428-Gb/s single-channel coherent optical OFDM
transmission over 960-km SSMF with
constellation expansion and LDPC coding
Qi Yang*, Abdullah Al Amin, Xi Chen, Yiran Ma, Simin Chen, William Shieh
Centre for Ultra-Broadband Information Networks and National ICT Australia
Department of Electrical and Electronic Engineering
The University of Melbourne, VIC 3010, Australia
*q.yang@ee.unimelb.edu.au
Abstract: High-order modulation formats and advanced error correcting
codes (ECC) are two promising techniques for improving the performance
of ultrahigh-speed optical transport networks. In this paper, we present
record receiver sensitivity for 107 Gb/s CO-OFDM transmission via
constellation expansion to 16-QAM and rate-1/2 LDPC coding. We also
show the single-channel transmission of a 428-Gb/s CO-OFDM signal over
960-km standard-single-mode-fiber (SSMF) without Raman amplification.
©2010 Optical Society of America
OCIS codes: (060 2330) Fiber optics communications; (060.1660) Coherent Communications
References and links
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band
multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.
S.L. Jansen, I. Morita, H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency
over 1,000 km of SSMF,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 2.
E. Yamada, A. Sano, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, K. Yonenaga, Y. Miyamoto, K.
Ishihara, Y. Takatori, T. Yamada, and H.Yamazaki, “1Tb/s (111Gb/s/ch × 10ch) no-guard-interval OOFDM
transmission over 2100 km DSF,” OECC/ACOFT Conf. 2008, paper PDP6.
S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a
digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007).
H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2),
873–879 (2008).
H. Takahashi, A. Al Amin, S.L Jansen, I. Morita, and H. Tanaka, “DWDM transmission with 7.0-bit/(s1Hz)
spectral efficiency using 8×65.1-Gbit/s coherent PDM-OFDM signals,” in Proc. Optical Fiber Commun. Conf.
2009, PDPB7.
X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM
transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
R. Dischler, and F. Buchali, “Transmission of 1.2 Tb/s continuous waveband PDM‐OFDM‐FDM signal with
spectral efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” in Proc. Optical Fiber Commun. Conf. 2009, PDP C2.
S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval
coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” ECOC’09, post-deadline paper PD2.6.
Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission
over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes
within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001).
I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for
ultra high-speed optical transmission,” IEEE/OSA, J. Lightwave Technol. 25(11), 3619–3625 (2007).
I. B. Djordjevic, and H. G. Batshon, Lei Xu and T. Wang, “Coded polarization-multiplexed iterative polar
modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. OFC/NFOEC 2010, Paper No.
OMK2, San Diego, CA, March 21–25, 2010.
I. B. Djordjevic, and B. Vasic, “Multilevel Coding in M-ary DPSK/Differential QAM High-Speed Optical
Transmission with Direct Detection,” IEEE/OSA J, Lightw. Technol. 24(1), 420–428 (2006).
M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Non-binary Quasi-Cyclic LDPC based coded
modulation for beyond 100 Gb/s transmission,” IEEE Photon. Technol. Lett. 22(6), 434–436 (2010).
I. B. Djordjevic, L. Xu, and T. Wang, “Beyond 100 Gb/s optical transmission based on polarization multiplexed
coded-OFDM with coherent detection,” J. Opt. Commun. Netw. 1(1), 50–56 (2009).
I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical
transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009).
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(C) 2010 OSA
Received 14 Apr 2010; revised 9 Jul 2010; accepted 15 Jul 2010; published 26 Jul 2010
2 August 2010 / Vol. 18, No. 16 / OPTICS EXPRESS 16883
18. T. Mizuochi, Y. Konishi, Y. Miyata, T. Inoue, K. Onohara, S. Kametani, T. Sugihara, K. Kubo, H. Yoshida, T.
Kobayashi, and T. Ichikawa, “Experimental demonstration of concatenated LDPC and RS codes by FPGAs
emulation,” IEEE Photon. Technol. Lett. 21(18), 1302–1304 (2009).
19. T. Mizuochi, “Next Generation FEC for optical communication,” Optical Fiber communication/National Fiber
Optic Engineers Conference, 2008. OFC/NFOEC 2008. Conference on, vol., no., pp.1–33, 24–28 Feb. 2008.
20. G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part I&II: Introduction,” Communications
Magazine, IEEE 25(2), 5–11 (1987).
21. H. Bülow, F. Buchali, G. Thielecke, ”Optical Trellis-coded modulation ”, in Proc. Optical Fiber Commun. Conf.
2004, WM5.
22. X. Liu, Q. Yang, S. Chandrasekhar, W. Shieh, Y. K. Chen “Transmission of 44-Gb/s coherent optical OFDM
signal with Trellis-cded 32-QAM subcarrier modulation”, in Proc. Optical Fiber Commun. Conf. 2010, OMR3.
23. D. J. C. Mackay, Ldpc database. Available at http://www.inference.phy.cam.ac.uk/mackay/codes/data.html.
24. A. Tychopoulos, O. Koufopavlou, and I. Tomkos, “FEC in optical communications - A tutorial overview on the
evolution of architectures and the future prospects of outband and inband FEC for optical communications,”
IEEE Circuits Devices Mag. 22(6), 79–86 (2006).
25. R. G. Gallager, Low Density Parity Check Codes, MIT Press, Cambridge, Mass., 1963.
26. D. J. C. MacKay, and R. M. Neal, “Near Shannon limit performance of low density parity check codes,”
Electron. Lett. 32(18), 1645–1646 (1996).
27. S. J. Johnson, S. R. Weller, “Low-density parity-check codes: design and decoding”, Wiley Encyclopedia of
Telecommunications, John Wiley and Sons, 2003.
28. Bernhard M. J. Leiner, “LDPC codes - a Brief Tutorial,” April 2005.
1. Introduction
Coherent optical OFDM has been actively pursued for long haul optical communications [1–
3], and currently is being investigated as an alternative to the single-carrier (SC) coherent
QPSK [4,5] for forthcoming 100 Gb/s Ethernet transport. Although compared to the SC
counterpart, coherent optical OFDM (CO-OFDM) requires higher complexity of high-speed
digital signal processing (DSP) elements at the transmitter, it brings the flexibility of adaptive
high-order modulation [6,7]. So far, this benefit was explored in realizing ultra-high spectral
efficiency transmission [6,7], but at the cost of significant increase in required OSNR limiting
the regeneration reach. In the mean time, it is widely believed that the 400 Gb/s or Tb/s
transport is poised to emerge in the next decade, and thus it is of great interest to study the
transmission aspects of the Terabit systems. Reports in [8–10] have already proposed and
demonstrated CO-OFDM as a promising pathway toward future Tb/s transport. Because one
of the key motivations for migration to 400 Gb/s or Tb/s transport is to lower the cost per bit,
it is of great important to improve the receiver OSNR sensitivity so that the optical signal can
be regenerated as less often as possible.
A key approach to improve the reach of these high-speed systems is the use of high
performance error correcting codes (ECC), among which low-density-parity-check (LDPC)
has been recently pioneered by Djordjevic and Mizuochi [12–19] in the optical
communication community. (LDPC) can achieve in theory as close as 0.0045dB to Shannon
limit [11]. Compared to the first and second generations of forward error correction (FEC),
LPDC as one of the main choices of the third generation FEC provides net coding gain
around 10dB (at BER=10−13) [19]. Increase overhead or use lower rate coding will further
improve the performance for LDPC codes, but it will also increase the bandwidth requirement
for optoelectronic components and therefore the overall cost as is true for many other codes
such as RS codes. So it is preferable that the coding gain can be achieved without increase of
the signal bandwidth. This was investigated by Ungerboeck in his seminal work on Trellis
coded modulation (TCM) [20]. TCM transmission has also been recently investigated for
optical communications [21,22]. In this report, following the similar spirit, we start with the
conventional system with 4-QAM of 2 bits/symbol modulation, and expand the constellation
to 16-QAM modulation of 4 bits/symbol that results in twice of data rate within the same
electrical and optical bandwidth. The extra data rate (50%) is then used for rate ½ LDPC
coding that results in the same net spectral efficiency as the conventional 4-QAM. The net
effective coding gain of rate ½ LDPC coded 16-QAM modulation over conventional 4-QAM
is demonstrated for the first time to the best knowledge of the authors, and the receiver OSNR
sensitivity of 12.5 dB at data rate of 107 Gb/s is found, which is a record sensitivity for 100
Gb/s transmission experiment. Finally, we show the first 400-Gb/s LDPC coded 16-QAM
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CO-OFDM transmission over 960-km SSMF without Raman amplification. The results of
this work show that CO-OFDM can be a potentially attractive candidate for 400 Gb/s or Tb/s
Ethernet long-haul transport over the installed link with the aid of high efficiency ECC. There
are two relevant categories of publications prior to this work: one is to improve the
transmission sensitivity by using stronger error correction codes, but requiring more overhead
and electronic bandwidth [18]; the other is high spectral efficiency transmission by using
higher order modulation, but requiring much higher OSNR and more stringent component
specifications such as high resolution for ADC/DAC [6]. Our approach distinguishes from
these two classes of the work in that we improve the sensitivity without a need for wider
electrical bandwidth, and stringent ADC/DAC resolution, which may lead to an attractive
solution for many applications.
2. Experiment setup and system configuration
The primary goal of this report is to demonstrate significant improvement of the receiver
sensitivity through the use of LDPC without requiring higher optoelectronic bandwidth.
Namely, we present a system design based on 16-QAM to provide coding overhead for
LDPC, achieving enhanced receiver sensitivity while maintaining the same spectral efficiency
of 3.3 b/s/Hz as the uncoded 4-QAM modulation [1]. For ECC, we choose LDPC in this work
as it provides flexibility of arbitrary rate coding compared to relatively rigid coding rate in
TCM. Figure 1 shows the system configuration for 400 Gb/s LDPC coded 16-QAM COOFDM system. Although longer block length can improve the coding performance, it also
increases the hardware complexity. We use the practical length of LDPC code that is close to
what have been demonstrated in real-time using state-of-art FPGA [17,18]. We use ReedSolomon codes as outer code to eliminate possible error-floor in LDPC [19]. The data is first
fed into RS (255, 239) and then the LDPC (4000, 2000) [23] encoder. In order to eliminate
the influence of burst-errors, an interleaver is placed between the two serially-concatenated
FEC codes [24], where the input signal is filled symbol by symbol, and output is sent
subcarrier by subcarrier. The encoded data are then fed into 16-QAM OFDM base band
generator to obtain digital OFDM time-domain signal, including procedures of serial-toparallel conversion, data mapping to 16 QAM constellation, IDFT and guard interval
insertion. The parameters for the OFDM baseband generation are as follows: 128 total
subcarriers; guard interval is 1/8 of the symbol period. Middle 102 subcarriers out of 128 are
filled, from which 4 pilot subcarriers are used for phase estimation. The middle two
subcarriers are fed with zeros, where the frequency signal and local lasers are located.
Polarization multiplexing doubles the raw rate to 53.3 Gb/s per band. After LDPC decoding,
the net data rate is 26.7 Gb/s (10 GHz · log2(16QAM) · 2 pols · 96) / (128 · 1.125GI)· 50%LDPC),
excluding the cyclic prefix, pilot tones, and unused middle two subcarriers. The real and
imaginary parts of the OFDM waveforms are uploaded into an AWG operated at 10 GS/s to
generate IQ analog signals, and subsequently fed into I and Q ports of an optical IQ
modulator respectively. The optical input to the optical IQ modulator is derived from a
recirculating frequency shifter (RFS), essentially a recirculating loop including an IQ
modulator and optical amplifiers [11]. A multitone-source is generated by using a CW laser
light replicated 16 times via the RFS [10], and is modulated into a 16-band CO-OFDM signal
after being driven by a complex electrical OFDM signal, carrying a data rate of 428 Gb/s. The
number of tones in the RFS is controlled by the bandwidth of the optical bandpass filter in the
RFS loop, and the RF tone frequency is 7.96875 GHz, phase-locked with the AWG using a
10 MHz reference clock. This is to ensure that all the subcarriers across the entire OFDM
spectrum are at the correct uniform frequency grids. There is no frequency guard band
between each sub-band. The optical OFDM signal from the RFS is then inserted into a
polarization splitter, with one branch delayed by one OFDM symbol period (14.4 ns) to
emulate the polarization multiplexing, resulting in a total line rate of 856 Gb/s. The signal is
then coupled into a recirculation loop comprising of 2x80 km SSMF fiber (span loss of 18.5
dB and 17.5 dB) and three EDFAs to compensate the loss. The signal is coupled out from the
loop and received with a polarization diversity coherent optical receiver [1,2]. The
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performance is detected on a per-band basis by aligning the local laser to the center of each
band, and the detected RF signal is anti-alias filtered with a 7-GHz low-pass filter. The four
RF signals for the two IQ components are then input into a Tektronix Time Domain-sampling
Scope (TDS) and are acquired at 20 GS/s and processed with a MATLAB program using 2x2
MIMO-OFDM models, which are detailed in [1,2]. Finally the complex symbol values are
input to the LDPC soft-decoder for data recovery.
Fig. 1. Experimental setup for 400 Gb/s LDPC coded CO-OFDM transmission.
LDPC codes was first invented by R. G. Gallager in 1960s [25], and rediscovered in
1990s by MacKay [26]. It was introduced to the optical communications during the last
decade by Djordjevic and Mizuochi [12–19]. The soft-decision algorithm for LDPC can be
best described using the Tanner graph [27]. The name of ‘low density parity’ is derived from
the fact that the number of ‘1’s in each column (or row) of the parity check matrix H
(dimension of m times n) is very small compared to the block length. Tanner graph consists of
m check nodes (the number of parity bits) and n variable nodes (the number of bits in a
codeword) [12].The connection between ci and fj is made if the parity check matrix element
(H)ij is a 1. Figure 2 shows a typical Tanner graph. The number of edges in the Tanner graph
is equal to the number of ones in the parity-check matrix. The inserted H in the figure is the
corresponding parity check matrix.
Fig. 2. The Tanner graph representation of the parity-check matrix
The LDPC soft decoding algorithm is based on so-called belief propagation where the
message is passed between the check and variable nodes [28]. The message sent by the
variable node to the check node contains the pair of probability (qij) for the ‘belief’ that the
variable node should be ‘0’ or ‘1’. qij(0) and qij(1) stands for the two probabilities. Similarly,
the message sent by the check node to the variable node also contains another probability (rij)
for the ‘belief’ that the variable node should be ‘0’ or ‘1’. At the beginning, the bit codes send
their qij to check nodes. qij(0) and qij(1) stands for the amount of belief that received yi is a 0
or 1. Then the check nodes will compute the response rji as
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rji (0) =
1 1
+ ∏ (1 − 2qi ' j (1)),
2 2 i '∈V j \ i
rji (1) = 1 − rji (0)
(1)
The variable nodes then will send the calculated response to bit node by
(2)
qij (0) = K ij (1 − Pi ) ∏ rj ' i (0),
qij (1) = K ij ∏ rj ' i (1)
j '∈C j \ i
j '∈C j \ i
where the Kij is used to ensure that qij(0) +qij(1)=1. The updating procedures of qij and rij are
illustrated in Fig. 2 (b) and (c). At this stage, the estimated cˆ j of the current variable c j is
using
Qi (0) = K i (1 − Pi ) ∏ rji (0),
j '∈Ci
Qi (1) = K i Pi ∏ rji (1)
(3)
j∈Ci
So if Qi (0) < Qi (1) , then cˆ j = 1 , and 0 vice versa. If the estimated codeword satisfies the
parity check equation, then the decoding procedures terminates. Otherwise, it will continues
in the next the iteration until the maximum number of iteration is exceeded. A convenient
way to represent the probability is using log likelihood ratios (LLR). LLR allows the
computation using sum and product operations, which is also used in our work. The details of
updating equations are discussed in [27]. The dimension of the parity matrix is 2000x4000,
and has the weight of 3 [23]. We use log-domain sum-product decoding algorithm and
number of iterations is set at 20. It is also worthy to point out that the used code from [23]
will bring much complexity due to its randomness. One preferred option is using quasi-cyclic
LDPC codes [14,15] with advantages of higher girth. The data after LDPC is input into a RS
decoder for possible error-floor in LDPC and BER is computed. More comprehensive
understanding of LDPC coding can be found in [12–18].
3. Experimental results and discussion
To identify net effective coding gain and the resultant improvement of the receiver sensitivity
for the LDPC coded 16-QAM OFDM signal, we first measure the receiver performance for
107 Gb/s at back-to-back and the result is shown in Fig. 3. Since we are comparing the two
signals with the same net data rate, this coding gain is equivalent to the coding gain per bit if
Fig. 3 is re-plotted as BER versus SNR per bit Because of the sharp drop off of the BER after
LDPC and maximum number of bits (1,500,000 bits per data point) measured, we defined the
receiver sensitivity as the OSNR for the BER of 1x10−3 before RS decoding (BER of 1x10−3
or lower always results in zero error count after RS outer decoder in the experiment). Any
error floor due to LDPC can be effectively eliminated by the interleaver/deinterleaver and RS
FEC. It can be seen that the OSNR sensitivity for rate ½ LDPC coded 16-QAM signal is 12.5
dB OSNR compared with 15.5 dB OSNR in conventional 4-QAM signal, indicating a 3 dB
improvement. We stress again this is achieved with the same electrical and optical bandwidth
for all the optical and electrical components encountered. In contrast to the application of
using high-order modulation for ultra-high spectral efficiency [6,7], the proposed rate ½
LDPC coded 16-QAM signal does not require higher OSNR, and the net coding gain could be
utilized to increase transmission reach and/or reduce the required bit resolution for
DAC/ADC compared to 4-QAM modulation case. The back-to-back 428 Gb/s BER
performance is also shown at Fig. 3 and the sensitivity is measured at 20.2 dB OSNR for
LDPC coded 16-QAM. The inset shows for 16-QAM CO-OFDM signal at the OSNR of 19
dB.
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Fig. 3. Back-to-back OSNR sensitivity for 107 Gb/s and 428 Gb/s signal. All the data rates
shown are before 7% RS FEC
Table 1. Detailed BER for the worst band of 428 Gb/s LDPC-coded 16-QAM signal at
reaches of 960 km and 800 km.
Reach (km)
BER: raw (Ypolarization)
0.077987
BER: LDPC
800
BER: raw (Xpolarization)
0.076993
0
BER: LDPC +
RS
0
960
0.093084
0.094213
0
0
Table 1 shows the detailed BERs for 400-Gb/s LDPC-coded OFDM signal at different
reaches. At the reach of 960 km with a launch power of 3dBm, only the performance of the
worst band, the 8th band of the 400-Gb/s is shown including its raw BER for the 16-QAM
signal or the input BER to LDPC decoder, BER after LDPC decoding, and BER after both
LDPC and RS decoding. It can be seen that LDPC-coded 16-QAM signal can be received
successfully (zero error counts for both polarizations) after 960-km transmission. We also
measure transmission performance in various reaches below 960 km, all error-free after
LDPC and RS decoding. Table 1 only shows one instance of the reach below 960 which is
800 km. Figure 4 shows the spectrum of the 400 Gb/s CO-OFDM signal at the reach of 960
km. Although each band is uniformly modulated with the same data, the chromatic dispersion
induces rapid inter-band walk off and de-correlate the multi-band signal. In fact, the
nonlinearity performance of such configuration is slightly conservative compared to the truly
uncorrelated multiband signal [1]. We note this is the first experimental demonstration of
LDPC coding for long-haul transmission.
Fig. 4. spectrum for 428 Gb/s LDPC-coded 16-QAM at reaches of 960 km.
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4. Conclusion
We have shown record receiver sensitivity for 100 Gb/s CO-OFDM transmission via
constellation expansion from 4-QAM to 16-QAM and rate 1/2 LDPC coding. As a result,
transmission of 400 Gb/s single-channel CO-OFDM signal over 960-km SSMF is
demonstrated without Raman amplification.
Acknowledgement
The authors would like to thank Dr. Tetsuya Kawanishi from National Institute of
Information and Communications Technology (NICT), Japan for providing the optical IQ
modulator in the experiment.
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