Henk Wymeersch

Code-Aided Turbo Synchronization

The introduction of turbo and low-density parity-check (LDPC) codes with iterative decoding that almost attain Shannon capacity challenges the synchronization subsystems of a data modem. Fast and accurate signal synchronization has to be performed at a much lower value of signal-to-noise ratio (SNR) than in previous less efficiently coded systems. The solution to this issue is developing specific synchronization techniques that take advantage of the presence of the channel code and of the iterative nature of decoding: the so-called turbo-synchronization algorithms. The aim of this paper within this special issue devoted to the turbo principle is twofold: on the one hand, it shows how the many turbo-synchronization algorithms that have already appeared in the literature can be cast into a simple and rigorous theoretical framework. On the other hand, it shows the application of such techniques in a few simple cases, and evaluates improvement that can be obtained from them, especially in the low-SNR regime.

Multidimensional mapping for bit-interleaved coded modulation with BPSK/QPSK signaling

In recent years, it has been recognized that bit-interleaved coded modulation with iterative decoding (BICM-ID) achieves excellent performance on virtually any channel, provided the signal mapping is carefully designed. In this paper, we introduce multidimensional mapping for BICM-ID, where a group of bits is mapped to a vector of symbols, rather than a single symbol. This allows for more flexibility and potential performance improvements. Our analysis shows that multidimensional mapping leads to an increase in Euclidean distance, thus boosting the performance compared to conventional mapping schemes. We derive a design criterion for optimal mappings and we provide such optimal mappings for BPSK and QPSK constellations.

True Cramer-Rao bound for timing recovery from a bandlimited linearly Modulated waveform with unknown carrier phase and frequency

This paper derives the Cramer-Rao bound (CRB) related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency. We consider the following two scenarios: joint estimation of the time delay, the carrier phase, and the carrier frequency; and joint estimation of the time delay and the carrier frequency irrespective of the carrier phase. The transmit pulse is a bandlimited square-root Nyquist pulse. For each scenario, the transmitted symbols constitute either an a priori known training sequence or an unknown random data sequence. In spite of the presence of random data symbols and/or a random carrier phase, we obtain a relatively simple expression of the CRB, from which the effect of the constellation and the transmit pulse are easily derived. We show that the penalty resulting from estimating the time delay irrespective of the carrier phase decreases with increasing observation interval. However, the penalty, caused by not knowing the data symbols a priori, cannot be reduced by increasing the observation interval. Comparison of the true CRB to existing symbol synchronizer performance reveals that decision-directed timing recovery is close to optimum for moderate-to-large signal-to-noise ratios.

Code-aided frame synchronization and phase ambiguity resolution

This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful error-correcting codes and operate at low signal-to-noise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a re-encoding (REEN) technique, an algorithm we previously derived from the expectation-maximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudo-ML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum-product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EM-based and the PML algorithms have excellent performance. The MS, PML, REEN, and EM-based algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance

On Maximum-Likelihood Timing Synchronization

In this paper, we address the issue of symbol timing recovery for a coded burst transmission system. As direct maximum-likelihood (ML) estimation is intractable, we resort to the expectation-maximization (EM) algorithm in order to derive a receiver that iterates between data detection and synchronization. Conventional data-aided (DA) and decision-directed (DD) synchronizers can be interpreted as special cases of the proposed algorithm. The EM-based technique takes into account code properties and is especially well suited to scenarios where conventional schemes fail to provide the detector with a reliable timing estimate. The performance of the proposed algorithm is compared with conventional techniques through computer simulations, both in terms of mean-square estimation error (MSEE) and bit error rate (BER).

Iterative code-aided ML phase estimation and phase ambiguity resolution

As many coded systems operate at very low signal-to-noise ratios, synchronization becomes a very difficult task. In many cases, conventional algorithms will either require long training sequences or result in large BER degradations. By exploiting code properties, these problems can be avoided. In this contribution, we present several iterative maximum-likelihood (ML) algorithms for joint carrier phase estimation and ambiguity resolution. These algorithms operate on coded signals by accepting soft information from the MAP decoder. Issues of convergence and initialization are addressed in detail. Simulation results are presented for turbo codes, and are compared to performance results of conventional algorithms. Performance comparisons are carried out in terms of BER performance and mean square estimation error (MSEE). We show that the proposed algorithm reduces the MSEE and, more importantly, the BER degradation. Additionally, phase ambiguity resolution can be performed without resorting to a pilot sequence, thus improving the spectral efficiency.

Spatial mapping for MIMO systems

This contribution proposes a new spatial mapping technique for bit-interleaved coded modulation (BICM) over multiple-input multiple-output (MIMO) channels. It is an extension of conventional BICM whereby the serial-to-parallel converter is replaced with a more general mapping strategy. Genie performance analysis of spatial mapping schemes results in very simple design criteria for the mapping function. Using an iterative detector, a significant performance gain is observed compared to a conventional BICM scheme, at no significant increase in computational complexity. The predicted performance gains are verified through computer simulations.

Code-aided joint channel estimation and frame synchronization for MIMO systems

This contribution deals with the problem of joint frame synchronization and channel estimation for a system using bit-interleaved coded modulation in a MIMO context. A receiver, based on the EM algorithm, is derived. This receiver iterates between detection and estimation. We illustrate how initial estimates may be obtained and how convergence problems may be avoided. Through computer simulations the performance of the proposed receiver is investigated, both in terms of frame error rate (FER) and estimation error variance. We show that exploiting code properties for estimation purposes allows to reduce the length of training sequences and thus results in an increase in spectral efficiency.

Computational complexity and quantization effects of decoding algorithms for non-binary LDPC codes

This contribution deals with the comparison of the sum-product algorithm (SPA) and its log-domain version (log-SPA) for decoding LDPC (low density parity check) codes over general binary extension fields. For both algorithms, we determine their computational complexity based on the number of real-valued operations and investigate their sensitivity to quantization effects. Whereas the log-SPA yields the shorter decoding time in the case of binary LDPC codes, we point out that increasing the field size tends to favor the SPA, especially when a multiplication takes only slightly more time than an addition. Further, we show that log-SPA requires fewer quantization levels and suffers less from a quantization induced error-floor.

Linear Precoders for Bit-Interleaved Coded Modulation on AWGN Channels: Analysis and Design Criteria

This paper investigates linear precoding for bit-interleaved coded modulation (BICM) on additive white Gaussian noise (AWGN) channels. Concatenating a linear precoder as an inner encoder with an outer (convolutional) encoder produces a powerful code with a limited decoding complexity. Linear precoders are examined and optimized for two scenarios: using (i) a noniterative decoding strategy and (ii) an iterative decoding strategy under a perfect feedback assumption. The precoder design is based on an information-theoretical approach, on the one hand, and a pair-wise error probability (PEP) analysis, on the other hand. Both approaches render convenient precoder design rules. For a binary phase-shift keying (BPSK) signal set, the optimal precoders that result from these rules are also derived. Numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach.