One of the research directions of interest in our group is to mitigate fiber-optic system performance degradation caused by signal impairments in the optical channel and components (transmitters, amplifiers, receivers etc.) through the use of equalization and error correction both in the optical and electrical domains. Until recently, the behavior of the optical channel was essentially ignored since the bandwidth and signal integrity requirements could be easily met by the available optical power. However, to meet the growing demand for bandwidth, current systems use dense wavelength division multiplexing (DWDM) and high-speed time domain multiplexing (TDM). In these systems, light pulses of shorter time duration and higher peak intensities are necessary to support higher repetition rates, and/or achieve the required signal integrity. Consequently, the effects of chromatic dispersion (CD), polarization mode dispersion (PMD), and nonlinear optical effects (NOE) in the optical communication channel can no longer be ignored. Furthermore, in an optical network environment, length dependent impairment can vary on a channel-by-channel basis depending on the path length for each channel.

Most optical communication research has been aimed at novel optical components and devices, with limited attention devoted to establishing realistic models of the communication channel that consist of not only the point-to-point optical fiber links but also include optical network systems elements such as amplifiers, filters, and multiplexers/demultiplexers. Moreover, little attention has been paid to determining a cost-effective balance between optical and electronic signal processing techniques such as pre-compensation, error correction, post-processing, and equalization. Existing high-speed integrated circuits (IC) are capable of processing 10 Gbit/s channels and the state of the art IC’s have demonstrated the ability to handle 40 Gbit/s data streams. There is an emerging convergence between optical communication line rates and processing power because of the challenges in building WDM networks that exceed 40 Gbit/s per wavelength. Therefore, more cost-effective, electronic signal processing operations per bit will become available for electronic compensation techniques in the future optical networks systems. Previous research in electronic compensation techniques for optical channels has also been limited in scope because it did not consider both random and nonlinear channel characteristics. From a coding perspective, there is a whole set of recent techniques such as turbo codes, low-density parity-check (LDPC) codes, and two-dimensional space-time codes that have not been fully investigated for use in optical channels. A unique feature of this project is to combine cutting edge research in electronic signal processing and coding techniques with novel optical domain processing of the phase of the optical signal. This type of processing is at the heart of optical filtering and dispersion compensation and provides functionality that cannot be replicated in the electrical domain.

Recently, our group has demonstrated the possibility of mitigating intrachannel four wave mixing effects in ultra long haul optical communication links utilizing binary phase encoding of transmitted marks [1]. The return to zero (RZ) transmission format has been recognized as an efficient method for approaching the ultrahigh information bandwidth offered by the single mode optical fiber. The “ghost” pulses appear in the RZ time slots carrying 0-bits in the transmitted data stream. They are generated by repeated nonlinear four-wave mixing (4WM) process of the dispersion broadened and overlapping tails of data pulses carrying 1-bits. The effect was first observed recently [2-4], and has attracted a considerable theoretical attention [5 -9]. However, the behavior of ghost pulses has not been fully understood. We investigated the effect of the optical phase coding applied to the transmitted data stream on the strength of generated “ghost” pulses. Our study was motivated by the optical duo-binary coding (DBC) technique used to overcome dispersion effects in a linear optical fiber channel [10]. Additionally, we introduced and analyzed a second novel data dependent optical phase coding method called alternate mark phase flipping (AMPF), which is based on flipping the phase of every consecutive 1-bit by pi.

Figure 1. a) A part of a 128 bit pseudo random sequence at the input. b) The same sequence with no phase modulation applied after 1200 km of propagation with DM and amplification. c) The same pseudo random bit stream with duobinary encoding applied prior to propagation.

If the phase of the ghost pulses is examined, it can be shown that their phase difference is related to that of the genuine 1-bits in the bit-stream. For this study, we considered binary phase coding of the marks, by assigning phases of 0 and pi. This method has the effect of sending 3 levels of amplitude of the pulses 1, 0 and -1, which, after performing the square law detection, will produce logical levels of 1 and 0. The simplest coding approach would be to use a duobinary coding (DBC) method, where the phase is changed by pi any time there is a single “space” surrounded by one or more “marks” on each side. However, we have demonstrated that the best performance is achieved with alternate mark phase flipping (AMPF) coding scheme that is based on changing the phase of the pulse by p at every mark.

In order to quantify the performance improvement, we applied the phase coding methods from the last paragraph in transmitting a 128-bit long pseudo random bit (PRB) pattern (see Fig. 1). On average, different methods of phase shaped modulation bring the increase of the eye diagram Q factor (not shown here) from 1.2 to 1.4 dB (under the assumption that the noise has Gaussian distribution), depending on the coding used. As we can see, even in the long PRB sequences, where the 4WM processes are much richer, if the formation of primary echoes (as seeds for the strong ghost pulses) is prevented by the means of destructive interference, the strong ghost pulses do not develop and, hence, the system performance is considerably improved.

Fig. 2. Pulse triplet interaction in a DM link of 1200 km. a) Effect of changing the phase of a side-pulse (k=1) by pi. b) Magnified version of Fig. 2a that emphasizes the reduction of the side ghosts.

As a continuation of the work previously conducted, we intend to further explore the possibility of finding better phase codes for the mitigation of random intersymbol interference and intrachannel four-wave mixing (FWM). These areas include developing accurate stochastic nonlinear channel models that incorporate the effects of not only the optical fiber, but also signal impairments that arise in the transmitter, amplifiers, and receivers. The basic concept in the previously proposed phase coding schemes [11,12] relies on the fact that the phase of a ghost pulse has a fixed relationship to the phases of the genuine "ones" in the bit-stream that enter the 4WM process. This implies that by tailoring the phase of the 1-bit slots, the strongest ghosts can be eliminated by achieving destructive interference between the various contributions. We intend to develop a new class of codes that, while not completely suppressing the side ghosts, provide substantial reduction of energy leakage from 1-bit slots to 0-bit slots as compared to the previously suggested coding schemes. Pulse propagation in single mode optical fibers is modeled by the Nonlinear Schrödinger (NLS) equation. The pulse amplitudes can be calculated from the pulse energy transfer equations. For instance [13]:

where, and, F(z) is a function dependent on the particular shape of the dispersion map and/or fiber link characteristics, and, the most important, initial pulse phases (at the launch point). In our three-pulse example, the phase difference is. For the values , equation (1) implies that energy will leak from the central pulse into the side pulses, however, by choosing and , this process will be reversed and the two side pulses will pump the energy into the central pulse (see Fig. 2), showing the outcome of 3-pulses interaction after 1200 km of propagation obtained by a split-step simulation. The simulated link consists of 24 spans of 40km long SMF and 10 km of DCF with full dispersion compensation and pulses with and pulse separation of 25 ps with the average power of 6 dBm. The features of interest, which are highlighted in Fig. 2b, are the side ghost pulses. We can see that if the appropriate phase coding is applied (i.e. and ), while the side pulses will aliment the central pulse, less energy will leak into the side ghosts. Following the described train of thought opens a new perspective to the phase coding for the suppression of intrachannel 4WM thorough energy redistribution among 1-bits in the bit-stream in order to prevent leakage into the surrounding 0-bit time slots. We are continually involved in exploring and defining data-dependent codes that achieve ghost pulse suppression for arbitrary bit patterns leading to the definition of the coding patterns that will bring about the largest ghost pulse suppression.

References

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