Linear turbo equalization for parallel ISI channels

We propose a method for exploiting transmit diversity using parallel independent intersymbol interference channels together with an iterative equalizing receiver. Linear iterative turbo equalization (LITE) employs an interleaver in the transmitter and passes a priori information on the transmitted symbols between multiple soft-input/soft-output minimum mean-square error linear equalizers in the receiver. We describe the LITE algorithm, present simulations for both stationary and fading channels, and develop a framework for analyzing the evolution of the a priori information as the algorithm iterates.     

Combined turbo equalization and turbo decoding

In this letter, the subject of turbo coding in the presence of an intersymbol interference channel is investigated. An iterative decoder structure is presented, which combines channel equalization and turbo decoding. At each iteration extrinsic information from the channel detector is fed into the turbo decoders, and then their extrinsic information is fed back to the channel detector. Simulation results are presented for a rate 1/2 turbo code with binary phase-shift keying (BPSK) modulation, transmitted over an intersymbol interference (ISI) channel having severe frequency distortion. The performance is about 0.8 dB from the ISI channel capacity at a bit-error rate of 10^-5     

Capacity-approaching turbo coding and iterative decoding for relay channels

In this paper, we design turbo-based coding schemes for relay systems together with iterative decoding algorithms. In the proposed schemes, the source node sends coded information bits to both the relay and the destination nodes, while the relay simultaneously forwards its estimate for the previous coded block to the destination after decoding and re-encoding. The destination observes a superposition of the codewords and uses an iterative decoding algorithm to estimate the transmitted messages. Different from the block-by-block decoding techniques used in the literature, this decoding scheme operates over all the transmitted blocks jointly. Various encoding and decoding approaches are proposed for both single-input single-output and multi-input multi-output systems over several different channel models. Capacity bounds and information-rate bounds with binary inputs are also provided, and it is shown that the performance of the proposed practical scheme is typically about 1.0-1.5 dB away from the theoretical limits, and a remarkable advantage can be achieved over the direct and multihop transmission alternatives.     

On the performance of turbo equalization for precoded ISI 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.     

Generalized APP detection of continuous phase modulation over unknown ISI channels

Techniques for computing soft information in the presence of unknown intersymbol interference are presented, with a particular focus on iterative detection of serially concatenated continuous phase modulation. The techniques are centered around the recursive least-squares algorithm, thus enabling unsupervised detection. In particular, we employ bidirectional estimation.     

Reduced-complexity equalization techniques for ISI and MIMO wireless channels in iterative decoding

Two reduced-complexity soft-input soft-output trellis decoding techniques are presented in this paper for equalizing single-input single-output intersymbol interference (ISI) channels and multiple-input multiple-output (MIMO) frequency selective fading channels. Given a trellis representing an ISI channel, the soft-output M-algorithm (SOMA) reduces the complexity of equalization by retaining only the best M survivors at each trellis interval. The remaining survivors are discarded. The novelty of the SOMA is the use of discarded paths to obtain soft-information. Through a simple update-and-discard procedure, the SOMA extracts reliable soft-information from discarded paths which enables a large trellis to be successfully decoded with a relatively small value of M. To decode a trellis representing a MIMO frequency selective fading channel, two challenges are faced. Not only that the trellis has a large number of states, the number of branches per trellis interval is also enormous. The soft-output trellis/tree M-algorithm (SOTTMA) expands each trellis interval into a tree-like structure and performs the M-algorithm twice: once at each trellis interval to reduce the number of states and the other at each tree sub-level to remove unwanted branches. With the proposed technique, high-order trellises with million of branches per interval can be decoded with modest complexity.     

Techniques for early stopping and error detection in turbo decoding

In this letter, we present three new criteria for early stopping and error detection in turbo decoding. The approaches are based on monitoring the mean of the absolute values of the log-likelihood ratio of the decoded bits, which we show to be directly related to the variance of the metachannel. We demonstrate that this mean value increases as the number of errors in a frame decreases, and as a result, propose the simple mean-estimate criterion. We show that the systematic component of a terminated recursive systematic convolutional encoder used in turbo codes provides a built-in cyclic redundancy check (CRC). To further improve the performance, we also propose the mean-sign-change (MSC) criterion and the MSC-CRCeb criterion, in which a short external CRC code and the built-in CRC are concatenated with the MSC criterion.     

Sequence detection for binary ISI channels using signal-spacepartitioning

Binary symbol detection based on a sequence of finite observation signals is formulated in the multidimensional signal space. A systematic space partitioning method is proposed to divide the entire space into two decision regions using a set of hyperplanes. The resulting detector structure consists of K parallel linear classifiers followed by a K-to-1 Boolean mapper, and is well suited to high-speed implementation. Compared to direct implementation of the fixed-delay tree search (FDTS) detection rule, the proposed signal-space formulation results in a considerable saving in digital hardware. Examples taken from binary-input intersymbol interference (ISI) channels are used to demonstrate the proposed technique. Block processing strategies suitable for high-speed applications are also discussed     

A MIMO turbo equalizer for frequency-selective channels with unknown interference

A new space-time turbo equalization algorithm is derived for frequency-selective multiple-input-multiple-output (MIMO) channels with unknown interference. The algorithm is an extension of our proposed MIMO equalization algorithm , which performs joint channel estimation, multiple users' signal detection, and decoding, all in an iterative manner. This paper's proposed algorithm uses estimates of the correlation matrix of composite unknown interference-plus-noise components to suppress the unknown interference while effectively separating multiple users' signals to be detected (referred to as "known user" later). The correlation matrix of the composite unknown interference-plus-noise components can be estimated by time averaging the instantaneous empirical correlation matrix over the training period. Since the iterative channel estimation yields better channel estimates as more iterations are performed, thereby the estimate of the correlation matrix of the unknown interference-plus-noise components also becomes more accurate. This results in better signal detection performances, even in the presence of unknown interferers. A series of computer simulations show that this paper's proposed algorithm can properly separate known users' signals while suppressing unknown interference.     

Joint MF combining and turbo equalization for wireless communications over ISI channels with diversity reception

A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.     

Iterative multiuser detection/decoding for turbo coded CDMA systems

We propose a novel scheme for iterative multiuser detection and turbo decoding. The multiuser detector and single-user turbo decoders are coupled such that after each turbo decoding iteration the extrinsic information of the interfering users is passed to the multiuser detector, and after each multiuser iteration, updated a posteriori probabilities are passed to the single-user turbo decoders as the soft input metrics. In synchronous systems, the proposed detector approaches the multiuser capacity limit within 1 dB in the low signal-to-noise ratio region     

New results about analysis and design of TCM for ISI channels andcombined equalization/decoding

New upper bounds for the performance of the optimum combined symbol-by-symbol (SbS) Abend-Fritchman-like equalizer and decoder are presented, and a related criterion for the actual design of good trellis-coded-modulated (TCM) schemes effectively matched to the distortion introduced by the intersymbol interference (ISI)-corrupted transmission channel is developed. The actual application of the proposed design criterion is also addressed     

Simple stopping criterion for turbo decoding

A simple and effective criterion for stopping the iteration process in turbo decoding with negligible degradation of the error performance is presented. The new, improved hard-decision-aided (IHDA) extends the existing hard-decision-aided (HDA). Unlike the HDA, it requires no extra data storage, while achieving similar performance in terms of the BER and average number of iterations     

Iterative detection/decoding for two-track partial response channels

In this letter, we investigate the iterative detection/decoding algorithms for two-track partial response channels. We first describe the iterative algorithm as an iterative message-passing/processing algorithm over a high-level normal graph and then propose two trellis-based detection algorithms. The natural one is based on a joint trellis, which can be implemented for low-order channels. For moderate-order channels, we propose a separated detection, which is based on two single-track trellises. Compared with the joint detection, the separated detection is simpler in most cases. Simulation results show that, for two-track EPR4 channels with minor intertrack interferences, the separated detection causes only marginal degradation in performance.     

Two simple stopping criteria for turbo decoding

This paper presents two simple and effective criteria for stopping the iteration process in turbo decoding with a negligible degradation of the error performance. Both criteria are devised based on the cross-entropy (CE) concept. They are as efficient as the CE criterion, but require much less and simpler computations     

A simple stopping criterion for turbo decoding

This article proposes a simple stopping criterion for turbo decoding that extends the existing sign change ratio (SCR) technique. The new sign difference ratio (SDR) criterion counts the sign differences between the a priori information and the extrinsic information. Unlike the SCR, it requires no extra data storage. Simulations comparing the new technique with other well known stopping criteria show that the proposed SDR scheme achieves similar performance in terms of the bit error rate (BER), frame error rate (FER), and the average number of iterations, while requiring lower complexity. A GENIE scheme is included as the limit of all possible stopping criteria     

Low-complexity turbo equalization and multiuser decoding for TD-CDMA

The authors propose a low complexity multiuser joint parallel interference cancellation (PIC) decoder and turbo decision feedback equalizer for code division multiple access (CDMA). In their scheme, an estimate of the interference signal (both multiple-access interference and intersymbol interference) is formed by weighting the hard decisions produced by conventional (i.e., hard-output) Viterbi decoders. The estimated interference is subtracted from the received signal in order to improve decoding in the next iteration. By using asymptotic performance analysis of random-spreading CDMA, they optimize the feedback weights at each iteration. Then, they consider two (mutually related) performance limitation factors: the bias of residual interference and the ping-pong effect. The authors show that the performance of the proposed algorithm can be improved by compensating for the bias in the weight calculation, and they propose a modification of the basic PIC algorithm, which prevents the ping-pong effect and allows higher channel load and/or faster convergence to the single-user performance. The proposed algorithm is validated through computer simulation in an environment fully compliant with the specifications of the time-division duplex mode of third-generation systems, contemplating a combination of time-division multiple access and CDMA and including frequency-selective fading channels, user asynchronism, and power control. The main conclusion of this work is that, for such application, soft-input soft-output decoders (e.g., implemented by the forward-backward BCJR algorithm) are not needed to attain very high spectral efficiency, and simple conventional Viterbi decoding suffices for most practical settings.     

Sequence detection and adaptive channel estimation for ISI channels under class-a impulsive noise

In this paper, sequence detection and channel estimation for frequency-selective, intersymbol interference (ISI)-producing channels under Class-A impulsive noise are considered. We introduce a novel suboptimum sequence detection (SSD) scheme and show that although SSD employs a simplified metric, it achieves practically the same performance as maximum-likelihood sequence detection (MLSD). For both SSD and MLSD, a lower bound on the achievable performance is derived, which is similar to the classical matched-filter bound for frequency-selective (fading) channels under Gaussian noise. For channel estimation, we adopt a minimum entropy criterion and derive efficient least-mean-entropy and recursive least-entropy algorithms. For both adaptive algorithms, we analyze the steady-state channel-estimation error variance. Theoretical considerations and simulation results show that in Class-A impulsive noise, the proposed sequence detection and adaptive channel-estimation schemes yield significant performance gains over their respective conventional counterparts (designed for Gaussian noise). Although the novel algorithms require knowledge of the Class-A noise-model parameters, their computational complexity is comparable to that of the corresponding conventional algorithms.     

Area-efficient high-speed decoding schemes for turbo decoders

Turbo decoders inherently have large decoding latency and low throughput due to iterative decoding. To increase the throughput and reduce the latency, high-speed decoding schemes have to be employed. In this paper, following a discussion on basic parallel decoding architectures, the segmented sliding window approach and two other types of area-efficient parallel decoding schemes are proposed. Detailed comparison on storage requirement, number of computation units, and the overall decoding latency is provided for various decoding schemes with different levels of parallelism. Hybrid parallel decoding schemes are proposed as an attractive solution for very high level parallelism implementations. To reduce the storage bottleneck for each subdecoder, a modified version of the partial storage of state metrics approach is presented. The new approach achieves a better tradeoff between storage part and recomputation part in general. The application of the pipeline-interleaving technique to parallel turbo decoding architectures is also presented. Simulation results demonstrate that the proposed area-efficient parallel decoding schemes do not cause performance degradation.