We transmit 250x100G PDM RZ-16QAM channels with 5.2 b/s/Hz spectral efficiency over 5,530 km using single-stage C-band EDFAs equalized to 40 nm. We use single parity check coded modulation and all channels are decoded with no errors after iterative decoding between a MAP decoder and an LDPC based FEC algorithm. We also observe that the optimum power spectral density is nearly independent of SE, signal baud rate or modulation format in a dispersion uncompensated system.
©2013 Optical Society of America
Increasing system capacity can help to reduce the cost per transported bit as the cost of the optical layer can be amortized over more capacity. The current record for total capacity per fiber core is 102.3 Tb/s over 240 km . For undersea applications much longer transmission distances are required posing much greater technical challenges. The previous capacity-distance record of 141 Pb/s•km was demonstrated by transmitting 198x100G over 6,860 km at 4 b/s/Hz  in the full C-band. Simultaneously increasing spectral efficiency (SE) and usable bandwidth (BW) is particularly challenging for long-haul coherent systems. For example, 4.7 Tb/s over 10,000 km transmission with 4.7 b/s/Hz SE has been reported using 16-Quadrature Amplitude Modulation (16QAM) over a limited 8 nm BW . Very recently, 30 Tb/s transmission over 6,630 km using 16QAM signals at 6.1 b/s/Hz SE was demonstrated using spectral shaping with digital-to-analogue converters (DACs) .
In this work we transmit 250 16QAM channels at 100G (104 Gb/s) over 5,530 km distance without DACs. We achieve 25 Tb/s capacity and a capacity distance product of 144 Pb/s•km with a SE of 5.2 b/s/Hz. We use single stage Erbium doped fiber amplifiers (EDFA) equalized to 40 nm (full C-band) in combination with large effective area, low loss pure silica core fiber spans. All channels decode with no errors using our single parity check (SPC) coded modulation and iterative decoding between a two symbol based soft-in/soft-output (SISO) maximum a posteriori probability (MAP) decoder and a low density parity check (LDPC) based forward error correction (FEC) algorithm. Finally, we compare our optimum power spectral density to previous work  and find that the optimum power spectral density is nearly independent of SE, signal baud rate or modulation format in dispersion uncompensated system.
A schematic of the transmitter is shown in Fig. 1 . We combine 250 lasers onto a 20 GHz frequency grid using two separate rails for odd and even channels. We add 4 additional external cavity lasers (ECL) for each rail which are tuned to 8 contiguous channels that replace coinciding lasers during the bit error ratio (BER) measurements. The bit pattern for the drive signal of the modulators is generated offline using digital signal processing (DSP) where the input information bit-stream (a truncated 218-1 PRBS) is demultiplexed (serial to parallel) into seven data streams that are independently encoded by seven identical LDPC encoders with rate 0.93 . The LDPC code used in this setup is of codeword length 32,000, girth 8 and column weight 4. The encoded bit streams are then multiplexed, interleaved and forwarded to a 7/8 rate SPC encoder and the resulting data is mapped onto the 16QAM constellation four bits at a time using Gray mapping. We use the encoded data to program a 4 channel pulse pattern generator (PPG) that drives our optical I/Q modulators at 16 GBd. To create the 4 level in phase (I) and quadrature (Q) drive signals, we combine the four outputs of the PPG two at a time with 6 dB power difference between the most significant bit and least significant bit using passive power combiners . No DAC or digital spectral shaping is used in our experiment. The drive signal for the second rail is generated in a similar fashion using the four inverted outputs of the PPG.
Each rail further comprises a pulse carving stage (RZ) and a polarization division multiplexing (PDM) stage where we split the signal into two equal parts, delay one part with respect to the other by ~100 symbols and recombine the two parts with orthogonal polarization using a polarization beam combiner (PBC) to create 128 Gb/s channels with 23% overhead and a net data rate of 104.16 Gb/s. To emulate four independent rails, we also de-correlate the nearest neighbors on both the odd and even channels using back-to-back 40 GHz optical interleaving filters (OIF) with a fiber delay. A 20 GHz OIF is added to each rail for pre-filtering and both rails are then combined with a third 20 GHz OIF. We transmit 250 PDM RZ-16QAM channels at all times during our transmission experiments.
The 16QAM receiver structure is shown in Fig. 2(a) as part of the loop setup schematic. The channels are first demultiplexed by a tunable optical band pass filter and by double passing through a 20 GHz OIF before the selected channel is mixed with a local oscillator in a polarization diversity 90° optical hybrid. The signals from the four balanced photo detectors connected to the optical hybrid are sampled at 50 GHz using a digital oscilloscope with 16 GHz analog BW. There are ~8 million bits used for the BER calculation from each data acquisition.
Our DSP algorithm first realigns the waveform and then performs chromatic dispersion compensation in the frequency domain. The resulting waveform is re-sampled with the recovered clock. We determine the intradyne frequency offset using the peak in the Fourier transform of the 4th power of the signal. Polarization demultiplexing, signal equalization and carrier phase recovery are carried out by adaptive butterfly finite impulse response filters with 15 taps using a modified constant modulus algorithm. After initial convergence, a decision-directed least-mean-square algorithm is applied to further optimize the performance. The demodulated data is then sent to a SISO MAP decoder two symbols at a time (Fig. 2(b)). The MAP decoder calculates the symbol log likelihood ratios (LLRs) of the two consecutive symbols based on the SPC codeword book. The two symbol LLRs are then passed to the bit LLR calculator to be prepared for LDPC decoding . The extrinsic information from the LDPC decoders (LDPCDs) is sent back to the MAP decoder as a priori information  to be used in the next iteration. The iteration starting at the MAP decoder and ending at the output of the LDPCDs is referred to as an “outer” iteration in contrast to the “inner” iterations required by the LDPCDs. We have previously shown  that the FEC algorithm used in this setup requires 5 outer and 10 inner iterations to provide a Q-factor threshold of 5.7 dB at a BER of 10−15. The positive feedback in the iterative process using a MAP decoder and independent LDPC engines, with LDPC code of column weight 4 and girth 8, eliminates any possible error flaring .
Figure 2 also shows a schematic of our circulating loop testbed. The transmission path consists of ten low loss 50-km spans (8.5 dB) with large effective area fiber (~132 μm2) and single stage C band EDFAs. The EDFAs are equalized to 40 nm BW and operate at 18 dBm output power which corresponds to an average power per channel of −6 dBm launched into the transmission fiber. We configure the 10 spans into a 503 km transmission loop that includes a gain equalization filter to correct residual gain error and a loop synchronous polarization controller (LSPC) to properly account for polarization dependent loss (PDL) and polarization mode dispersion (PMD) in the loop. The average fiber dispersion is 20.7 ps/nm/km at 1550 nm and the average differential group delay of the loop is ~1.5 ps.
3. Transmission results
Figure 3 shows performance vs. transmitter pre-emphasis curves at 1529.6 nm, 1547.4 nm and 1560.1 nm after 5,530 km transmission along with the noise loaded back to back performance of our 16QAM setup at 5.2 b/s/Hz SE. We achieve a minimum required OSNR of 14.6 dB at the FEC threshold which corresponds to an implementation penalty of 1.4 dB compared to the single channel theoretical limit. We change the pre-emphasis by varying the power of a group of 8 contiguous channels and plot the performance of the channel at the center of the group vs. received OSNR. Zero dB pre-emphasis (flat launch) corresponds to the nominal operating point of the loop with 17.3 dB average OSNR across all channels.
Similar to what is commonly observed in transmission using EDFAs with >30 nm BW, the short wavelength region is more noisy  for several reasons. First, the EDFA noise figure is wavelength dependent and higher in the short wavelength region for single stage EDFA. Second, the fiber loss exhibits a parabolic shape with minimum loss near 1575 nm resulting in higher loss in shorter wavelength region. Third, the Raman effect becomes significant at wide BW increasing the apparent loss in the short wavelength region even further. Therefore, to achieve a uniform OSNR over the wavelength range, more signal power is required in the short wavelength region and the short wavelength channels reach their nonlinear limit at lower OSNR. Therefore, the OSNR at the nonlinear limit in the short wavelength region is typically 1-2 dB lower as shown in Fig. 3. Furthermore, we observe a residual offset from the back to back curve at low transmitter pre emphasis. We believe that this offset is caused by broadband nonlinear interaction of the measurement channel with the rest of the 40 nm amplifier BW . The magnitude of this impairment depends on the amplifier BW, amplifier output power, and fiber characteristics. All above makes it difficult to extrapolate high SE transmission results obtained with narrow amplifier BW  to the full C band.
Figure 4 shows the mean performance for the same three channels as a function of distance at nominal power. The FEC limit is reached at the longest distance (7,500 km) for the longest wavelength channel measured (1560.1 nm). At this point the operating OSNR for this channel is ~1.5 dB lower than optimum (see Fig. 3). For full capacity measurement we choose a distance of 5,530 km to allocate some margin for Q fluctuations due to PDL. The recovered 16QAM constellation for Ch125 after 5,530 km is shown in the inset of Fig. 4.
Figure 5 shows the received OSNR (1 dB/div) and optical spectrum (5 dB/div) for 250 channels after 5,530 km transmission with flat launch (no transmitter pre-emphasis). In our experiment we purposefully tilt the gain of the test bed to achieve nearly equalized OSNR and Q-factor across the band. The received OSNR is constant within ± 0.5 dB at an average of 17.3 dB. As seen in Fig. 5, the optical power of short wavelength region is higher in order to achieve similar OSNR as in long wavelength region.
The result of the full loading experiment (again with no transmitter pre-emphasis) is shown in Fig. 6 . For each channel we report the polarization averaged BER converted to Q factor obtained from ten data acquisitions. This corresponds to ~80 million bits processed for each channel and more than 20 billion bits processed in total. An additional advantage of our SPC code is making our 16QAM receiver algorithms tolerant to cycle slips and no cycle slips were detected in all of the data. The average Q-factor of all 250 channels is ~6.5 dB with individual channels ranging from 6.2 dB to 6.8 dB. The whiskers show the best and worst recorded Q-factor out of the ten data sets for each channel and polarization to give an indication of performance variations with PDL. The lowest performance data set was measured with a Q-factor of ~5.9 dB.
All data sets are further processed with our FEC decoder and decoded with no errors within 3 outer iterations as shown in Fig. 7 . The total number of bits processed experimentally (20 billion) supports our expectation of no error flaring to at least BER = 5x10−11.
4. Optimum power spectral density
We also compare our optimum power spectral density (PSDopt) for PDM 16QAM to previous results from  for PDM QPSK in dispersion uncompensated systems. The procedure to find the PSDopt is detailed in . We find PSDopt ~18 mW/THz at the center of the transmission band. Figure 8 plots PSDopt vs. SE for 40G and 100G PDM QPSK  and our result for 100G PDM 16QAM. Within the experimental uncertainty, PSDopt is nearly independent of SE (from 1.2 to 5.2 b/s/Hz), nearly independent of baud-rate (12G, 16G, and 28G) and nearly independent of modulation format (PDM QPSK, and PDM 16QAM), as predicted in .
We successfully transmitted 250x100G PDM RZ-16QAM channels with 5.2 b/s/Hz SE over 5,530 km distance using 50 km spans of 132 μm2 fiber and single stage EDFAs equalized to 40 nm BW. We achieved a total capacity-distance product of 144 Pb/s•km. All channels were decoded with no errors after transmission using SPC bit interleaved coded modulation with iterative decoding between an LDPC based FEC algorithm and a MAP decoder, which allows us to get both high SE and good receiver sensitivity. Finally, we compared our optimum power spectral density to previous results for PDM QPSK and find that the optimum power spectral density is nearly independent of SE, signal baud rate or modulation format in dispersion uncompensated system.
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