Modulated coded zero-forcing decision feedback equalizer

The authors consider the use of multidimensional signaling and block demodulation for digital transmission over intersymbol interference (ISI) channels. As an example, the theory is developed for the unit-memory 1+ alpha z/sup -1/ channel. The authors first explain why multidimensional signals should be used over ISI channels by showing how the minimum Euclidean distance and the cutoff rate R/sub 0/ increase by increasing the dimensionality of the signals transmitted. Two ways of increasing the reliability of transmission over an ISI channel are discussed. The first way consists of increasing the energy associated with the symbols more affected by ISI. The second way uses a coding scheme which selectively protects those symbols. Generalized concatenated-codes are advocated for this purpose. >

Wiener filter is widely used to equalize the signals over inter-symbol interference (ISI) channels because of its low complexity and optimality in terms of mean square error (MSE). However, Wiener filter is generally not optimal in terms of symbol detection error and thus can exhibit considerable error performance degradation in ISI channels. Recently, to enhance the performance of linear equalizers, lattice reduction (LR) technique is proposed, which shows significant gain for multi-input multi-output systems. In this paper, we propose LR-aided Wiener filter that aims at minimizing the MSE for the symbols in lattice-reduced domain. Simulations show that the LR-aided Wiener filter exhibits significant error performance improvement over the Wiener filter, especially for higher-order modulations.

Motivated by recent high bandwidth communication systems, Inter-Symbol Interference (ISI) channels with 1-bit quantized output are considered under an average-power-constrained continuous input. While the exact capacity is difficult to characterize, an approximation that matches with the exact channel output up to a probability of error is provided. The approximation does not have additive noise, but constrains the channel output (without noise) to be above a threshold in absolute value. The capacity under the approximation is computed using methods involving standard Gibbs distributions. Markovian achievable schemes approaching the approximate capacity are provided. The methods used over the approximate ISI channel result in ideas for practical coding schemes for ISI channels with 1-bit output quantization.

We present a novel iterative (turbo) receiver with tunable complexity for reliable detection of (uncoded) payload data transmitted over long intersymbol interference (ISI) channels affected by crosstalk, as those typically encountered in emerging HDSL2 services standardized by ANSI T1.418 recommendation. The proposed receiver combines in an original way "minimum mean square error (MMSE) estimation principle," "turbo-processing principle" and "crosstalk-prediction principle" for achieving both suboptimal maximum a posteriori probability channel equalization and reliable soft-mitigation of ISI tail plus crosstalk. More in detail, according to the turbo-processing principle, at each iteration suitable extrinsic information is extracted from the equalizing and interference-canceling modules and used as "a priori information" for the next iteration. Several simulation results on typical HDSL-like test-loops confirm the superiority of the proposed turbo-detector (TD) over current solutions based on conventional MMSE decision-feedback equalizers and precoders (such as the Tomlinson-Harashima precoder). The numerical tests also point out that performance of the presented TD on typical high bit-rate digital subscriber lines (HDSL) is not limited by error-floor phenomena, even at error-probabilities below 10/sup -7/.

In this paper, we introduce a simulation-based method to compute the information rates of intersymbol interference (ISI) channels with signal-dependent Gaussian noise when the inputs are binary and independent identically distributed. The method extends the idea in Arnold et al. (2001), which focuses on the ISI channels with additive white Gaussian noise (AWGN). With the new method, we can compute the information rates of the Lorentzian channels with media noise that represents a suitable model for practical magnetic recording channels.

This paper studies the application of neural networks to Viterbi detection of FTN signals in an intersymbol interference (ISI) channel. The main contribution of this paper is to propose a receiver structure for detecting FTN signals in unknown static ISI channel. In particular, we propose a novel low-complexity neural network structure for calculating the branch metrics, and we explore its suitability for FTN signalling with channel uncertainty. We compare the proposed network, which we call the Metric Net (MetNet), to a benchmark neural network-based technique for metric calculation, the ViterbiNet, which was originally designed for ISI channels. The simulation results confirm that the MetNet outperforms the ViterbiNet, with two orders of magnitude lower complexity, and is much more resilient to channel uncertainty than the traditional Viterbi detector, which uses Euclidean distance for metric calculations. We further show that the MetNet exhibits robustness to being trained at mismatched SNR values and FTN pulse acceleration factors, meaning that the number of trained models required can be significantly reduced. Additionally, the results show that the proposed MetNet remains a favorable alternative at much higher levels of channel uncertainties. The results also reflect that we can generalize the MetNet to work with different channel models defined by different decaying factors. Finally, we show that we succeed in achieving a bandwidth efficiency gain of 33% due to FTN by using the MetNet in the presence of channel uncertainty.

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

In this paper, we present a semi‐analytical approach for analyzing the serial concatenation (SCC) of a high rate convolutional code and a precoded intersymbol interference (ISI) channel. The significance of the proposed approach is that it can be used to identify, for a given outer high rate code and fixed ISI channel, the precoder that results in the lowest error rate floor. In estimating the bit error performance in the floor region, we use analytical techniques developed for trellis codes to compute the overall system minimum squared Euclidean distance, and then use a semi‐analytical approach to find the corresponding multiplicity. We also demonstrate via simulations that the proposed technique may be extended to fading ISI channels with favorable results. We give examples that support our analysis. Copyright © 2006 John Wiley & Sons, Ltd.

Recently relay networks have attracted a lot of attention for their potential to increase spatial diversity. However, limited attention has been paid to practical detector design and implementation issues. In this paper, we investigate the design of maximum-likelihood detectors for half-duplex amplify-and-forward relay networks in intersymbol interference (ISI) channels. In particular, we study the case when the relay period is long, which results in an effective channel impulse response that is sparse and periodically time-varying. The proposed design provides a good performance/complexity tradeoff.

The subject of turbo coding in the presence of an intersymbol interference (ISI) channel whose characteristics are unknown is investigated. An iterative blind turbo detector, is presented, which combines the channel estimation, the channel equalization, and the turbo decoding. Simulation results are presented for rate 1/2 recursive systematic convolutional (RSC) codes and rate 1/3 turbo codes with BPSK modulation, transmitted over an ISI channel having severe frequency distortion. We can improve the performance when we use a good choice of RSC encoder of which the denominator is a primitive polynomial.

This paper introduces the decision feedforward equalizer (DFFE), a new low complexity iterative equalization architecture for high speed receivers used on channels with large intersymbol interference (ISI). The decision feedback equalizer (DFE) is one of the preferred receivers for high ISI channels. The high data and symbol rate of current communications systems often require parallel processing receiver implementations [1]. Unfortunately, the complexity of parallel architectures of the DFE grows exponentially with the channel memory [2] and limits their application to low ISI channels. The DFFE avoids the exponential growth of the DFE by using tentative decisions to iteratively cancel the ISI. We show that the DFFE can achieve performance similar to the DFE. These benefits make it an excellent choice for high-speed receivers required to operate over highly dispersive channels.

Rate and diversity impose a fundamental trade-off in communications. This trade-off was investigated for flat-fading channels in as well as for Inter-symbol Interference (ISI) channels in . A different point of view was explored in where high-rate codes were designed so that they have a high-diversity code embedded within them. These diversity embedded codes were investigated for flat fading channels both from an information-theoretic viewpoint and from a coding theory viewpoint in . In this paper, we explore the use of diversity embedded codes for inter-symbol interference channels. In particular the main result of this paper is that the diversity multiplexing trade-off for fading MISO/SIMO/SISO ISI channels is indeed successively refinable. This implies that for fading ISI channels with a single degree of freedom one can embed a high diversity code within a high rate code without any performance loss (asymptotically). This is related to a deterministic structural observation about the asymptotic behavior of frequency response of channel with respect to fading strength of time domain taps as well as a coding scheme to take advantage of this observation.

This paper computes the optimal diversity multiplexing curve for intersymbol interference (ISI) channels and reveal it equals the matched filter bound. A simple transmission scheme that achieves this bound is presented and analyzed. The scheme provides a tractable method of extracting maximal diversity gain for any spatial multiplexing gain, when communicating over multipath fading channels.

Optimal Viterbi decoding of trellis codes transmitted over channels exhibiting long intersymbol interference (ISI) can be computationally infeasible. Suboptimal trellis search schemes promise much better general performance than decision feedback equalization (DFE) or linear equalization, M. Eyuboglu and S. Qureshi's (1989) reduced-state sequence estimation (RSSE) is the most general. It is shown that two reduced-search breadth-first trellis decoders, namely the M-algorithm and the newer T-algorithm, can provide performance equivalent to RSSE, but at a substantially reduced computational load. This advantage is especially pronounced for (minimum-phase) ISI responses with precursors. With the M or T-algorithms, a more powerful trellis code can be used to achieve a better error rate. These decoders operate on the original trellis without the need for the partitioning required by RSSE. >

A multi-stage turbo decoding scheme combined with equalization using precoding for ISI channels is presented. The precoder and intersymbol interference (ISI) channel are jointly modeled as a finite-state probabilistic channel to provide the multistage turbo decoder with its statistics information. Both a priori and a posteriori probabilities are used in the metric function of the decoding scheme to improve the system performance. Structures of the combined turbo-encoder, interleaver and precoder in the transmitter and multi-stage turbo decoder in the receiver are presented. Performance of the introduced scheme in various ISI channels and different conditions are evaluated by simulation. The results indicate that the combined multistage turbo decoding and precoding techniques provide a considerable improvement.