Iterative Turbo Decoding Research Articles

Design of a turbo-based deep semantic autoencoder for marine Internet of Things

With the rapid growth of the global marine economy and flourishing maritime activities, the marine Internet of Things (IoT) is gaining unprecedented momentum. However, current marine equipment is deficient in data transmission efficiency and semantic comprehension. To address these issues, this paper proposes a novel End-to-End (E2E) coding scheme, namely the Turbo-based Deep Semantic Autoencoder (Turbo-DSA). The Turbo-DSA achieves joint source-channel coding at the semantic level through the E2E design of transmitter and receiver, while learning to adapt to environment changes. The semantic encoder and decoder are composed of transformer technology, which efficiently converts messages into semantic vectors. These vectors are dynamically adjusted during neural network training according to channel characteristics and background knowledge base. The Turbo structure further enhances the semantic vectors. Specifically, the channel encoder utilizes Turbo structure to separate semantic vectors, ensuring precise transmission of meaning, while the channel decoder employs Turbo iterative decoding to optimize the representation of semantic vectors. This deep integration of the transformer and Turbo structure is ensured by the design of the objective function, semantic extraction, and the entire training process. Compared with traditional Turbo coding techniques, the Turbo-DSA shows a faster convergence speed, thanks to its efficient processing of semantic vectors. Simulation results demonstrate that the Turbo-DSA surpasses existing benchmarks in key performance indicators, such as bilingual evaluation understudy scores and sentence similarity. This is particularly evident under low signal-to-noise ratio conditions, where it shows superior text semantic transmission efficiency and adaptability to variable marine channel environments.

Sliding-Window Turbo Equalization and Its Reduced-Complexity Decoding Techniques

Turbo equalization is a cooperative error-correcting approach to achieve a target bit-error rate over inter-symbol interference channels. In this paper, we proposed a new turbo equalization, called sliding-window turbo equalization (SW-TE), consisting of the Bahl-Cocke-Jelinek-Raviv detector and a spatially coupled, low-density, parity-check decoder. Moreover, the Protograph-based Extrinsic Information Transfer (P-EXIT) chart was modified to investigate the asymptotic behavior of SW-TE. Our analyses showed that SW-TE outperformed conventional turbo equalization in terms of decoding threshold. Based on the P-EXIT chart analysis, we further proposed a guideline of the reduced-complexity decoding techniques for SW-TE, eliminating unnecessary branch metric updates during turbo iterative decoding. Our simulations corroborated the analytical results, showing that SW-TE outperformed conventional turbo equalization while maintaining an acceptable level of complexity.

Performance improvement of visible light communication links based on coded unipolar OFDM

Visible light communications are limited by the narrow bandwidth of their sources as the light-emitting diodes, which restricts the high data rates transmission. A potential technique such as multi-carrier modulation is considered promising for achieving a high-speed data rate and enhancing system performance. This paper proposes turbo coding with unipolar orthogonal frequency-division multiplexing (U-OFDM) for indoor environments. The system under U-OFDM considerations can reduce the inter-symbol interference caused by multiple paths and mitigate burst errors by adopting an iterative turbo decoding. The system performance is evaluated regarding the bit error rate (BER) for the range of the signal-to-noise ratio (SNR) under receiver field-of-view (FOV) restriction. The obtained results show that the performance system of the target BER (below the threshold limit of 3.8×10<sup>−3</sup>) has a power penalty of ~9 dB for modulation order of 64 for quadrature amplitude modulation scheme, FOV of 50°, and incidence angle of half power assigned to 30°. The obtained results also showed a ~10.8 dB improvement in the SNR when comparing the present system with coded-DC-biased optical OFDM under the same considerations.

The effects of the cross-entropy stopping criterion and quadrature amplitude modulation on iterative turbo decoding performance

One of the most often-used stopping criteria is the cross-entropy stopping criterion (CESC). The CESC can stop turbo decoder iterations early by calculating mutual information improvements while maintaining bit error rate (BER) performance. Most research on iterative turbo decoding stopping criteria has utilised low-modulation methods, such as binary phase-shift keying. However, a high-speed network requires high modulation to transfer data at high speeds. Hence, a high modulation technique needs to be integrated into the CESC to match its speed. Therefore, the present paper investigated and analysed the effects of the CESC and quadrature amplitude modulation (QAM) on iterative turbo decoding. Three thresholds were simulated and tested under four situations: different code rates, different QAM formats, different code generators, and different frame sizes. The results revealed that in most situations, the use of CESC is suitable only when the signal-to-noise ratio (SNR) is high. This is because the CESC significantly reduces the average iteration number (AIN) while maintaining the BER. The CESC can terminate early at a high SNR and save more than 40% AIN compared with the fixed stopping criterion. Meanwhile, at a low SNR, the CESC fails to terminate early, which results in maximum AIN.

Faster than Nyquist signaling with limited computational resources

This paper focuses on performance analysis of Faster than Nyquist (FTN) signaling schemes that employ low-density parity-check (LDPC) codes, trellis-based detector and turbo equalization decoding principle. We propose an optimization procedure for shaping pulse design, that takes into account number of trellis states used for equalization. By using proposed numerical procedure, we identify information rate limits, achievable by FTN signaling technique, with identically and uniformly distributed (i.u.d.) inputs, from a discrete constellation. Furthermore, based on EXIT chart analysis, we provide a numerical upper bound on achievable information rate (AIR) of FTN communication systems with i.u.d. inputs, finite number of turbo decoding iterations or code complexity limitations. Additionally, we derive a tighter upper bound on AIR and demonstrate its usefulness by showing that it is possible to design irregular repeat accumulate LDPC codes that operate within 0.2 dB of the proposed bound for a wide range of code rates.

Iterative Doppler Frequency Offset Estimation in Satellite High-Mobility Communications

Satellite communication systems are able to provide diverse services for ground terminals in ubiquitous global coverage, which play a vital role in high-mobility communication environments. Existing technologies developed primarily for satellite communications cannot be readily applied to satellite high-mobility communication scenarios, since high Doppler frequency offset caused by the fast movement of wireless terminals, and low signal-to-noise ratio (SNR) circumstances caused by limited link budgets in satellites incur more difficulty of the synchronization, especially for short burst transmission. To solve such a problem in satellite high-mobility communications, we propose a novel method named GP-MASO-MLE, which consists of a coarse estimation algorithm based on the Gaussian process (GP) model and Newton-Raphson method, and a fine correction algorithm based on the improved maximum likelihood estimation (MLE) jointly with turbo decoding iterations. Simulation results show that the proposed algorithm can approach to the bit error rate (BER) performance bound of ideal Doppler frequency offset correction within 0.1 dB, which can be well applied in code-aided (CA) satellite high-mobility communication systems for its good performance. In addition, the computational complexity of the proposed algorithm is lower than other traditional turbo synchronization algorithms.

Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes

An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs). The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm. The extrinsic information is calculated using the reliability of these hard-output decisions and is passed as soft-input to the iterative turbo decoding process. RLL based decoding of constituent codes estimate the optimal transmitted codeword through a directed minimal search. The proposed RLL based decoder for the constituent code replaces the Chase-2 based constituent decoder in the conventional SISO scheme. Simulation results show that the proposed algorithm has a clear advantage of performance improvement over conventional Chase-2 based SISO decoding scheme with reduced decoding latency at lower noise levels.

Threshold-Based Bit Error Rate for Stopping Iterative Turbo Decoding in a Varying SNR Environment

Abstract Online bit error rate (BER) estimation (OBE) has been used as a stopping iterative turbo decoding criterion. However, the stopping criteria only work at high signal-to-noise ratios (SNRs), and fail to have early termination at low SNRs, which contributes to an additional iteration number and an increase in computational complexity. The failure of the stopping criteria is caused by the unsuitable BER threshold, which is obtained by estimating the expected BER performance at high SNRs, and this threshold does not indicate the correct termination according to convergence and non-convergence outputs (CNCO). Hence, in this paper, the threshold computation based on the BER of CNCO is proposed for an OBE stopping criterion (OBEsc). From the results, OBEsc is capable of terminating early in a varying SNR environment. The optimum number of iterations achieved by the OBEsc allows huge savings in decoding iteration number and decreasing the delay of turbo iterative decoding.

On the LLR Metrics for DPSK Modulations Over Two-Symbol Observation Intervals for the Flat Rician Fading Channel

We consider the differential phase-shift keying modulation over the flat Rician fading channel with perfect channel model information (PCMI), and derive the two-symbol-observation-interval log-likelihood ratio (LLR) metric from first principles. The work generalizes the previous LLR derivations in [16] – [19] , and demonstrates the necessity of the knowledge of the statistical channel model in the exact LLR computation. Assuming the channel is slowly time-varying, we also propose a simple approximate LLR metric based on the generalized likelihood ratio test (GLRT), which requires only the information of the noise spectral density. The advantage of the newly derived PCMI-LLR metric over the approximate metric and the other LLR metrics in the literature is explained from the information-theoretic perspective via the generalized mutual information. Computer simulations are also provided to demonstrate the superiority of the PCMI-LLR metric in both error rate performance and convergence speed for iterative decoding of turbo and low-density parity-check codes in practical systems. This paper aims to present the fundamental principles of LLR computation, emphasizing the importance of selecting the appropriate metric for iterative decoding over fading channels.

Robust stopping criterion in signal‐to‐noise ratio uncertainty environment

A robust stopping criterion (called online-BER [OB]) that can terminate iterative turbo decoding in a signal-to-noise ratio (SNR) uncertainty environment is proposed. OB is based on the online bit error rate (BER) estimation and the BER thresholds. Both values are used to detect convergence and non-convergence decoder output and also to halt iterative decoding in various SNRs. Unlike other well-known stopping criteria, OB does not depend on SNR information in its stopping rules and hence it is less complex. OB is also more robust than other stopping criteria in a SNR uncertainty environment while being capable of reducing the average iteration number and resulting in less degradation in BER performance.

Improved Physical Layer Implementation of VANETs

Vehicular Ad-hoc Networks (VANETs) are comprised of wireless mobile nodes characterized by a randomly changing topology, high mobility, availability of geographic position, and fewer power constraints. Orthogonal Frequency Division Multiplexing (OFDM) is a promising candidate for the physical layer of VANET because of the inherent characteristics of the spectral efficiency and robustness to channel impairments. The susceptibility of OFDM to Inter-Carrier Interference (ICI) is a challenging issue. The high mobility of nodes in VANET causes higher Doppler shifts, which results in ICI in the OFDM system. In this paper, a frequency domain comb- type channel estimation was used to cancel out ICI. The channel frequency response at the pilot tones was estimated using a Least Square (LS) estimator. An efficient interpolation technique is required to estimate the channel at the data tones with low interpolation error. This paper proposes a robust interpolation technique to estimate the channel frequency response at the data subcarriers. The channel induced noise tended to degrade the Bit Error Rate (BER) performance of the system. Parallel concatenated Convolutional codes were used for error correction. At the decoding end, different decoding algorithms were considered for the component decoders of the iterative Turbo decoder. A performance and complexity comparison among the various decoding algorithms was also carried out.

Online log‐likelihood ratio scaling for robust turbo decoding

Optimal iterative log-MAP decoding of turbo codes requires accurate knowledge of the operating signal-to-noise ratio (SNR). However, the SNR information, available at practical decoders for bit-interleaved coded modulation systems, such as the third generation partnership project high-speed packet access and long-term evolution wireless cellular systems, may be inaccurate. In this study, two decoder architectures for improved turbo decoding in the presence of SNR mismatch are proposed. The SNR-mismatch aware turbo decoder selects the decoder which is estimated to have the best performance at the current mismatch, according to the test criterion. The SNR-mismatch compensated turbo decoder provides a more accurate estimation of the noise variance and concurrently scales the channel and the decoder log-likelihood ratios (LLRs) to continue decoding. Two different methods are proposed to find the optimal scaling factors online, one on the symbol level and the other on the bit level. This study shows that online LLR scaling, without prior knowledge about the noise mismatch statistics, can result in near-optimal turbo decoding regardless of the initial SNR mismatch.

Soft Estimates for Doubly Iterative Decoding with 8-PSK and 16-PSK Modulations

The paper addresses the doubly iterative decoding of space-time turbo codes with a large number of transmit and receive antennas. In the doubly iterative scheme, the decoder uses preliminary soft values of the coded symbols and the soft estimates only for Quadratic-Phase-Shift-Keying (QPSK) modulation have been determined. In this paper we propose and explain the soft estimates related to the signal constellations for 8-PSK and 16-PSK modulations. The coding gains, given in dB, have been determined through simulations for two situations: without double iterations and for doubly iterative decoding for a number of 1 and 4 iterations, using 16 transmit and receive antennas, respectively showing the compromise between the spectral efficiency and the coding gain.

Unified scaling factor approach for turbo decoding algorithms

Turbo (iterative) decoding can be implemented with a large family of soft-input soft-output (SISO) algorithms, including suboptimal but practical algorithms such as the soft-output Viterbi algorithm (SOVA) and max-log-MAP algorithm. The performance with these practical algorithms can be improved with simple scaling factor methods. However, their theoretical analysis was mainly based on the relaxed assumption proposed by Papke et al. that the extrinsic information is Gaussian distributed. This study proposes a novel scaling factor approach for reducing both the overestimation of reliability values and the correlation between the intrinsic and extrinsic information. Explicit formulae for computing the scaling factors are derived based on mathematical statistics. A key difference compared to the scaling factor method of Papke et al. is that the proposed scaling factors can be computed off-line. The numerical results show that when implemented in the decoding algorithm of block component codes, the proposed scaling factor approach improves the performance of turbo decoding over additive white Gaussian noise and Rayleigh fading channels. It is superior than the method by Papke et al. in both performance and complexity.

On Cross-Layer Design of AMC Based on Rate Compatible Punctured Turbo Codes

This paper extends the work on cross-layer design which combines adaptive modulation and coding at the physical layer and hybrid automatic repeat request protocol at the data link layer. By contrast with previous works on this topic, the present development and the performance analysis as well, is based on rate compatible punctured turbo codes. Rate compatibility provides incremental redundancy in transmission of parity bits for error correction at the data link layer. Turbo coding and iterative decoding gives lower packet error rate values in low signal-to-noise ratio regions of the adaptive modulation and coding (AMC) schemes. Thus, the applied cross-layer design results in AMC schemes can achieve better spectral efficiency than convolutional one while it retains the QoS requirements at the application layer. Numerical results in terms of spectral efficiency for both turbo and convolutional rate compatible punctured codes are presented. For a more comprehensive presentation, the performance of rate compatible LDPC is contrasted with turbo case as well as the performance complexity is discussed for each of the above codes.

Pilot overhead reduction in turbo coded OFDM systems employing an iterative channel estimation under low signal-to-noise ratio environments

The authors evaluate the improved energy and spectral efficiency by pilot overhead reduction of turbo coded orthogonal frequency division multiplexing (OFDM) systems employing an iterative phase estimation algorithm. Developed from the recently proposed iterative phase estimation schemes, the phase estimation and compensation process is embedded into the basic iterative turbo decoding process for the application to OFDM systems with just a slight complexity overhead. At each decoding iteration, sub-carrier phase rotations are estimated from the extrinsic information arranged in each sub-carrier and are compensated for the next decoding iteration. This enables the iterative phase estimation algorithm to successfully work under very low signal-to-noise ratios even without pilot symbols. The pilot symbols are just very rarely inserted only for breaking the erroneous phase estimation propagation frame to frame in case of large residual phase offset beyond reliable decoding range. Simulation results show that the iterative phase estimation algorithm drastically reduces the pilot insertion overhead and thus, it achieves improved spectral efficiency as well as bit error rate (BER) performance by saving pilot energy compared to the conventional method.

Residual Frequency Offset Compensation-Embedded Turbo Decoder

We propose a modified turbo decoder that internally includes the residual frequency offset compensation function in an iterative decoding process. Based on the recently proposed phase offset compensation scheme that embeds phase compensation into iterative turbo decoding, we extend it to cover frequency offset compensation. At each decoding iteration, we estimate the residual frequency offset from the extrinsic information and compensate it for the next iteration. As the iteration goes on, the frequency offset is gradually and drastically reduced. Consequently, the severe turbo decoding failure due to even a small residual frequency offset can be significantly recovered, and then, almost ideal decoding performance is achieved. In particular, for power-limited communications under a very-low-SNR environment where even a tiny frequency offset is critical to turbo decoding, the proposed scheme is efficient since it does not require additional transmission power for compensation.

Iterative channel estimation and decoding for the multipath channels with RAKE reception

We study an improved receiver with iterative channel estimation and decoding for wireless multipath channels with RAKE reception. To keep the complexity low, iterative channel estimation is done on the equivalent channel at the RAKE output. Output after Turbo decoding iteration(s) is processed to yield a better channel estimate.

Robust Frequency Hopping for Interference and Fading Channels

A robust frequency-hopping system with noncoherent detection, iterative turbo decoding and demodulation, and channel estimation is presented. The data modulation is the spectrally compact nonorthogonal continuous-phase frequency-shift keying, which strengthens the frequency-hopping system against multiple-access interference and multitone jamming. An analysis based on information theory provides the optimal values of the modulation index when there is a bandwidth constraint. The channel estimator, which is derived by applying the expectation- maximization algorithm, accommodates both frequency-selective fading and interference. Simulation experiments demonstrate the excellent system performance against both partial-band and multiple-access interference.

On the New Stopping Criteria of Iterative Turbo Decoding by Using Decoding Threshold

Although many stopping methods of iterative decoding have been discussed in the literature extensively, many of them only focus on the solvable decoding (information is enough for successful decoding). In this paper, we discuss the limitation of the decoding ability based on the extrinsic information transform (EXIT) chart. Then, we propose a new information measurement by using cross correlation to predict the decoding threshold. Moreover, we propose two early termination (ET) schemes (ET-I and ET-II) based on the predicted decoding threshold. The iterative decoding can stop in either high-signal-to-noise ratio (SNR) situations where the decoded bits are highly reliable (solvable decoding), or low-SNR situations where the decoder already has no capability to decode (unsolvable decoding). The simulation results show that the reduced iterations due to the ET-I scheme almost will not affect the SNR performance, and the ones due to the ET-II scheme can still satisfy the requirement of the specification. Based on our analysis and simulation results, we can further modify the conventional GENIE chart by considering the decoding threshold. By using our new ET concepts, the previous stopping techniques can also be modified to stop in low-SNR situations. The ET property for the iterative decoding can help reduce the unnecessary iterations, so as to save computational complexity and power consumptions in digital signal processors (DSPs) or application-specific integrated circuits (ASICs) in mobile handsets.