the OMA, after the 2~nm band-pass filter. The pronounced noise background predominantly originates from the ASE of the pump EDFA that is used for frequency comb generation. }
\label{Fig6}
\end{figure*}



To improve the signal quality, it is possible to filter out ASE by using a band-pass filter before the DUT as demonstrated in the second experiment. When performing the first experiment, however, we did not have any filters that could safely handle the 37~dBm of pump power right after the EDFA. We showed that by further optimizing the fabrication process, we can increase the microresonator's Q-factor and hence significantly decrease the required threshold power \citep{kippenberg2004a}, such that filtering of the pump signal was possible. In addition the comb may be extracted by a second waveguide which is coupled to the microresonator, see Fig.~\ref{Fig1}. This avoids direct transmission of broadband ASE noise transmitted through the resonator device. Using resonators with higher Q-factor, it might even be possible to use a high-power pump laser diode without requiring amplification at all.


\section*{Supplementary Information}

\subsection*{Feedback-stabilization of a Kerr frequency comb}

To maintain low phase-noise comb states during the second experiment, we have implemented a control loop that takes the power $P_{comb}$ measured at the output of FBG~2 as a feedback signal and adjusts the wavelength of the pump laser to ensure a constant detuning. Fig.~\ref{Fig5}a shows the comb generation setup along with the control loop. The principle of the feedback stabilization is illustrated in Fig.~\ref{Fig5}b, which shows $P_{comb}$ (orange trace, left axis) and the total chip output power $P_{tot}$ (black trace, right axis) as a function of the detuning $\delta\lambda$ between the pump wavelength and the resonance wavelength of the cold cavity. As the wavelength of the pump is scanned, it drags along the resonance through thermal locking. This leads to a continuous decrease of $P_{tot}$ until locking is lost for large detuning. At the same time, $P_{comb}$ exhibits a pronounced increase once the power coupled to the cavity reaches the threshold for Kerr comb generation. Our control loop is based on a commercially available PID controller (TEM Messtechnik LaseLock) and operates at the rising edge of $P_{comb}$. The circle in Fig.~\ref{Fig5}b indicates the operation point that corresponds to the low phase-noise comb state for which the pump parameters have been manually optimized before starting the control. Moreover, for stable comb generation, it is crucial that also the fibre-chip coupling efficiency is actively stabilized. To this end, we use an independent control loop based on commercially available hardware (Melles Griot NanoTrak) to keep the lensed fibres in the optimum coupling position. We confirm the functionality of the feedback stabilization by recording the feedback signal and the comb power for more than 3h, Fig.~\ref{Fig5}c. The pump wavelength follows the thermal drifts of the resonance, and residual comb power fluctuations are found to be well below 1~\%. Comb spectra measured at the beginning and at the end of the extended data transmission experiment are indistinguishable within the accuracy of our spectrometer (ANDO AQ 6317B).

\subsection*{Experimental setup for WDM data transmission}

To emulate a WDM communication system, we transmit data on all channels simultaneously, using one pseudo-random bit sequence (PRBS) on the even channels and another independent PRBS on the odd channels. Neighbouring channels hence carry uncorrelated data streams, and inter-channel crosstalk translates directly into a degradation of signal quality. For the first data transmission experiment, the corresponding setup is depicted in Fig.~\ref{Fig6}. Carriers belonging to odd and even channels are first separated by a tunable delay interferometer (DI) \citep{li2011}. The superposition of both spectra is displayed in Inset 1 of Fig.~\ref{Fig6}. Two home-built multi-format transmitters \citep{schmogrow2010} are then used to encode QPSK or 16QAM signals with a symbol rate of 14~GBd on the sets of even and odd carriers using independent PRBS with a length of $2^{15} - 1$. Polarization-division multiplexing (PDM) is emulated by splitting the optical signal, and recombining the original and a sufficiently delayed copy to form two decorrelated data streams on orthogonal polarizations. The data stream is transmitted to the receiver, where the signal is amplified, filtered and coherently detected using an optical modulation analyser (OMA, Agilent N 4391 A) with a standard tunable laser (Agilent 81680A) acting as a local oscillator (LO). An optical bandpass filter with a 2~nm passband is used to avoid saturation of the receiver photodiodes. Individual WDM channels are selected by appropriate choice of the LO wavelength and by digital brick-wall filtering in the baseband. Inset 2 of Fig.~\ref{Fig6} shows the optical spectrum at the input of the OMA. The effect of the 2~nm band-pass filter is clearly visible; the noise in the pass-band predominantly originates from the ASE of the pump EDFA that is used for frequency comb generation. 

For the second data transmission experiment, the setup differs only slightly from the one depicted in Fig.~\ref{Fig6}: Instead of the delay interferometer, we use a programmable filter (Finisar WaveShaper) to separate the comb lines, which additionally allows flattening the spectral envelope of the comb. Moreover, we only use QPSK as a modulation format, and increase the symbol rate to 18~GBd. In addition to back-to-back testing, we transmit the signal over up to four spans of 75~km standard single mode fibre (SSMF) with an EDFA set to an output power of 10~dBm before each span.

In both transmission experiments, digital post-processing comprises demultiplexing of the polarization channels, compensation of the frequency offset between the LO and the optical carrier, clock recovery, equalization, and dispersion compensation where applicable. For performance evaluation we use the error-vector magnitude (EVM) metric, which describes the effective distance of a received complex symbol from its ideal position in the constellation diagram. Provided that the signal is impaired by additive white Gaussian noise only, the EVM is directly related \citep{schmogrow2012a} to the bit-error ratio (BER). For 16QAM, we estimate a BER of $3\times10^{-4}$ from the measured EVM of 10~\%, which is in fair agreement with the measured BER of $7.5\times10^{-4}$. This confirms the validity of the EVM-based estimation of the BER in our experiment. For the other QPSK channels, the BER of $3\times10^{-7}$, $7\times10^{-8}$, $1\times10^{-8}$, $1\times10^{-11}$, and $5\times10^{-20}$ are estimated accordingly from the measured EVM values of 20~\%, 19~\%, 18~\%, 15~\%, and 11~\%. Channels 4 and 5 hence feature BER, well below the threshold of $10^{-9}$, which is commonly considered error-free in telecommunications. This clearly demonstrates that error-free data transmission with Kerr combs is possible and that the achievable BER is rather limited by the components of the transmission system such as modulators, amplifiers and filters than by the coherence of the light source.

Apart from the ASE of the pump EDFA as discussed in the Methods Section, we investigated coherent crosstalk as a potential source of signal degradation: In the first experiment, the tunable DI used to separate the carriers has a finite extinction ratio (ER), see Inset 1 in Fig.~\ref{Fig6}. As a consequence, the data signals of the even channels are superimposed by residual carriers modulated with odd-channel data and vice versa, which leads to further signal degradation. However, in our experiment this effect was not relevant: With an ER better than ($22.2\pm1.5$)~dB for all channels, no correlation of channel ER and EVM can be observed. In the second experiment using the programmable filter we achieve an ER of ($24.6\pm4.0$)~dB. Coherent crosstalk can therefore safely be excluded as a source of signal degradation.

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