JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY15, 2015 1961
Performance Investigation of Pilot-Aided
Log-Likelihood Ratios for LDPC Coded CO-OFDM
Shengjiao Cao, Pooi-Yuen Kam, Fellow, IEEE, Changyuan Yu, Member, IEEE,
and Xiaofei Cheng, Senior Member, IEEE
Abstract—Pilot-subcarrier and pilot-tone aided log-likelihood
ratios (PA-LLR, PT-LLR), proposed for LDPC coded coherent op-
tical OFDM (CO-OFDM) system, is reviewed in this paper. The
knowledge of common phase error based on pilot-subcarriers or
pilot-tone is incorporated into the new PA-LLR or PT-LLR metric,
which eliminates the need for prior common phase error estimation
and compensation. The formulation of both metrics is presented in
a unified way. The performance of both metrics, in their approxi-
mate versions, is compared against the approximate conventional
LLR (AC-LLR) for different modulation formats using different
LDPC codes in a back-to-back case. APA-LLR or APT-LLR out-
performs AC-LLR for higher-order QAM, with smaller number of
pilot-subcarriers (PSCs) or at smaller pilot-tone-to-signal power
ratios (PSRs). A time-domain blind intercarrier interference (BL-
ICI) mitigation algorithm is employed to improve the performance,
which eliminates the error floor at large laser linewidth. Further-
more, we examine the tolerance of different LLR metrics to linear
fiber impairment (chromatic dispersion) or nonlinear phase noise
(self-phase modulation), in which case, our metrics still outperform
the conventional one. Iterative demodulation using new tentative-
decision-based phasor offers almost 1-dB OSNR improvement for
smaller number of PSCs. Finally, we also analytically prove that
APA-LLR or APT-LLR converges to AC-LLR as the number of
PSCs or PSR value increases. The optimal OSNR for calculating
noise power is found to be around 10 dB for actual OSNR values
beyond 10 dB in either the back-to-back case or after 13 600-
ps/nm/km dispersion with channel compensation. APA-LLR and
APT-LLR offer better performance than AC-LLR without any in-
crease in complexity.
Index Terms—Common phase error, inter-carrier interference,
LDPC coded CO-OFDM, linear phase noise, log-likelihood ratio,
pilot-subcarrier aided, pilot-tone aided.
I. INTRODUCTION
W
ITH the fast Internet traffic growth and its high band-
width demands, optical transport networks need to in-
crease capacity and decrease transmission costs simultaneously.
At ultra-high data rates beyond 100 Gb/s, the signal quality is
Manuscript received October 13, 2014; revised December 18, 2014; accepted
January 10, 2015. Date of publication January 18, 2015; date of current ver-
sion March 16, 2015. This work was supported by AcRF Tier 2 under Grant
MOE2013-T2-2-145 from MOE Singapore.
S. Cao and X. Cheng are with the A*STAR Institute for Infocomm Research,
138632 Singapore (e-mail: caosj05@gmail.com; chengxf@i2r.a-star.edu.sg).
P. Y. Kam is with the Department of Electrical and Computer Engineer-
ing, National University of Singapore, 117576 Singapore (e-mail: elekampy@
nus.edu.sg).
C. Yu is with the Department of Electrical and Computer Engineering, Na-
tional University of Singapore, 117576 Singapore, and also with the A*STAR In-
stitute for Infocomm Research, 138632 Singapore (e-mail: eleyc@nus.edu.sg).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2015.2392772
significantly degraded by various linear and nonlinear fiber im-
pairments. To deal with these impairments, forward error correc-
tion (FEC) has been extensively studied in the optical communi-
cation system, ever since one of the first demonstration in a 565-
Mbit/s system based on a single error correcting (224 216) short-
ened Hamming code [1]. ITU-T recommendations G.975 [2] and
G.975.1 [3] have standardized more powerful FEC codes for
multigigabit-per-second optical fiber submarine cable systems,
like Reed–Solomon (RS) code, Bose–Chaudhuri-Hocquenghem
(BCH) code and concatenated RS and BCH codes. More re-
cently, low-density parity-check (LDPC) codes [4], achieving
close to Shannon limit performance [5], have gained much at-
tention as a candidate for long-haul optical transmission sys-
tems [6], [7]. Coherent optical orthogonal frequency division
multiplexing (CO-OFDM) offers an efficient way to deal with
chromatic dispersion (CD) and polarization mode dispersion
(PMD). The use of FEC code in CO-OFDM system is espe-
cially important as to avoid the overall BER being dominated
by the worst performing subcarriers, because the four-wave mix-
ing between different subcarriers and its interplay with CD and
PMD will result in different subcarriers being affected differ-
ently [8]. Recently, there have been quite a few experimental
demonstrations using LDPC coded CO-OFDM for high speed
long-haul transmission [9]–[11].
Linear phase noise (LPN), caused by both transmitter laser
and receiver local oscillator, will cause both common phase
error and intercarrier interference (ICI) in CO-OFDM system.
The performance of LDPC decoder depends on the calculation
of the decoding metric, i.e., the log-likelihood ratio (LLR). In
the presence of LPN, pilot-subcarrier aided (PA) [12], [13] or
pilot-tone aided (PT) [14] common phase error compensation
is usually conducted first, followed by LDPC decoding using
the conventional LLR (C-LLR) [6], [10], [11]. Djordjevic and
Wang [15] employs Monte–Carlo integration to calculate sym-
bol LLR based on the Gaussian distribution of phase increment
for single-carrier system, which cannot be directly applied to
OFDM system. Pilot-aided LLR was first proposed for LDPC
coded pilot-symbol assisted single carrier system with BPSK
format in [16]. Previously, we have analytically derived the LLR
metric based on pilot-subcarriers [17], [18] and pilot-tone [19]
for LDPC coded CO-OFDM system in the presence of LPN.
However, our previous papers [17]–[19] only simulate one sim-
ple LDPC code (204,102) in a back to back case. Compared to
[17]–[19], this paper carries out more detailed performance in-
vestigation of both PA and PT LLRs over different LDPC codes
and various modulation formats. Moreover, the proposed LLRs
are also investigated under ICI, linear fiber impairments (i.e.,
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