Optimized LDPC codes for partial response channels

We present a systematic way to construct multilevel concatenated codes for partial response (PR) channels using: (1) a structured set partition (SSP) of multiple channel output sets and (2) a set of conventional block codes with different error correcting capabilities. A lower bound on the minimum squared Euclidean distance of the constructed codes is given. This bound is based on the interset minimal Euclidean distances of the SSP and the minimum Hamming distances of the used block codes. An example of SSP for the extended class 4 partial response channel (EPR4) is presented. Iterative suboptimal decoding, which combines Viterbi detection on the trellis of the PR channel with algebraic error detection/correction, can be applied to the constructed concatenated codes. Truncated versions of the iterative decoding scheme are simulated and compared with each other.

We develop density evolution methods for evaluating the performance of Gallager's low-density parity-check (LDPC) codes over binary intersymbol interference (ISI) channels. In contrast to previous work on memoryless channels, the noise tolerance thresholds for ISI channels depend on the transmitted sequences. The concentration statements are appropriately adjusted to reflect this difference. We compare the thresholds of regular Gallager codes over the 1-D partial response channel to the i.i.d. information rate, showing that at high code rates, regular Gallager codes are asymptotically optimal.

Summary form only given. The ultimate performance limit or threshold of low-density parity-check (LDPC) codes is close to capacity over various memoryless channels (S.-Y. Chung, IEEE Trans. Info. Theory, vol. 47, pp. 657-670, 2001). Since the capacity of binary-input partial response (PR) channels is unknown, we estimate the capacity by calculating the threshold of capacity-approaching LDPC codes over these channels. We assume a BCJR equalizer for the channel and a sum-product message-passing decoder for the LDPC code. We also assume that the log-likelihood ratios (LLRs) in the channel BCJR and the LDPC decoder are Gaussian. We use our results to guide the design of decoder schedules that minimize the number of computationally expensive BCJR steps. The threshold calculation method can be used to optimize the left and right degree sequences of the LDPC code factor graph, using fast linear programming methods, to provide better thresholds than regular codes.

This paper describes a low-latency LDPC- (low-density parity-check) based iterative equalizer, using pre-FFT (time-domain) signal processing, for OFDM (orthogonal frequency division multiplexing) inter-symbol interference (ISI) channels. Combined with a novel channel estimator, the proposed receiver can estimate both channel-state information (CSI) and ISI accurately even under a fast-fading environment. At a data rate of 100 Mbps, and vehicle speed of 100 km/h (at a carrier frequency of f/sub c/=5 GHz), where almost 40% of the OFDM symbols face ISI, the receiver provides a block-error-rate (BLER) of 10/sup 2/ at 0.8-dB degradation from that of an ISI-free environment with perfect CSL. By introducing an adaptive iteration control (AIC) technique, our receiver maintains good performance with a maximum latency of 8 OFDM symbol durations. Computer simulations showed that the proposed scheme is robust and has potential applications in broadband, high-quality communication systems.

This paper addresses the design of a protograph-based LDPC code which can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels. We propose a method to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic information transfer (EXIT) chart. We then describe a simple method to search for a protograph code whose threshold is close to the i.u.d. capacity limit. This new class of codes is needed because experiments show a protograph that is capacity approaching in the AWGN channel may not perform well in partial response channels. In particular, protographs with punctured nodes are often used to produce good AWGN codes, but they perform poorly with the BCJR equalizer. Numerical results support our analysis.

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.

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.

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.

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.

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/.

Turbo codes are attractive compared with Low Density Parity Check (LDPC) codes for Forward Error Correction (FEC) applications mainly due to their superior performance, especially at low Signal-to-Noise Ratio (SNR) such as are common in Powerline channels. For example, IEEE 1901-FFT PHY used the Turbo coding scheme defined in the HomePlug AV standards. However, patent fees are usually required for each turbo-code enabled manufactured device. The objective of this paper is to examine whether unlicensed LDPC codes, with optimized choices of block lengths, could be a viable alternative for future Powerline Communications (PLC) applications. The paper shows that the performance of the LDPC codes can approximate that of the Turbo codes with higher block lengths, on channels with typical and realistic PLC characteristics. The paper also shows that the additional complexity associated with this increase in block length can be mitigated by the use of Quasi-Cyclic LDPC (QC-LDPC) codes.

We investigate a systematic construction of regular low density parity check (LDPC) codes based on (γργ-1, ργ, ρ, γ{0,1}) combinatorial designs. The proposed (γ,ρ) regular LDPC ensemble has rate $${\left( {1 - \tfrac{1}{\rho }} \right)^\gamma }$$ girth ≥2γ+1, and exists for all γ≥2. The codes are a subset of Gallager's random ensemble, but contains a good combination of structure and (pseudo)randomness. In particular, the simple case of γ=2 results in a class of codes that are high-rate, systematic, quasi-cyclic, linear-time encodable and decodable, and free of length-4 and length-6 cycles. Analysis on distance spectrum shows that they are better than the Gallager ensemble of the same parameters. Simulation of the proposed codes on intersymbol interference channels show that they perform comparably to random LDPC codes. Unlike random codes, the proposed structured LDPC codes can lend themselves to a low-complexity implementation for high-speed applications.

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.

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.