Iterative Decoding Research Articles

Kalman Combining Based Iterative Detection and Decoding for MIMO Systems With Hybrid ARQ

This study proposes Kalman combining-based iterative detection and decoding (KC-IDD) schemes for multiple-input multiple-output (MIMO) systems with hybrid automatic repeat request (HARQ). The conventional Kalman filtering (KF) operation for Kalman combining performs the linear minimum mean-square error (LMMSE) detection with symbol-level combining (SLC), but it is unable to utilize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of retransmitted symbols. Therefore, a new KF operation is derived, wherein an observation adjustment is employed to adjust the observation for a given state of the state-space model with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information instead of directly utilizing it into the KF operation. Based on the modified KF operation, two KC-IDD schemes are developed: i) KC-IDD with the single-state observation adjustment, i.e., the observation adjustment for the current HARQ round, and ii) KC-IDD with multi-state observation adjustment (KC-IDD-MS), i.e., the observation adjustments throughout the HARQ rounds of a packet. Therefore, the proposed schemes can perform SLC-based LMMSE-IDD, where the complexity for a given number of turbo iterations is similar or smaller to that of the conventional LMMSE-IDD scheme with bit-level combining (BLC). Furthermore, the simulation results show that regardless of the retransmission strategy, the proposed schemes, especially the KC-IDD-MS scheme, outperformed the conventional LMMSE-IDD scheme in terms of error performance and decoding convergence speed for retransmissions.

Precoded Filterbank Multicarrier Index Modulation With Non-Orthogonal Subcarrier Spacing

In this paper, we propose a novel precoded non-orthogonal frequency division multiplexing (NOFDM) with subcarrier index modulation (SIM) to increase spectral efficiency for multicarrier systems. The proposed NOFDM-SIM scheme is constituted by a filterbank multicarrier system under reduced subcarrier spacing, where precoded index modulated symbols are mapped onto the subcarriers. The detrimental effects of inter-carrier interference (ICI) resulting from the non-orthogonality between subcarriers are efficiently mitigated with the aid of eigenvalue-decomposition-based precoding. Our simulation results demonstrate that the proposed precoded NOFDM-SIM system exhibits a similar peak-to-average power ratio to OFDM and OFDM-SIM counterparts while achieving the bit error rate limit of zero-ICI OFDM in a channel-uncoded setting. We analyze the power spectral density of the proposed scheme to demonstrate that the proposed scheme is strictly bandlimited, unlike its orthogonal counterpart. Furthermore, we present detailed investigations of the effects on ICI in the proposed scheme with and without precoding as well as power allocation. Finally, we introduce a three-stage iterative decoding architecture for our proposed scheme and show near-capacity error performance.

Normalized Min-Sum Neural Network for LDPC Decoding

The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.

Iterative double-differential direct-sequence spread spectrum reception in underwater acoustic channel with time-varying Doppler shifts.

Conventional double differential phase-shift keying modulation amplifies the phase noise and performs poorly under the time-varying direct-sequence spread-spectrum (DSSS) communication system. Therefore, the authors propose an iterative reception for DSSS communication in time-varying underwater acoustic channels. First, bit-interleaved coded modulation with iterative decoding integrated with multi-symbol differential detection is used. Second, this paper uses cross correlation method to estimate and track the Doppler shift of each symbol. Based on Doppler estimates, a dynamic linear prediction model is proposed to estimate and track the channel phase variation. Third, an algorithm for adaptive selection of reference signals is utilized to recover the magnitude attenuation of correlation peaks. Numerical simulation results demonstrate that the proposed reception achieves around 9 dB gain compared to conventional differential decision reception under constant acceleration of 0.14 m/s2. During the acoustic communication experiment in Songhua Lake, the proposed reception was tested by using a moving source at a speed of 1-6 knots at 2-m depth and the farthest distance between the transceivers is 2.8 km. The proposed reception achieves only one frame error from a total of 205 frames collected in the lake experiment, and it also achieves error-free communications over 96 frames during a 10 km depth deep-sea experiment.

Concatenated turbo polar-convolutional codes based on soft cancellation algorithm

This paper presents the Parallel and Serial Concatenated Turbo Polar-Convolutional Codes (CTPCCs) to improve the performance of polar codes in the finite code length regime. Both proposed concatenated codes use the Systematic Polar Code (SPC) and Recursive Systematic Convolutional (RSC) code as constituent codes. The iterative decoding algorithms of the proposed systems consist of a Soft Cancellation (SCAN) decoder with a single internal iteration for the SPC and SOVA or LogMap decoder for the RSC code. The simulation results show that the performance of the Parallel Concatenated Turbo Polar-Convolutional Code (PCTPCC) at low signal-to-noise ratios (SNRs) is better than that of the Serial Concatenated Turbo Polar-Convolutional Code (SCTPCC) and also better than the performance of other Turbo Polar Codes (TPCs). At BER=10−2, the proposed PCTPCC with SOVA and LogMap algorithms has about 0.3 dB and 0.25 dB performance gains over the SCTPCC models, respectively. In the high SNR regions, the performance of the SCTPCC with the LogMap algorithm significantly outperforms that of other models. At BER=10−6, the proposed SCTPCC models with SOVA and LogMap algorithms outperform the PCTPCC model by gains of 0.3 dB and 0.25 dB, respectively. The PCTPCC model with the SOVA decoder is superior to other models in terms of complexity.

LCIF-Net: Local criss-cross attention based optical flow method using multi-scale image features and feature pyramid

Although CNN-based optical flow methods have achieved remarkable performance in terms of computational accuracy and efficiency, the issue of edge-blurring caused by large displacements remains an open challenge. To address this problem, we propose a local criss-cross attention based optical flow estimation method using multi-scale image features and feature pyramid. First, we design an image pyramid-based feature extraction sub-network and then incorporate it into the feature pyramid network to construct a hybrid feature extraction module, which is able to extract multi-scale structural and semantic information from the input images. Second, we concatenate a local criss-cross attention module with the hybrid feature extraction module to build a global feature encoder. The global feature encoder further captures the long-range dependencies within the feature map to improve the large displacement estimation performance. Finally, we combine the global feature encoder with an iterative optical flow decoder, and thus propose a novel network named LCIF-Net. We demonstrate its significant performance benefits on MPI-Sintel and KITTI datasets. Compared with the existing optical flow estimation methods, our LCIF-Net remarkably improves the accuracy and robustness for the optical flow estimation, especially in the regions with large displacements and motion edges.

Tree-Search Techniques for Joint Iterative Compressive Sensing and LDPC Decoding in Wireless Sensor Networks

Novel techniques are conceived for joint compressive sensing (CS) and low-density parity check (LDPC) coding in wireless sensor networks (WSNs), namely, a soft-input soft-output (SISO) tree search sphere decoding (SD) technique and an SISO Hamming distance (HD)-based solution. Factor graphs are utilized to describe the connectivity between the signals and sensors, as well as with the LDPC codes. In the fusion center (FC), the factor graphs may be used for iterative joint LDPC-CS decoding in order to recover the signals observed. However, the CS decoder of the FC suffers from high complexity if the exhaustive Maximum A Posteriori (e-MAP) technique is employed, which considers all possible combinations of source signals detected by each of the associated sensors. Hence, in the proposed SD and HD schemes, only the more likely combinations of source signals are tested for reducing the CS decoding complexity. More specifically, a tree search technique is used in the first step to find the most likely combination of source signal values. Then, in the second step, the proposed SD continues the tree search to find a set of alternative hypotheses. This facilitates the generation of high-quality extrinsic information, which may be iteratively exchanged with the LDPC decoder. By contrast, in the HD approach, the second step obtains the alternative hypotheses within a certain HD of the most likely source signal combination. Both our BLock Error Rate (BLER) results and EXtrinsic Information Transfer (EXIT) charts show that the proposed SD and HD techniques approach the performance of the full-search e-MAP approach at a significantly reduced complexity. In particular, we show that the e-MAP solution is about 56 times more complex than the SD approach and around 210 times more complex than the HD approach. Compared to a separate source-channel coding (SSCC) hard information benchmarker, the proposed SISO schemes improve the decoding performance by about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${1}.{7} \text {dB}$ </tex-math></inline-formula> . Furthermore, the SISO schemes allow the iterations inside the CS decoding to eliminate the error floors and obtain a further <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${2}.{45}$ </tex-math></inline-formula> -dB gain.

Анализ и оптимизация схем кодирования для каналов с рэлеевскими замираниями

Conventional approach to perform error-correcting decoding in channels with memory is an adoption of interleaving, which increases the receiver complexity and delay. In order to avoid these limitations, approaches for adapting an error-correcting scheme for memory channels may be used. One approach is to use error-correcting codes with modified design and decoding procedure, taking into account the presence of error bursts in the channel. Another approach to adapting the coding scheme for burst error correction is to use product codes with iterative decoding algorithms. Component codes of product codes themselves may not be able to correct error bursts, but a two-dimensional structure of product codes operating as an artificial interleaver and iterative decoding allow for correction of grouping errors. Purpose: The purpose of the study is to analyze the methods of error-correcting code adaptation to burst error correction in channels with memory in order to reduce the probability of error. Results: The study considered methods of error-correcting code scheme adaptation for low-density parity-check codes, polar codes, and product codes for burst error correction in Gilbert-Elliott channel (GE) and correlated Rayleigh fading channel with different correlation coefficients. Degree distribution of low-density parity-check code was optimized for GE channel. The influence of selected parameters of product code component codes on burst error correction in the GE channel was analyzed. The structure of the polar code has been optimized using a genetic algorithm for the correlated Rayleigh channel, which outperforms the 5G polar code design in terms of error probability. Discussion: Existing error-correcting code schemes do not provide theoretically possible limits, so the question remains of developing coding and decoding schemes capable of reaching theoretical limits.

Simultaneous Active and Passive Information Transfer for RIS-Aided MIMO Systems: Iterative Decoding and Evolution Analysis

This paper investigates the potential of reconfigurable intelligent surface (RIS) for passive information transfer in a RIS-aided multiple-input multiple-output (MIMO) system. We propose a novel simultaneous active and passive information transfer (SAPIT) scheme. In SAPIT, the transmitter (Tx) and the RIS deliver information simultaneously, where the RIS information is carried through the RIS phase shifts embedded in reflected signals. We introduce the coded modulation technique at the Tx and the RIS. The main challenge of the SAPIT scheme is to simultaneously detect the Tx signals and the RIS phase coefficients at the receiver. To address this challenge, we introduce appropriate auxiliary variables to convert the original signal model into two linear models with respect to the Tx signals and one entry-by-entry bilinear model with respect to the RIS phase coefficients. With this auxiliary signal model, we develop a message-passing-based receiver algorithm. Furthermore, we analyze the fundamental performance limit of the proposed SAPIT-MIMO transceiver. Notably, we establish the state evolution to predict the receiver performance in a large-size system. We further analyze the achievable rates of the Tx and the RIS, which provides insight into the code design for sum-rate maximization. Numerical results validate our analysis and show that the SAPIT scheme outperforms the passive beamforming counterpart in achievable sum rate of the Tx and the RIS.

Probabilistic Prediction of Consolidation Settlement and Pore Water Pressure Using Variational Autoencoder Neural Network

This paper explores the use of a variational autoencoder to predict the embankment settlement and pore water pressure based on monitoring data. A variational autoencoder can learn intrinsic patterns in embankment behavior through unsupervised deep machine learning. The proposed approach implemented the observational method efficiently because updating soil parameters was no longer a necessary step, unlike in previous research. The embankment response was predicted directly through Gibbs sampling, which involves an iterative encoding and decoding process in the variational autoencoder. The variational autoencoder was trained using simulated embankment responses from the numerical (Plaxis) model. The approach was applied at the Ballina site to predict the embankment response, based on monitoring data with varying time periods. The prediction intervals captured the actual trends satisfactorily, with the intervals becoming more aligned with actual values as more monitoring data were incorporated. The predictions were also more reasonable, compared to those based entirely on representative soil parameters from laboratory or in-situ tests. The variational autoencoder was also applied to another case involving synthetic monitoring data based on the Ballina site, which demonstrates the capability of the variational autoencoder to predict multiple scenarios of embankment behavior.

Design of LDPC Coded Multi-User Massive MIMO Systems With MMSE-Based Iterative Joint Detection and Decoding

Design of LDPC Coded Multi-User Massive MIMO Systems With MMSE-Based Iterative Joint Detection and Decoding

On the Use of FFH-MFSK for Ultra-Low Power Communications in a Jamming Environment

We are interested in a communication system that operates in the presence of an intelligent jammer, under stringent power constraints, but with flexible bandwidth constraints.We optimize some of the key elements in the transceiver design for low power consumption, and thus high complexity components of the system, such as matched filters (MF), forward error correction (FEC) that employs iterative decoders, coherent demodulators, and bandwidth-efficient modulation formats, are not feasible for this research. Rather, our system is designed using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary frequency shift keying (MFSK) with non-coherent detection and fast frequency hopping (FFH), optimized two-pole bandpass filters (BPF), and Reed-Solomon (RS) codes with hard-decision decoding. Among other things, we show that by properly optimizing the key parameters of the BPFs and RS codes, we can design the system to be significantly less complex than the MF system with a performance loss of less than 1.4 dB for most scenarios that we considered. Further, the 2-pole BPF system can actually outperform the corresponding MF system by up to 2.4 dB in the presence of multi-tone jamming.

Performance Analysis of Different Flexible Decoding Algorithms for NR-LDPC Codes

Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.

Semantic Coding for Text Transmission: An Iterative Design

We consider the wireless text transmission using joint source-channel coding (JSCC). Classical source coding only considers the syntactic information based on probabilistic models, ignoring the meaning of source messages. Neural network based joint source and channel coders handle the source semantic information more efficiently. However, existing semantic transmission using end-to-end neural networks do not generalize well under varying channel conditions. To tackle this, we propose a semi-neural framework with an iterative architecture, named iterative semantic JSCC (IS-JSCC). Specifically, at each iteration, the remaining semantics is extracted from the intermediate decoded text and is then used as a priori information for the channel decoder in the next iteration. Instead of reconstructing text explicitly, we synthesize the semantics of candidate words in the embedding space, weighted by their posterior probability. This soft semantic synthesis alleviates the error propagation and reduces the complexity of iterative decoding as well. Results show that compared to full-neural designs, the proposed framework can improve the quality of text reconstruction by joint iterative decoding and exhibit better robustness over wireless channels.

Hadamard–Viterbi Joint Soft Decoding for MFSK Underwater Acoustic Communications

Multiple Frequency-Shift Keying (MFSK) has been used widely for underwater acoustic communications due to its low complexity and channel robustness. However, the traditional MFSK has the limitation of a low bit rate compared with coherent acoustic communication. To increase the bit rate, this study designs a new MFSK with the concept of orthogonal frequency division multiplexing (OFDM). We also adopt a channel-concatenated coding to resist the multipath interference and design the iterative joint decoding. The channel-concatenated coding consists of a Hadamard code and a convolutional code. Correspondingly, the iterative joint decoding uses the Hadamard–Viterbi joint soft decoding framework with a newly designed branch metric, which uses the Hadamard structure. As an important preprocessing link for a received signal, frame synchronization and Doppler compensation are also described in detail in this study. Simulations and experiments are conducted to show the effectiveness of the proposed MFSK underwater acoustic communications.

Energy consumption modeling and analysis for short-reach optical transmissions using irregular LDPC codes.

As the transmission rate of data center (DC) related short-reach optical transmissions quickly increases to keep up with internet services' data demand pace, advanced FEC technology starts to establish its key role in short reach optical transmission systems. Coding strategy using Quasi-Cyclic LDPC (QC-LDPC) codes with hard-decision (HD) decoders stands out due to its excellent error correction ability and simple hardware implementation. Meanwhile, with the introduction of green communication concept and increasingly extensive applications of DC, energy consumption of short-reach links has become an urgent problem to be studied. Based on tanner-graph, energy consumption models of regular LDPC codes' HD decoding circuits over AWGN channel have been proposed. In this work, for the first time, we introduce energy consumption of optical transmitters and characteristics of short reach optical channels into energy consumption modeling. Besides, probability distributions of flipping operation as well as bit errors during irregular QC-LDPC codes' HD decoding iterations are analytically derived using density evolution algorithm. Based on our proposed model and post-layout circuit simulation, systems' total power when using four QC-LDPC codes in IEEE and 3GPP with Gallager A/B decoders together with the case of using no FEC are analyzed in two typical scenarios. Numerical results show that, in short range scenario with slight bandwidth limit, uncoded strategy is much more energy-saving than all adopted LDPC-coded strategies in 50Gbaud OOK and 25Gbaud PAM4 transmissions. While in severely band-limited case when FEC is necessary, a tradeoff between energy consumption of transmitters and decoders occurs in 70Gbaud OOK and 35Gbaud PAM4 transmissions. Besides, LDPC codes with longer length at similar rate are proved to consume less power for their better error correction ability. And in long range scenario, power differences among coding strategies grow significantly when pre-bit error rate (BER) approaches their error correction threshold, reflecting the great influence of error correction threshold on the energy consumption of LDPC decoders. Among all adopted coding strategies, a (19200, 15872) LDPC code with Gallager B decoder consumes minimum power in both two scenarios. However, it is also found that decoding algorithm minimizing the total power differs at different pre-BER if we concentrate on decoding algorithm, justifying the significance of our modeling in minimizing system energy consumption.

Improved Soft-Aided Decoding of Product Codes With Dynamic Reliability Scores

Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid algorithms have been proposed aimed to improve the performance of iBDD decoders via the aid of a certain amount of soft information while keeping the decoding complexity similarly low as in iBDD. We propose a novel hybrid low-complexity decoder for PCs based on error-and-erasure (EaE) decoding and dynamic reliability scores (DRSs). This decoder is based on a novel EaE component code decoder, which is able to decode beyond the designed distance of the component code but suffers from an increased miscorrection probability. The DRSs, reflecting the reliability of a codeword bit, are used to detect and avoid miscorrections. Simulation results show that this policy can reduce the miscorrection rate significantly and improves the decoding performance. The decoder requires only ternary message passing and a slight increase of computational complexity compared to iBDD, which makes it suitable for high-speed communication systems. Coding gains of up to 1.2 dB compared to the conventional iBDD decoder are observed.

Improving the Security of Split Data When Using Multidimensional Parity Algorithms

A model of distributed storage split data using algorithms, multidimensional parity, resistance to partial losses of the storage sites, is regarded as an alternative way of security that can replace the conventional multiple reservations and carrying costs of growth of the physical volume. In this model, the generated redundant data allows you to restore partial loss of the split parts. In this case, the recovery is performed at the expense of the parity files formed during the splitting procedure, in which the main action is the calculation of bitwise parity with summation modulo "two". With this additional operation between the source files, you can restore the corrupted file without distortion. A comparison with several models that use checksum codes for recovery shows that the estimated probability of losses due to storage failure in the case of multidimensional parity codes is significantly less than when using other split data storage options. Using the operation of adding the bits of undamaged files, you can completely restore corrupted files. According to the calculated data, even when theoretically non-recoverable losses are reached, it is always possible to find combinations of chain recovery. The complexity of alternative methods, including the iterative decoding method, makes a distributed split data storage system using multidimensional parity algorithms a more convenient error correction technology.&#x0D; Keywords— , , , , loss recovery, .

Performance Improvement of Polar Codes via UEP Product Coding

Aiming to improve the error correction performance of polar codes, researchers have proposed employing the product coding structure involving RS codes of different rates in the horizontal direction and the short polar codewords along the vertical direction. However, there is no efficient algorithm optimizing the rate allocation of RS codes. In order to address this problem, this paper provides an analytical formulation by maximizing the number of correctly decoded information bits. The proposed rate allocation formulation takes the channel statistics into consideration, and we further find that the number of different RS code rates could be limited to a small value. By doing so, the complexities of both the rate allocation optimization and the iterative product decoding could be reduced. Simulation results demonstrate the superiority of RS-polar product codes with the proposed rate allocation method over both additive white Gaussian noise channels and Gilbert–Elliott channels. When the inner polar codes of rate 1/2 are utilized, the optimized RS-polar product codes of low-to-medium rates significantly outperform the successive cancellation decoding of long polar codes, in the regime of a frame error rate ≥10−3.

Efficient Decoder for Turbo Product Codes Based on Quadratic Residue Codes

In this letter, we study turbo product codes with quadratic residue codes (called QR-TPCs) as the component codes. We propose an efficient decoder based on Chase-II algorithm with two convergence conditions for the iterative decoding of QR-TPCs. For each row and column, the Chase-II decoder will stop immediately when one of the conditions is met. The simulation results show that the proposed algorithm has a lower computational complexity compared with existing decoding methods. Moreover, a comparison with 5G low-density parity-check codes shows that the proposed turbo product codes have better performance for short code lengths.