Frank Kschischang
Permanent URI for this collectionhttps://hdl.handle.net/1807/68858
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Item Optical Nonlinear-Phase-Noise Compensation for 9x32 Gbaud PolDM-16 QAM Transmission using a Code-Aided Expectation-Maximization Algorithm(2015-09) Pan, Chunpo; Buelow, Henning; Idler, Wilfried; Schmalen, Laurent; Kschischang, Frank R.Nonlinearity-induced phase noise has become a major obstacle in long-haul coherent fiber-optic communication systems. Such phase noise has been shown to be signal-dependent and hence correlated over time. We propose a code-aided expectation-maximization algorithm to mitigate such nonlinear phase-noise, iteratively utilizing both the time correlation of the nonlinearity-induced impairments, and a soft-decision error-control code. Simulation and experimental results show that on a dual-polarization wavelength-division-multiplexed 16 QAM system, launch-power tolerance can be increased by 1.5 dB, and the optical signal-to-noise ratio requirement can be relaxed by 0.3 dB to achieve the same Q^2 -factor.Item Staircase Codes with 6% to 33% Overhead(2014-05) Zhang, Lei M.; Kschischang, Frank R.We design staircase codes with overheads between 6.25% and 33.3% for high-speed optical transport networks. Using a reduced-complexity simulation of staircase coded transmission over the BSC, we select code candidates from within a limited parameter space. Software simulations of coded BSC transmission are performed with algebraic component code decoders. The net coding gain of the best code designs are competitive with the best known hard-decision decodable codes over the entire range of overheads. At 20% overhead, staircase codes are within 0.92 dB of BSC capacity at a bit error-rate of 10^{−15} . Decoding complexity and latency of the new staircase codes are also significantly reduced from existing hard-decision decodable schemes.Item Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation(2014-07) Yousefi, Mansoor I.; Kschischang, Frank R.Motivated by the looming “capacity crunch” in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schroedinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Item Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods(2014-07) Yousefi, Mansoor I.; Kschischang, Frank R.In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable communication channels including the nonlinear Schroedinger channel, modeling pulse propagation in optical fibers. These methods are subsequently tested and their ability to estimate the spectrum are compared against each other. These methods are used to compute the spectrum of various signals commonly used in the optical fiber communications. It is found that the layer-peeling and the spectral methods are suitable schemes to estimate the nonlinear spectra with good accuracy. To illustrate the structure of the spectrum, the locus of the eigenvalues is determined under amplitude and phase modulation in a number of examples. It is observed that in some cases, as signal parameters vary, eigenvalues collide and change their course of motion. The real axis is typically the place from which new eigenvalues originate or are absorbed into after traveling a trajectory in the complex plane.Item Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools(2014-07) Yousefi, Mansoor I.; Kschischang, Frank R.The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This first paper explains the mathematical tools that underlie the method.Item Communication over Finite-Chain-Ring Matrix Channels(2014-10) Feng, Chen; Nobrega, Roberto W.; Kschischang, Frank R.; Silva, DaniloThough network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over a finite-ring matrix channel $Y = AX + BE$, where $X$ is the channel input, $Y$ is the channel output, $E$ is random error, and $A$ and $B$ are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under the assumption that $A$ is uniform over all full-rank matrices and $BE$ is uniform over all rank-$t$ matrices, extending the work of Silva, Kschischang and K\"{o}tter (2010), who handled the case of finite fields. This extension is based on several new results, which may be of independent interest, that generalize concepts and methods from matrices over finite fields to matrices over finite chain rings.Item Energy Consumption of VLSI Decoders(2015-06) Blake, Christopher G.; Kschischang, Frank R.Thompson's model of VLSI computation relates the energy of a computation to the product of the circuit area and the number of clock cycles needed to carry out the computation. It is shown that for any sequence of increasing-block -length decoder circuits implemented according to this model, if the probability of block error is asymptotically less than $\half$ then the energy of the computation scales at least as $\Omega\left(n\sqrt{\log n}\right)$, and so the energy of decoding per bit must scale at least as $\Omega\left(\sqrt{\log n}\right)$. This implies that the average energy per decoded bit must approach infinity for any sequence of decoders that approaches capacity. The analysis techniques used are then extended to show that for any sequence of increasing-block-length serial decoders if the asymptotic block error probability is less than $\half$ then the energy scales at least as fast as $\Omega\left(n\log n\right)$. In a very general case that allows for the number of output pins to vary with block length, it is shown that the energy must scale as $\Omega\left(n\left(\log n\right)^{\fifth}\right)$. A simple example is provided of a class of circuits performing low-density parity-check decoding whose energy complexity scales as $O\left(n^2 \log \log n\right)$.