INTRODUCTION
With the continuous growth of highspeed data services, such as Internet Protocol
Television (IPTV), HighDefinition Television (HDTV) and large interactive network
games, the boom in access bandwidth demands will increase dramatically. Recently,
the Orthogonal Frequency Division Multiplexing (OFDM) modulation which has been
widely used in the wired and wireless wideband communications, is introduced
into the optical fiber communication systems due to its excellent resistance
to the channel dispersion and the efficient spectrum utilization (Armstrong
and Lowery, 2006; Shieh and Athaudage, 2006). Meanwhile,
the Direct Detectionoptical orthogonal frequency division multiplexing (DDOOFDM)
systems have some advantages such as simple structure, flexible dynamic bandwidth
allocation, transparency to heterogeneous services and good compatibility with
existing network and a novel architecture with Passive Optical Network (PON)
(Fisher, 2009). Therefore, OFDMPON is proposed as a
key optical access network technique in the future.
Considering the huge increase of subscribers and freedom flexibility in the
DDOOFDM systems, security has become a critical issue in the future optical
network. However, most of the previous literatures have focused on the encrypted
data but have left the control frames and headers without protection. Thanks
to the convenient digital processing of OFDM signals, it is easily to encrypt
the data without changing any optical module or electrical circuit. Logistic
sequence is sensitive to its initial condition. And the transmitted signals
can be concealed with logistic carrier or sequence which has a highly unpredictable
and randomlooking nature (Chen et al., 2010).
Hence, it can efficiently counteract illegal users in the DDOOFDM systems.
Some works show that Chaosbased OFDM signal has successfully transmitted over
25 km in an OFDMPON (Zhang et al., 2011), while
Low Density Parity Check (LDPC) coding has an effective correction capability
coupled with the logistic mapping which can enable DDOOFDM systems to gain
a better BER performance.
In this study, the authors have proposed and experimentally demonstrated a
logisticmapping based secure strategy for the LDPCDDOOFDM systems. Onedimensional
logistic sequence is employed to serve as the secure key. A 2.5 Gb sec^{1}
encrypted 16QAM LDPCOFDM signal can be successfully transmitted in the DDOOFDM
systems. The experiment results show high secure key sensitivity and robustness
against illegal invader at the receiver, while increasing the transmission distance
in SSMF by using Forward Error Correction (FEC) technique.
PRINCIPLE
The block diagram for the principle of OFDM is shown in Fig.
1. The Digital Signal Processing (DSP) which is a part of the baseband OFDM
transceiver can be realized offline. In the OFDM transmitter, the LDPC coding
is used as a Forward Error Correction (FEC) technique to improve the correction
capability of the system. The long irregular LDPC code acts as the channel error
correction coding to resist the impact of the subcarriersubcarrier interference.

Fig. 1: 
Block diagram for the principle of OFDM 
In this study, long irregular LDPC coded OFDM with 0.75 coding rate is used
effectively for longdistance single mode fiber transmission. The channel coding
can be taken into account according to the quality of transmission system. Then,
the bit streams will be mapped into MQAM or MPSK symbols. Onedimensional
logistic map can be adopted to realize the data encrypt described by the follows.
X_{n+1} = μx_{n}(1x_{n}), xε(0,1) and με(3.5699,4).
When μ falls into this domain, the logistic sequence will fall into chaos.
A korder scrambling matrix can be used to encrypt the frequency information
of the LDPCOFDM signals. The time domain sample of the LDPCOFDM can be represented
as:
d_{k} = IFFT {D_{k}xW}, k = 0, 1…..,
K1 
where, W can be defined as:
W_{n} = {w_{n},w_{n+1},...,w_{n+k1}}^{T} 
and:
cov (w_{a}, w_{b}) = O,a≠b 
where, K denotes the Nth scrambling matrix with the initial value of W_{0} when n = 0. We choose the midpoint of each subdomain as an initial value which can be defined as:
where, X_{o,n} is the initial value of korder subdomain. In order to obtain W_{n}, we define a matrix P:
To get W_{n}, we have X = W_{n1}. P. Due to the chaotic nature
of the sequence, it is possible for the same position to get different initial
values. After inverse fast Fourier Transforms (IFFT), a certain length of cyclic
prefix (CP) can be added to combat intersymbol interference (ICI). Over 40
km SSMF, at the receiver, the processing of the OFDM signal is reverse to that
of the transmitter. As described above, the LDPCOFDM data is encrypted by the
scrambling matrices. It is difficult to extract the data without the knowledge
of initial values.
EXPERIMENT AND RESULTS
Figure 2 shows the experiment setup for the 16QAM OFDM signal
with the LDPC coding and security technique in the DDOOFDM systems. In this
experiment, the encrypted LDPCOFDM signals are generated offline with MATLAB
program. The total number of subcarriers is 256, Cyclic Prefix (CP) is 1/8 of
the OFDM symbol in each OFDM frame and it is used to mitigate intercarrier
interference (ICI) and intersymbol interference (ISI). Long irregular LDPC
coded OFDM with 0.75 coding rate with 16QAM is applied for subcarrier modulation
scheme. For security strategy, onedimensional logistic sequence is applied
where μ is set as 4. A continuouswave generated by an external cavity
laser (ECL) at 1558.52 nm is fed into a MZM biased at 1.9 V and the OFDM signals
generated by a Tektronix Arbitrary Waveform Generator (AWG) are injected into
the MZM to generate optical OFDM signals. The sampling rate of the AWG is 2.5
GSa sec^{1} The halfwave voltage of the MZM is 3.8 V. The driving
amplitude of OFDM signals is 2 V and the output power of the ECL is 12 dBm.

Fig. 2: 
Experiment setup for the 16QAM OFDM transmission system 

Fig. 3: 
BER curves for the signals without using LDPC coding 
The optical launch power into fiber is 3.2 dBm. After the MZM, the optical
OFDM signals are then transmitted over a 40 km SSMF. They are amplified by an
erbiumdoped fiber amplifier (EDFA) to 5.8 dBm. A tunable attention (ATT) is
used to change the power of detected optical signal. At the optical receiver,
the optical/electrical conversion of the OFDM signals is performed by a commercial
optical receiver of PD HP83433 with a 3 dB bandwidth of 10 GHz. The electrical
OFDM signals will be captured by a 20 GSa sec^{1} Tektronix TDS684B
realtime oscilloscope and stored for offline processing by MATLAB program
as an OFDM receiver.
For offline DSP processing, an optical network unit can recover its own data
through logistic demap with the dedicated secure matrix, while the optical network
unit cannot obtain the information delivered without the knowledge of the secure
key. In our experiment, we choose N = 256 = 2^{8} and the 8^{2}x8^{2}
matrix to study the performances of the system. Figure 3 shows
the measured BER curves and the constellations with/without the secure key before
and after the transmission.

Fig. 4: 
BER curves for the signals using LDPC coding 
Figure 4 shows the measured BER curves and the constellations
with/without the secure key before and after the transmission based on the LDPC
coding. Since there is little difference of initial condition, almost all the
constellation symbols are error at the receiver, there is about 5 dB power penalty
after 40 km SSMF when the BER is 1x10^{3} without using FEC technique.
The LDPC coding can also improve the performance of the system, there is more
than 10 dB power gain when the BER is 1x10^{3}.
CONCLUSION
We have proposed and experimentally demonstrated a novel securityenhanced
transmission strategy for the LDPCDDOOFDM system, where onedimension logistic
sequence is used to encrypt the signals. The 16QAM OFDM data with the logistic
encryption and the LDPC coding cannot be obtained at the receiver due to the
unknown secure key with the initial value. However, the onedimensional encryption
algorithm is hardly implemented in the COOFDM system due to the signal phaseshift.
Higher dimensional algorithm is needed to meet the requirements of highorder
modulation in the COOOFDM systems. Being combined with FEC technique, higher
dimensional encryption algorithm can be widely used in different optical networks.
ACKNOWLEDGMENT
The study results were generated from a research project fully sponsored by National Science Youth Foundation of China with No. 61205091.