Iterative Carrier Phase Recovery Suited to Turbo-Coded Systems

Soft demodulation is a basic module of traditional communication receivers. It converts received symbols into soft bits, that is, log likelihood ratios (LLRs). However, in the nonideal additive white Gaussian noise (AWGN) channel, it is difficult to accurately calculate the LLR. In this letter, we propose a demodulator, DemodNet, based on a fully convolutional neural network with variable input and output length. We use hard bit information to train the DemodNet, and we propose log probability ratio (LPR) based on the output layer of the trained DemodNet to realize soft demodulation. The simulation results show that under the AWGN channel, the performance of both hard demodulation and soft demodulation of DemodNet is very close to the traditional methods. In three non-ideal channel scenarios, i.e., the presence of frequency deviation, additive generalized Gaussian noise (AGGN) channel, and Rayleigh fading channel, the performance of channel decoding using the soft information LPR obtained by DemodNet is better than the performance of decoding using the exact LLR calculated under the ideal AWGN assumption.

The rateless multiple access (RMA) scheme is a promising distributed multiple access scheme to achieve simultaneous high reliability, low latency and massive connectivity. In this paper, we investigate the maximum likelihood (ML) decoding performance of the RMA scheme in an Additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) modulation. For the first time, this paper derives the ensemble weight distribution of the RMA scheme. We derive an upper bound on the decoding error performance of the RMA scheme under ML decoding in an AWGN channel with BPSK modulation. Using the derived bound as the fitness function, we adopt the continuous genetic algorithm to optimize the parameters of the RMA scheme. Simulation results show the tightness of the derived bound and the superiority of the optimized degree distribution over the conventional degree distributions.

An iterative receiver structure is proposed for decoding multiuser information data in a turbo-coded DS-CDMA system. The receiver performs two successive soft-output decisions, achieved by a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders, through an iterative process. At each iteration, extrinsic information is extracted from detection and decoding stages and is then used as a priori information in the next iteration, just as in turbo decoding. A low-complexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft-interference cancellation and instantaneous linear MMSE filtering. Turbo multiuser detectors for both the simple synchronous CDMA channels and the more complex asynchronous multipath CDMA channels are developed.

Turbo codes facilitate near-capacity transmission throughputs by achieving a reliable iterative forward error correction. However, owing to the serial data dependence imposed by the logarithmic Bahl–Cocke–Jelinek–Raviv algorithm, the limited processing throughputs of the conventional turbo decoder implementations impose a severe bottleneck upon the overall throughputs of real-time communication schemes. Motivated by this, we recently proposed a floating-point fully parallel turbo decoder (FPTD) algorithm, which eliminates the serial data dependence, allowing parallel processing and hence significantly reducing the number of clock cycles required. In this paper, we conceive a technique for reducing the critical datapath of the FPTD, and we propose a novel fixed-point version as well as its very large scale integration (VLSI) implementation. We also propose a novel technique, which allows the FPTD to also decode shorter frames employing compatible interleaver patterns. We strike beneficial tradeoffs amongst the latency, core area, and energy consumption by investigating the minimum bit widths and techniques for message log-likelihood ratio scaling and state metric normalization. Accordingly, the design flow and design tradeoffs considered in this paper are also applicable to other fixed-point implementations of error correction decoders. We demonstrate that upon using Taiwan Semiconductor Manufacturing Company (TSMC) 65-nm low-power technology for decoding the longest long-term evolution frames (6144 b) received over an additive white Gaussian noise channel having $E_{b}/N_{0}=1~ \text {dB}$ , the proposed fixed-point FPTD VLSI achieves a processing throughput of 21.9 Gb/s and a processing latency of $0.28~ \mu \text {s}$ . These results are 17.1 times superior to those of the state-of-the-art benchmarker. Furthermore, the proposed fixed-point FPTD VLSI achieves an energy consumption of $2.69~ \mu \text {J}$ /frame and a normalized core area of $5~ \text {mm}^{\vphantom {R^{'}}2}/\text {Gb/s}$ , which are 34% and 23% lower than those of the benchmarker, respectively.

It is well known that binary error-correcting codes with iterative decoders can achieve near Shannon-limit performance on the additive white Gaussian noise (AWGN) channel, but their performance on more realistic wireless channels can become degraded due to the presence of burst errors or impulsive noise due to interference. A better performing coding scheme is the class of non-binary codes, which are known to be more effective in correcting burst errors, but interestingly there is no research reported in the literature investigating non-binary codes on impulsive noise channels. In this paper, we investigate the performance of non-binary turbo codes defined in a finite field GF(4) on symmetric alpha-stable impulsive noise channels and compare with comparable binary turbo codes. A Cauchy receiver is also employed to mitigate the effects of the channel to assist the turbo decoding. Our simulation results show that although the non-binary turbo code performs similarly to the binary turbo code on the AWGN channel, it achieves a significant coding gain over the binary turbo code as impulsiveness increases.

Turbo codes (TC) is a powerful branch of error-control coding that has exhibited performances close to the Shannon limit, whilst offering a reasonable level of computational complexity. Repeat-punctured turbo codes (RPTCs) exploit the fact that the use of larger interleavers correspond to better bit-error rate (BER) performances for the conventional turbo code, and makes use of repetition and puncturing to improve the performance of the conventional turbo code for moderate to high signal-to-noise ratios (SNRs). Motivated by turbo codes and repeat-punctured turbo codes, we study the use of a new scheme, dual-repeat-punctured turbo codes (DRPTC) in the additive white Gaussian noise (AWGN) channel. DRPTCs primarily make use of repetition and puncturing and the structure of the conventional turbo code to yield a more superior performance. The decoding in principle follows the technique of turbo decoding but needs some changes to yield the performance improvement. Simulation results for the AWGN channel is presented together with the analytical union bounds derived from transfer-function bounding techniques, and the codeword distance-spectrum for the proposed scheme is presented and evaluated.

In order to enhance the performance of 112 Gb/s polarization-multiplexed quadrature phase-shift keying (PM-QPSK) coherent optical receivers, a novel digital signal processing (DSP) framework is presented in this study. The suggested method combines cutting-edge signal processing techniques to address important constraints in long-distance, high data rate coherent systems. The framework uses overlap frequency domain equalization (OFDE) for chromatic dispersion (CD) compensation, which offers a cheaper computational cost and higher dispersion control precision than traditional time-domain equalization. An adaptive carrier phase recovery (CPR) technique based on mean-squared differential phase (MSDP) estimation is incorporated to manage phase noise induced by cross-phase modulation (XPM), providing dependable correction under a variety of operating situations. When combined, these techniques significantly increase Q factor performance, and optimum systems can handle transmission distances of up to 2400 km. The suggested DSP approach improves phase stability and dispersion tolerance even in the presence of nonlinear impairments, making it a viable and effective choice for contemporary coherent optical networks. The framework’s competitiveness was evaluated by comparing it against the most recent, cutting-edge DSP methods that were released after 2021. These included CPR systems that were based on kernels, transformers, and machine learning. The findings show that although AI-driven approaches had the highest absolute Q factors, they also required a large amount of computing power. On the other hand, the suggested OFDE in conjunction with adaptive CPR achieved Q factors of up to 11.7 dB over extended distances with a significantly reduced DSP effort, striking a good balance between performance and complexity. Its appropriateness for scalable, long-haul 112 Gb/s PM-QPSK systems is confirmed by a complexity versus performance trade-off analysis, providing a workable and efficient substitute for more resource-intensive alternatives.

Distributed Luby transform (DLT) codes achieve a significant performance improvement in multi-source relay networks compared with the individual Luby transform (LT) code designed for each source. Since the DLT codes preserve the properties of the LT codes, the error floor is dominated by the low variable-node degrees in the bipartite graph, developed for iterative message passing decoding. Therefore, we analyze the error floor of the DLT codes for a multi-source, single relay, and a single destination network over additive white Gaussian noise (AWGN) channels. We modify the encoding process at the sources and propose a new relay combining scheme at the relay. The encoding process at the sources and the combining scheme at the relay are coordinated with the aim of improving the error floor performance of the proposed DLT codes. We derive a lower bound of the bit error probability of the DLT codes over AWGN channels. Furthermore, we optimize the relay degree distribution in terms of the overhead by using the framework of extrinsic information transfer chart analysis. The numerical results confirm that the proposed DLT coding scheme significantly outperforms the conventional scheme, especially in the error floor region.

In this paper, we consider an impulse-based ultra- wideband (UWB) receiver and assess the performance of different multiple access and modulation schemes, including time-hopping pulse position modulation (TH-PPM), time-hopping binary phase shift keying (TH-BPSK), and BPSK-BPSK, under both the additive white Gaussian noise (AWGN) and indoor multipath (CM3) channel assumptions. The assumed receiver combines the received pulses to increase the signal to noise ratio (SNR) and correlates the summed signal with the locally generated template. The performance of the different techniques are estimated using Monte-Carlo simulations and validated by comparing them with the theoretical results obtained for the AWGN channel with the characteristic function (CF) method presented in [1], Amongst other results, we show that the AWGN channel assumption provides rather optimistic results as compared to the more realistic CM3 indoor channel assumption.

An iterative detection and decoding (IDD) receiver which combines a soft-input soft-output (SISO) detector and a SISO double binary (DB) turbo decoder improves the bit-error rate performance. However, the amount of the extrinsic information sent from the DB turbo decoder to the detector is much different from the amount of the extrinsic information sent from the detector to the decoder. Herein, a parity-enhanced DB turbo decoder is designed to provide the bit-level extrinsic information of systematic and parity bits for the WiMAX-based turbo-coded IDD receiver. Compared to the conventional turbo decoder, the proposed decoder achieves ~0.3 dB coding gain with a 6.06% area overhead.

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.

In this paper we investigate turbo decoding based on maximum a posteriori algorithm (MAP). A new reduced complexity scheme of turbo decoder is proposed in which we apply some modifications to the original MAP-based turbo decoder. The basic idea in the proposed method is to derive a simplified trellis at the end of each iteration, based on the information about transmitted symbols obtained in that iteration. The performance of convolutional turbo codes over additive white Gaussian noise (AWGN) channel using the proposed decoding algorithm is evaluated. Simulation results reveal that the proposed decoding algorithm reduces the computational complexity of the system and has negligible bit-error rate (BER) degradation in comparison with the full-search MAP-based decoding algorithm.

This paper proposes an OFDM receiver that iteratively estimates the channel during the iterative decoding process of a serially-concatenated code. To track a slowly time-varying channel, the receiver can update the channel estimate using decision-direction based on soft symbols to mitigate error propagation. When the channel changes so quickly that decision-directed updates cannot keep up, the receiver re-estimates the channel during the decoding process using the EM algorithm based on the transmitted symbol probabilities provided by the turbo decoder. The EM algorithm is used to approximate a maximum likelihood solution given the distribution of the transmitted symbols. With this technique, the iterative process of the EM algorithm is naturally combined with the decoding iteration. Improved coded performance is observed for both static and fast time-varying channels.

In this paper, we propose a novel rate-adaptive system where the receiver adjust demodulation schema to the channel condition, by using controlled soft demodulation (CSD) and rateless erasure code. In CSD, the receiver demodulates only those reliable bits which determined by log likelihood ratio (LLR) criterion and treats non-demodulated bits as deleted. Dynamic LLR threshold strategy and fix LLR threshold strategy were presented to supply some implementations of this system. We analyzed the performance of these strategies over an additive white Gaussian noise channel, and compared the results with the Adaptive Demodulation system. The adaptive solutions were also provided, by analyzing the simulation results with the Raptor codes. The analysis indicates that the CSD system could avoid some defects of traditional rate-adaptive schemes, such as feedback overhead and complexity of the system, it also has better performance than the Adaptive Demodulation system, with much more flexible approach.

This paper proposes a stochastic framework for dynamic modeling and analysis of turbo decoding. By modeling the input and output signals of a turbo decoder as random processes, we prove that these signals become ergodic when the block size of the code becomes very large. This basic result allows us to easily model and compute the statistics of the signals in a turbo decoder. Using the ergodicity result and the fact that a sum of lognormal distributions is well approximated using a lognormal distribution, we show that the input-output signals in a turbo decoder, when expressed using log-likelihood ratios (LLRs), are well approximated using Gaussian distributions. Combining the two results above, we can model a turbo decoder using two input parameters and two output parameters (corresponding to the means and variances of the input and output signals). Using this model, we are able to reveal the whole dynamics of a decoding process. We have discovered that a typical decoding process is much more intricate than previously known, involving two regions of attraction, several fixed points, and a stable equilibrium manifold at which all decoding trajectories converge. Some applications of the stochastic framework are also discussed, including a fast decoding scheme