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We transmit 160x100G PDM RZ 16QAM channels with 5.2 bits/s/Hz spectral efficiency over 6,860 km. There are more than 3 billion 16 QAM symbols, i.e., 12 billion bits, processed in total. Using coded modulation and iterative decoding between a MAP decoder and an LDPC based FEC all channels are decoded with no remaining errors.
©2012 Optical Society of America
1. Introduction
Digital coherent transmission technology has enabled access to high level modulation formats providing a dramatic increase in spectral efficiency [1]. However, as the spectral efficiency (SE) increases, receiver sensitivity decreases making high SE transmission particularly challenging for undersea systems with their extremely long transmission distances. Spectral efficiency up to 4 bits/s/Hz has been demonstrated over 6,000 km (transatlantic distance) using polarization division multiplexed (PDM)-QPSK with super Nyquist signaling [2] and super channel based transmission [3], and over 10,181 km (transpacific distance) using PDM-8QAM OFDM [4]. Recently, spectral efficiency is further improved to 4.7 bits/s/Hz over 10,181 km by transmission of 40x117.6 Gbit/s PDM-16QAM OFDM signals at 25 GHz channel spacing [5]. At SE > 5 bits/s/Hz, the maximum transmission distance achieved was 4,242 km with 8x80 Gbit/s PDM-16QAM OFDM [6].
In this work we present 160x104.2 Gbit/s single carrier PDM-16QAM transmission at 20 GHz channel spacing with 5.2 bits/s/Hz SE over 6,860 km. To the best of our knowledge, this is the first demonstration of SE beyond 5 bits/s/Hz at transatlantic distance. We use single parity check (SPC) coded modulation and a new iterative decoder 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 to improve receiver sensitivity to 5.7 dB input Q-factor. We decode more than 3 billion symbols (>12 billion bits) after transmission without remaining error.
2. Experiment
A schematic of the transmitter is shown in Fig. 1 . We combine 160 lasers onto a 20 GHz frequency grid using two separate transmitters for even and odd channels. We add 4 additional external cavity lasers (ECL) for each set of channels that are tuned to 8 contiguous channels and replace the coinciding lasers during the 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 (truncated PRBS 218-1) is demultiplexed (S/P) into seven data streams that are independently encoded by seven identical LDPC encoders (LDPCEs) with rate 0.93. The LDPC code used in this setup is shortened regular LDPC with codeword length of 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 (SPCE) 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 and quadrature drive signals, we combine the four outputs of the PPG two at a time with a 6 dB power difference between the most significant bit and least significant bit using passive couplers [7]. 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 multiplexing 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 Gbit/s channels with 23% overhead and a net data rate of 104.2 Gbit/s. Each rail is then pre-filtered with a 20 GHz optical interleaving filter (OIF) before combining both rails using a third OIF.
At the receiver the channels are demultiplexed by a tunable optical band-pass filter and by double passing an OIF before the selected channel is mixed with a local oscillator in a polarization diverse 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 electrical bandwidth. There are ~8 million bits used for the bit error ratio calculation from the acquired waveforms for each data acquisition. Our DSP algorithm first realigns the waveform, and performs chromatic dispersion compensation in the frequency domain. The resulting waveform is then 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 a modified constant modulus algorithm. The adaptive butterfly filters have 15 fractionally-spaced (T/4) taps. 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. 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 in a similar fashion as in [8]. The LDPC decoders (LDPCDs) calculate the extrinsic information after 10 inner iterations within the LDPCDs, and send it back to the MAP to be used as a priori information (as in [9]) for the next outer iteration between the MAP and the LDPCDs. In this scheme an “outer” iteration starts at the input of the MAP decoder and ends at the output of LDPCD. Final decision is made after 5 outer iterations. A schematic of our receiver DSP is shown in the inset of Fig. 2 .
To test the performance of our FEC scheme we run our setup in a noise loaded back-to-back configuration where we set the optical signal to noise ratio (OSNR) to achieve line Q-factors between 5 and 7.2 dB. Figure 2 shows the BER performance of our SPC bit interleaved coded modulation (BICM) with iterative decoding (ID) as a function of line Q-factor. With iterative decoding, the SISO MAP improves the Q threshold by 1.6 dB in the first iteration allowing the LDPC decoders to correct more errors. The extrinsic information from the LDPC decoders helps the MAP to further improve the Q threshold for the second iteration by 0.3 dB, and so on. The positive feedback in the iterative process as shown in the figure keeps improving the Q threshold with every iteration as the MAP helps correcting more errors, resulting in a steeper waterfall region in the LDPC code performance. In addition to improving the FEC threshold, using independent LDPC engines with positive feedback to the SISO MAP decoder eliminates any possible error flaring. The concept of error floor elimination by iterative decoding and reverse concatenation of LDPC codes with short FEC codes with small overheads is discussed in [10]. We estimate a decoder threshold of 5.7 dB at a BER 10−15 after 5 iterations similar to other high performance FEC codes for this overhead [11].
Figure 3 shows the noise loaded back-to-back performance of our 16QAM setup at 5.2 bits/s/Hz SE. We achieve a minimum required OSNR of 14.6 dB/0.1nm at the FEC threshold which corresponds to an implementation OSNR penalty of 1.4 dB compared to the theoretical limit.
3. Transmission results
Our transmission path consists of twelve 52 km spans of large effective area fiber (~150 μm2) and single-stage C-band Erbium doped fiber amplifiers (EDFAs). The EDFAs are equalized to 26 nm bandwidth and operate at 17 dBm output power which corresponds to an average power per channel of −5 dBm launched into the transmission fiber. We configure 12 spans into a transmission loop of 624 km length including a gain equalization filter (GEF) 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 as shown in Fig. 4 . The average fiber dispersion is 20.6 ps/nm/km and the average differential group delay (DGD) of the loop is 1.7 ps.
Figure 5 shows the measured mean performance of a channel at 1,550 nm as a function of distance at nominal power. The FEC limit is reached slightly beyond 8,000 km. For our capacity measurement we choose a transmission distance of 6,860 km to allow some margin for Q-fluctuations due to PDL. The recovered 16QAM constellation after 6,860 km is shown in the inset of Fig. 5.
Fig. 5 Transmission performance at 1,550 nm. The inset shows the recovered constellation after 6,860 km.
Figure 6 shows the received OSNR and received spectrum for 160 channels after 6,860 km transmission distance. Average OSNR is 17.3 dB/0.1nm. The result of the full loading experiment is shown in Fig. 6. For each channel we report the polarization averaged BER converted to Q-factor obtained from ten data acquisitions. An additional advantage of our SPC code is making our 16QAM receiver algorithms cycle slip tolerant and no cycle slips were detected in all of the data in this experiment. For each channel we also show the best and worst recorded Q-factor out of the ten data sets for each polarization as error bars to give an indication of performance variations with PDL. All data sets are further processed with our FEC decoder and decode to error free within 2 outer iterations.
We observe that a margin improvement could have been achieved by FEC encoding both polarization tributaries together. To illustrate we calculate the polarization averaged Q-factor (BER average) for each measurement, subtract the mean Q-factor (BER average) of all 10 measurements for the channel and plot the result in a normalized histogram in the inset of Fig. 7 (green triangles). For comparison we also plot the histogram of the Q difference between each polarization measurement and the mean Q-factor of the channel in the histogram (red squares). An additional 0.4 dB margin can be achieved by fast polarization scrambling within one FEC frame [12], two polarization super-symbol method [13], or FEC encoding both polarization tributaries together.
Fig. 7 Performance at 5.2 bits/s/Hz SE after 6,860 km. The inset shows Q-factor fluctuation distributions for separate and combined polarization tributary processing.
4. Conclusions
We successfully transmit 160x100G PDM RZ 16QAM channels with 5.2 bits/s/Hz SE over 6,860 km distance using 52 km spans of 150 μm2 fiber and single-stage EDFAs. We achieved a total capacity-distance product of 114.4 Pb/s•km. This result is enabled by a new single parity check bit interleaved coded modulation scheme with iterative decoding between a low density parity check code and a maximum a posteriori probability decoder, which allows us to get both high spectral efficiency and good receiver sensitivity.
References and links
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