Michael Tüchler

Turbo equalization: principles and new results

We study the turbo equalization approach to coded data transmission over channels with intersymbol interference. In the original system invented by Douillard et al. (1995), the data are protected by a convolutional code and the receiver consists of two trellis-based detectors, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate. We introduce new approaches to combining equalization based on linear filtering, with decoding.. Through simulation and analytical results, we show that the performance of the new approaches is similar to the trellis-based receiver, while providing large savings in computational complexity. Moreover, this paper provides an overview of the design alternatives for turbo equalization with given system parameters, such as the channel response or the signal-to-noise ratio.

Design of serially concatenated systems depending on the block length

We study the convergence behavior of iterative decoding for a number of serially concatenated systems, such as a serially concatenated code, coded data transmission over a n inter-symbol interference channel, bit-interleaved cod ed modulation, or trellis-coded modulation. We rederive an ex isting analysis technique called EXIT chart, simplify its construction, and construct simple irregular codes to impr ove the convergence of iterative decoding. An efficient and optimal optimization algorithm yields systems, which appr oach information theoretic limits very closely. However, these systems exhibit their performance only for very long b lock lengths. To overcome this problem, we optimize the decoding convergence after a fixed, finite amount of iteratio ns yielding systems, which perform very well for short block lengths, too. As an example, optimal system configurat ions for communication over an additive white Gaussian noise channel are presented.Based on extrinsic information transfer (EXIT) charts, the convergence behavior of iterative decoding is studied for a number of serially concatenated systems, such as a serially concatenated code, coded data transmission over an intersymbol interference channel, bit-interleaved coded modulation, or trellis-coded modulation. Efficient optimization algorithms based on simplified EXIT chart construction are devised to find irregular codes improving the convergence of iterative decoding. One optimization criterion is to find concatenated systems exhibiting thresholds of successful decoding convergence, which are close to information-theoretic limits. However, these thresholds are approached only for very long block lengths. To overcome this problem, the decoding convergence after a fixed, finite number of iterations is optimized, which yields systems performing very well for short block lengths, too. As an example, optimal system configurations for communication over an additive white Gaussian noise channel are presented.

Convergence prediction for iterative decoding of threefold concatenated systems

We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows us to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. Convergence thresholds are obtained to determine the minimal signal-to-noise ratios for which convergence is possible. It turns out that threefold concatenated systems do not achieve any additional performance gain compared to suitably designed twofold systems. We conclude that a threefold concatenation should be considered only when the decoders cannot be chosen freely.We show how to use EXIT charts for convergence prediction of a threefold serially concatenated system. The corresponding chart has three dimensions and allows us to appropriately select system parameters and to find an optimal schedule of decoding iterations between the three decoders of such a system. Convergence thresholds are obtained to determine the minimal signal-to-noise ratios for which convergence is possible. It turns out that threefold concatenated systems do not achieve any additional performance gain compared to suitably designed twofold systems. We conclude that a threefold concatenation should be considered only when the decoders cannot be chosen freely.

Performance of soft iterative channel estimation in turbo equalization

To combat the effect of intersymbol interference (ISI) while transmitting data over an ISI channel in a coded data transmission system, the impulse response of the channel is required. As part of the turbo equalization approach, which facilitates iterative equalization and decoding, we introduce a method to iteratively improve the quality of the estimate of the channel characteristics. This is done by incorporating soft information fed back by the decoder to improve the initial estimate, obtained for example using a training sequence. Decision criteria based on the analytical calculation of the variance of the channel estimation error are derived to decide whether the soft information improves the quality of the estimate. The considered estimation algorithm is the well-known recursive-least-squares algorithm. It turns out that incorporating soft information for iterative channel estimation does not always improve the quality of the estimate. If it does, the bit-error-rate performance improves significantly over a system not using soft iterative channel estimation.

Scalable decoding on factor trees: a practical solution for wireless sensor networks

We consider the problem of jointly decoding the correlated data picked up and transmitted by the nodes of a large-scale sensor network. Assuming that each sensor node uses a very simple encoder (a scalar quantizer and a modulator), we focus on decoding algorithms that exploit the correlation structure of the sensor data to produce the best possible estimates under the minimum mean-square error (MMSE) criterion. Our analysis shows that a standard implementation of the optimal MMSE decoder is unfeasible for large-scale sensor networks, because its complexity grows exponentially with the number of nodes in the network. Seeking a scalable alternative, we use factor graphs to obtain a simplified model for the correlation structure of the sensor data. This model allows us to use the sum-product decoding algorithm, whose complexity can be made to grow linearly with the size of the network. Considering large sensor networks with arbitrary topologies, we focus on factor trees and give an exact characterization of the decoding complexity, as well as mathematical tools for factorizing Gaussian sources and optimization algorithms for finding optimal factor trees under the Kullback-Leibler criterion.

Low-complexity turbo equalization for time-varying channels

Low-complexity soft-in soft-out (SISO) equalizers based on time-varying linear filters and soft inter-symbol interference cancellation are known to be a viable alternative to the optimal trellis-based SISO equalizers when used in receivers based on iterative equalization and decoding. In particular, when the signal constellation is large and/or the channel impulse response is long, the computational complexity of trellis-based equalizers becomes prohibitive while linear equalizers can still be used. In this paper, a SISO linear equalization algorithm is derived for the case of a time-varying channel impulse response, which is either known or estimated. Simulation results are presented showing that the error rate performance of the SISO linear equalizer is close to that using an optimal trellis-based equalizer. The performance of iterative channel estimation is also investigated.

On iterative equalization, estimation, and decoding

We consider the problem of coded data transmission over an inter-symbol interference (ISI) channel with unknown and possibly time-varying parameters. We propose a low-complexity algorithm for joint equalization, estimation, and decoding using an estimator, which is separate from the equalizer. Based on existing techniques for analyzing the convergence of iterative decoding algorithms, we show how to find powerful system configurations. This includes the use of recursive precoders in the transmitter. We derive a novel a-posteriori probability equalization algorithm for imprecise knowledge of the channel parameters. We show that the performance loss implied by not knowing the parameters pf the ISI channel is entirely a loss in signal-to-noise ratio for which a suitably designed iterative receiver algorithm converges.

Design of serially concatenated systems for long or short block lengths

We study the convergence behavior of iterative decoding of various serially concatenated systems such as a concatenated code, coded transmission over a channel introducing inter-symbol interference, bit-interleaved coded modulation, trellis coded modulation, a.s.o. We use EXIT charts to construct simple irregular codes, which can significantly improve the convergence behavior of iterative decoding. An efficient optimization algorithm is presented yielding system which approach information theoretic limits very closely. However, these systems exhibit a satisfactory performance only for very long block lengths. To overcome this problem, we also show how to optimize a concatenated system such that the decoding performance is optimal after a certain fixed number of iterations. It turns out that these systems perform very well for short block lengths, too. As an example, optimal system configurations for data transmission over an AWGN channel are presented.We study the convergence behavior of iterative decoding of various serially concatenated systems such as a concatenated code, coded transmission over a channel introducing inter-symbol interference, bit-interleaved coded modulation, trellis coded modulation, a.s.o. We use EXIT charts to construct simple irregular codes, which can significantly improve the convergence behavior of iterative decoding. An efficient optimization algorithm is presented yielding system which approach information theoretic limits very closely. However, these systems exhibit a satisfactory performance only for very long block lengths. To overcome this problem, we also show how to optimize a concatenated system such that the decoding performance is optimal after a certain fixed number of iterations. It turns out that these systems perform very well for short block lengths, too. As an example, optimal system configurations for data transmission over an AWGN channel are presented.

Graphical models for coded data transmission over inter-symbol interference channels

We derive graphical models for coded data transmission over channels introducing inter-symbol interference. These models are factor graph descriptions of the transmitter section of the communication system, which serve at the same time as a framework to define the corresponding receiver. The graph structure governs the complexity and nature (e.g. non-iterative, iterative) of the receiver algorithm. A particular graph yields several algorithms optimizing various cost functions depending on the choice of messages communicated along the edges of the graph. We study these different outcomes of message passing and how the corresponding receiver algorithms are related to existing ones. We also devise strategies to find suitable graphs for communication problems of interest.

Scalable source/channel decoding for large-scale sensor networks

We consider the sensor reachback problem, in which a large number of sensor nodes are deployed on a field, and the goal is to reconstruct at a remote location the correlated data collected and transmitted by all the nodes. In this paper, we assume that each sensor node uses a very simple encoder (a scalar quantizer and a modulator) and focus on decoding algorithms that exploit the correlation structure of the sensor data to produce the best possible estimates under the minimum mean square error (MMSE) criterion. Our analysis shows that the optimal MMSE decoder is unfeasible for large scale sensor networks, because its complexity grows exponentially with the number of nodes in the network. Seeking a scalable alternative, we use factor graphs to obtain a simplified model for the correlation structure of the sensor data. This model allows us to use an iterative decoding algorithm whose complexity can be made to grow linearly with the size of the network.