Linear MMSE-Optimal Turbo Equalization Using Context Trees

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin

Integrated Transversal Equalizers in High-Speed Fiber-Optic Systems

Intersymbol interference (ISI) caused by intermodal dispersion in multimode fibers is the major limiting factor in the achievable data rate or transmission distance in high-speed multimode fiber-optic links for local area networks applications. Compared with optical-domain and other electrical-domain dispersion compensation methods, equalization with transversal filters based on distributed circuit techniques presents a cost-effective and low-power solution. The design of integrated distributed transversal equalizers is described in detail with focus on delay lines and gain stages. This seven-tap distributed transversal equalizer prototype has been implemented in a commercial 0.18-µm SiGe BiCMOS process for 10-Gb/s multimode fiber-optic links. A seven-tap distributed transversal equalizer reduces the ISI of a 10-Gb/s signal after 800 m of 50-µm multimode fiber from 5 to 1.38 dB, and improves the bit-error rate from about 10^-5 to less than 10^-12

A survey on fiber nonlinearity compensation for 400 Gbps and beyond optical communication systems

Optical communication systems represent the backbone of modern communication networks. Since their deployment, different fiber technologies have been used to deal with optical fiber impairments such as dispersion-shifted fibers and dispersion-compensation fibers. In recent years, thanks to the introduction of coherent detection based systems, fiber impairments can be mitigated using digital signal processing (DSP) algorithms. Coherent systems are used in the current 100 Gbps wavelength-division multiplexing (WDM) standard technology. They allow the increase of spectral efficiency by using multi-level modulation formats, and are combined with DSP techniques to combat the linear fiber distortions. In addition to linear impairments, the next generation 400 Gbps/1 Tbps WDM systems are also more affected by the fiber nonlinearity due to the Kerr effect. At high input power, the fiber nonlinear effects become more important and their compensation is required to improve the transmission performance. Several approaches have been proposed to deal with the fiber nonlinearity. In this paper, after a brief description of the Kerr-induced nonlinear effects, a survey on the fiber nonlinearity compensation (NLC) techniques is provided. We focus on the well-known NLC techniques and discuss their performance, as well as their implementation and complexity. An extension of the inter-subcarrier nonlinear interference canceler approach is also proposed. A performance evaluation of the well-known NLC techniques and the proposed approach is provided in the context of Nyquist and super-Nyquist superchannel systems.Comment: Accepted in the IEEE Communications Surveys and Tutorial

Analysis and equalization of data-dependent jitter

Data-dependent jitter limits the bit-error rate (BER) performance of broadband communication systems and aggravates synchronization in phase- and delay-locked loops used for data recovery. A method for calculating the data-dependent jitter in broadband systems from the pulse response is discussed. The impact of jitter on conventional clock and data recovery circuits is studied in the time and frequency domain. The deterministic nature of data-dependent jitter suggests equalization techniques suitable for high-speed circuits. Two equalizer circuit implementations are presented. The first is a SiGe clock and data recovery circuit modified to incorporate a deterministic jitter equalizer. This circuit demonstrates the reduction of jitter in the recovered clock. The second circuit is a MOS implementation of a jitter equalizer with independent control of the rising and falling edge timing. This equalizer demonstrates improvement of the timing margins that achieve 10/sup -12/ BER from 30 to 52 ps at 10 Gb/s