Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalization" approach, which can be applied to coded data transmission over channels with intersymbol interference (ISI). In the original system invented by Douillard et al., the data is protected by a convolutional code and a receiver consisting of two trellis-based detectors are used, 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 (BER). We introduce new approaches to combining equalization based on linear ltering with the decoding. The result is a receiver that is capable of improving BER performance through iterations of equalization and decoding in a manner similar to turbo ...

We track the density of extrinsic information in iterative turbo decoders by actual

In this paper, we review recent developments concerning the application of lowdensity parity-check (LDPC) codes to the Gilbert-Elliott (GE) channel. Firstly, we discuss the analysis of LDPC estimation-decoding in these channels using density evolution. We show that the required conditions of density evolution are satisfied in the GE channel, and that analysis demonstrates that large potential gains over the memoryless assumption. We also give results which mitigate the complexity of characterizing the GE parameter space using DE. Subsequently, we give a design tool for finding good degree sequences for irregular LDPC codes in the GE channel.

Abstract—In this paper, we consider soft decision directed channel estimation for turbo equalization. To take advantage of soft information provided by the decoder, a minimum mean square error linear channel estimator is derived under an uncorrelated channel tap model, and a soft input recursive least squares algorithm is also developed by modifying the cost function of the conventional recursive least squares algorithm. The performance of the proposed channel estimators are analyzed in terms of mean square identification error (MSIE) for stationary channels. Simulation results for both time-invariant and time-varying frequency-selective Rayleigh fading channels are also presented. Index Terms—Channel estimation, soft input, turbo equalization. I.

Abstract—We consider the performance analysis and design optimization of low-density parity check (LDPC) coded multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems for high data rate wireless transmission. The tools of density evolution with mixture Gaussian approximations are used to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios (SNRs) for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations, which include a different number of antennas, different channel models, and different demodulation schemes; the optimized performance is compared with the corresponding channel capacity. It is shown that along with the optimized irregular LDPC codes, a turbo iterative receiver that consists of a soft maximum a posteriori (MAP) demodulator and a belief-propagation LDPC decoder can perform within 1 dB from the ergodic capacity of the MIMO OFDM systems under consideration. It is also shown that compared with the optimal MAP demodulator-based receivers, the receivers employing a low-complexity linear minimum mean-square-error soft-interference-cancellation (LMMSE-SIC) demodulator have a small performance loss ( 1dB) in spatially uncorrelated MIMO channels but suffer extra performance loss in MIMO channels with spatial correlation. Finally, from the LDPC profiles that already are optimized for ergodic channels, we heuristically construct small block-size irregular LDPC codes for outage MIMO OFDM channels; as shown from simulation results, the irregular LDPC codes constructed here are helpful in expediting the convergence of the iterative receivers. Index Terms—Code design, density evolution, ergodic capacity,

Recent literature presents methods for the analysis of concatenated coding schemes by solely characterizing the behavior of the component codes [4], [12], [16], [9], [7]. Component codes are analyzed either analytically using unique properties of special component codes, e.g., single--parity--check code or accumulator, or via simulations.

Abstract — In recent years, network coding has been investigated as a method to obtain improvements in wireless networks. A typical assumption of previous work is that relay nodes performing network coding can decode the messages from sources perfectly. On a simple relay network, we design a scheme to obtain network coding gain even when the relay node cannot perfectly decode its received messages. In our scheme, the operation at the relay node resembles message passing in belief propagation, sending the logarithm likelihood ratio (LLR) of the network coded message to the destination. Simulation results demonstrate the gain obtained over different channel conditions. The goal of this paper is not to give a theoretical result, but to point to possible interaction of network coding with user cooperation in noisy scenario. The extrinsic information transfer (EXIT) chart is shown to be a useful engineering tool to analyze the performance of joint channel coding and network coding in the network. I.

Recently very good iterative decoding performance close to Shannon's capacity limit [12] has been obtained by using a serially concatenated structure consisting of an outer repetition code and an inner rate one scrambler [5, 7]. In this paper we show that these codes can also be interpreted as parallel concatenated \turbo" codes, if we apply some restrictions on the interleaver design which, however, do not aect the decoding performance.

Recent literature presents methods for the analysis of concatenated coding schemes by solely characterizing the behavior of the component codes [4, 12, 14, 9, 7]. Component codes are analyzed either analytically using unique properties of special component codes, e.g., single–parity–check code or accumulator, or via simulations. The goals of this paper are to find fundamental insights into concatenated codes by analyzing the input–output relation of their components from an information– theoretic point of view. We derive a Information Processing Characteristic (IPC), which completely characterizes the behavior of a coding scheme comprising encoder, code and decoder for the general class of linear codes. For time invariant convolutional codes it is studied how the IPC can be obtained in practice. 1

ABSTRACT nels was computed. Wiberg [3] in his dissertation has We model the density of extrinsic information in iterative turbo decoders by Gaussian density functions. This model is verified by experimental measurements. We consider evolution of these density functions through the iterative turbo decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes are analyzed based on this method. Many mysteries of turbo codes can be explained based on this analysis. For exshown that the extrinsic information in iterative decoding can be approximated by a Gaussian density function. El Gama1 [5] in his dissertation considered the soft-input soft-output APP module in turbo decoders as a signal-to-noise ratio (SNR) transformer, and also suggested a method for analyzing the overall turbo decoder. A method for analyzing the convergence of the decoder similar to the one developed here, but based on mutual information, was discussed in [13]. ample we can explain why certain codes converge better In this paper, we analyze turbo codes and serially with iterative decoding than more powerful codes which concatenated codes by approximating the density funcare only suitable for maximum likelihood decoding. The tions for the extrinsics as Gaussian densities, and then roles of systematic bits and of recursive convolutional computing the mean and variance in the Gaussian dencodes as constituents of turbo codes are explained based sity evolution. This approximation was used to obtain on this analysis. a threshold on minimum bit signal-to-noise ratio &/No for LDPC codes [6], based on using only the means of I.