Current novel view synthesis methods are typically designed for high-quality and clean input images. However, in foggy scenes, scattering and attenuation can significantly degrade the quality of rendering. Although NeRF-based dehazing approaches have been developed, their reliance on deep fully connected neural networks and per-ray sampling strategies leads to high computational costs. Furthermore, NeRF's implicit representation limits its ability to recover fine-grained details from hazy scenes. To overcome these limitations, we propose DehazeGS, the first physics-driven 3D Gaussian Splatting (3DGS) framework for dehazing. We adopt an explicit Gaussian representation to model fog formation via a physically consistent forward rendering process, enabling reconstruction and rendering of fog-free scenes using only multi-view foggy images as input. Specifically, based on the atmospheric scattering model, we simulate the formation of fog by establishing the transmission function directly on Gaussian primitives via depth-to-transmission mapping. During training, we jointly learn the atmospheric light and scattering coefficients while optimizing the Gaussian representation of foggy scenes. At inference time, we remove the effects of scattering and attenuation in Gaussian distributions and directly render the scene to obtain dehazed views. Experiments on both real-world and synthetic foggy datasets demonstrate that DehazeGS achieves state-of-the-art performance.

This paper proposes the Low Upload and Storage Cost (LUSC) scheme, a coded distributed computing (CDC) approach that accelerates Convolutional Neural Network (CNN) inference on resource-constrained edge devices. LUSC introduces a new encoding and decoding mechanism that exploits the periodicity and evenness of cosine functions, reducing communication and storage overhead while ensuring numerical stability. Orthogonal decoding matrices derived from this cosine-based design guarantee stable inversion and preserve numerical precision. By leveraging the duality property of cosine functions, LUSC reduces the number of workers required for decoding, enabling finer-grained task decomposition and further lowering upload and storage costs. When combined with a spatial and channel grid partition (SCGP) strategy, LUSC (including other matrix-multiplication-based CDC schemes) can be applied to convolutions, accelerating CNN inference while maintaining resilience to stragglers. Experimental results demonstrate that LUSC consistently outperforms existing numerically stable CDC schemes, providing efficient inference with reduced communication and storage costs and maintaining robustness under straggler conditions.

This paper investigates distributed link selection (LS) for a multi-hop buffer-aided relay network consisting of one source, one destination, and multiple relays, where each node has access only to local instantaneous channel state information (CSI) and the buffer status of its adjacent nodes. In particular, by improving the alternate-transmission strategy, we propose a novel flexible distributed LS scheme that flexibly selects odd- and even-numbered links in each time slot. Notably, acquisition of local buffer-state information is integrated into the distributed LS agreement process, so it incurs no extra signaling overhead. We also derive the average throughput and packet delay of the proposed scheme by constructing a two-layer Markov model and enumerating all feasible buffer-state transitions. In addition, a simplified expression and an asymptotic analysis are provided to give further insight into the average throughput. Theoretical analysis and simulations show that the proposed flexible scheme substantially outperforms a baseline alternate scheme and closely approaches the performance of a related centralized LS scheme.

This paper presents a general framework for probabilistic relay selection (RS) in asymmetric buffer-aided cooperative relaying systems, which caters to scenarios with both perfect and imperfect channel state information (CSI) during the RS process. The framework extends and generalizes many existing buffer-aided RS schemes. In particular, we introduce an auxiliary stochastic process which assigns varying selection probabilities to different links, considering the dynamic wireless channel and buffer states. Subsequently, we leverage the obtained outage probability and average packet delay (APD) to formulate outage optimization problems while adhering to APD. To address the intricate high-dimensional optimization problems, we employ a deep learning (DL) approach, which involves designing probability mass functions for the auxiliary stochastic process and developing an effective loss function to update the neural network. Simulation results unequivocally demonstrate the superior performance of the proposed DL-based probabilistic RS scheme compared to benchmark schemes, particularly in scenarios involving imperfect CSI.

In this paper, we propose stacking codes and decoding algorithms to correct burst deletion/insertion and random substitution errors in a non-binary segment-Lmaxburst-Ddeletion and maxburst-Sinsertion (NB-SBDI(L,D,S)) channel without knowing the codeword boundaries. Specifically, in the NB-SBDI(L,D,S) channel, at most a single non-binary burst (a block of consecutive bits/symbols) of deletions or insertions of length up toDorS, respectively, exists in a block ofLconsecutive non-binary symbols. The proposed stacking-codes are constructed by stacking multiple Reed-Muller(RM)/modified BCH/modified binary representation of Reed-Solomon (BRRS) codes, respectively, and no marker codes are involved. We show that, in the NB-SBDI(L,D,S) channel, the proposed approach can not only correct both burst deletions/insertions and random substitution errors, but also achieve error-free decoding for stacking-RM/modified stacking-BCH/modified stacking-BRRS codes for burst deletions/insertions as long as no substitution errors exist. Also, the modified stacking-BRRS code is more rate efficient than the existing Song code [1], the stacking-RM/modified stacking-BCH codes are more rate efficient than the Song code if max(D,S) and code length are small.

In this paper, an effective approach is proposed to recognize the order among codewords from the randomly binary and non-binary interleaved linear block coded streams if the code minimum distance is known, where the interleaver lengthNn+dis not the multiple of the linear block code lengthn. Then, an efficient approach is developed without knowing linear block code parameters such as code rate and the code generator matrix (except the code length) to recognize the whole random interleaving pattern if the greatest common divisor (GCD) ofnanddis GCD(n, d) = 1 for both binary and non-binary interleaved linear block coded symbols. Further, for the case GCD(n, d) =q̸= 1, the whole random interleaving pattern can be recognized with the probability of no more than (q!)−(Nn+d)/qfor the following cases: (1) the non-binary interleaved coded symbols without knowing the non-binary code generator matrix; (2) the binary interleaved coded symbols.

Ultra-massive multiple-input multiple-output (UM-MIMO) has been considered as one of the promising technologies for terahertz (THz) wireless communications to compensate for the severe path loss. However, the widely acknowledged hybrid beamforming approaches in massive MIMO cannot deal with the beam split effect caused by the increased scale of array dimension and system bandwidth in THz UM-MIMO systems. In this paper, the hybrid beamforming specifically designed for wideband THz UM-MIMO systems with the beam split effect is proposed. Firstly, a novel technique of hybrid beamforming is formulated as a sub-beam coherent combination method to cover the dispersed spatial directions. Subsequently, the dynamic hybrid hardware architecture is considered to flexibly adapt to various beam splits on different path directions, in which the optimal number of the activated subarray is elaborately designed to alleviate beam split while reducing power consumption. Simulation results indicate that our scheme achieves desirable beamforming gain distribution across the entire bandwidth, as well as achieving higher energy efficiency than other fixed hybrid hardware architectures designed for alleviating the beam split effect.

In this paper, we develop a non-coherent differential chaos shift keying based index modulation by using initial value index (IVI-DCSK) to convey additional information for wireless communications. In the proposed scheme,mcmapped bits are carried by 2mcchaotic sequences by exploiting the quasi-orthogonality of different chaotic signals, while the modulated bit is carried by DCSK. To diminish the multiuser interference, the references allocated to different users are sent in individual time slots, while the information-bearing sequences for the mapped bits of users are sent simultaneously. We then derive the bit error rate (BER) expression of multi-user IVI-DCSK over multipath Rayleigh fading channels. The theoretical and consistent simulation results show that the proposed IVI-DCSK achieves significant gains over the conventional chaotic-based index modulations, i.e., permutation index DCSK (PI-DCSK) and code index modulation DCSK (CIM-DCSK). This gain can be more than 4 dB in fading channels with high multipath delay. In addition, it achieves higher energy and spectral efficiencies over the latter ones. The superiority of the proposed scheme is further verified in practical ultra-wideband (UWB) communications. Thus, this proposed scheme is efficient and promising for chaotic-based low-complexity communications, such as in wireless local area network (WLAN) and indoor applications.

In this paper, we construct non-binary codes of lengthNwhich correct errors under a non-binary segment-Nmaxburst-Ddeletion and maxburst-Sinsertion (NB-SBDI(N, D, S)) channel without knowing the codeword boundaries. In this NB-SBDI(N, D, S) channel, at most a single non-binary burst (a block of consecutive bits/symbols) of deletions or insertions of length up toDorS, respectively, exists in a block ofNconsecutive non-binary symbols. One code named as BM-DB-MDS consists of a maximum distance separable (MDS) code, a block of periodic de Bruijn (DB) symbols, and a block of proposed periodic binary marker (BM) patterns with a period ofS+D+ 2. The other code called BM-MDS code consists of a BM code and an MDS code. We show that the rates of BM-DB-MDS and BM-MDS codes achieve λ/λ+1 (1 - 1/2t), λ ∈ N+and 1 - 1/t, respectively, whenN→ +∞, where λ represent the MDS code shortening factor, and 1/tis the rough proportion of the maximum length of burst deletions or insertions allowed in a code.

Low-density parity-check (LDPC) codes with protograph-based raptor-like (PBRL) structure have been chosen as the data channel coding scheme for the fifth-generation (5G) enhanced mobile broad band (eMBB) services. However, these 5G LDPC codes are not optimized for the scenarios of Ultra Reliable and Low Latency Communications (URLLC) and massive Machine Type Communications (mMTC) in which small transport block sizes are usually used. In this paper, a new method is proposed to construct PBRL LDPC codes for URLLC and mMTC. This method incorporates degree-distribution optimization, base matrix derived from parity-check matrix of quadratic residue codes, masking technique and modified progressive-edge-growth (PEG) algorithm. Simulation results show that the proposed PBRL LDPC codes outperform 5G LDPC short codes in terms of error-correcting performance.

This paper investigates the problem of secure transmission over a two-user discrete memoryless multiple-access wiretap channel with partial rate-limited feedback (MAC-WT-PLF). The receiver can causally and securely transmit feedback to one of the transmitters at a limited rate. Three achievable rate regions and one outer bound on the secrecy capacity are presented based on three proposed coding schemes and the Sato-type bounding approach. The proposed coding schemes show that the feedback can play multiple roles, i.e., encrypting part of messages, enlarging the size of the dummy message, and increasing the correlation between the channel inputs, to enhance the secrecy performance. Of particular interest is identifying the novel role of enlarging the size of the dummy message at one of the transmitters, which enables both transmitters to benefit from the feedback significantly. In addition, the proposed achievable rate regions and outer bound are computed for the Gaussian MAC-WT-PLF, and comparative numerical results are provided under different eavesdropping cases.

This paper investigates the performance of key generation between two nodes assisted by a relay in the presence of correlated eavesdropping channels. A cooperative jamming scheme is utilized to impose superimposed channel measurements on the relay and eavesdropper. Both lower and upper bounds on key capacities for both secret key (SK) and private key (PK) generation are evaluated, where the lower bounds are derived by using minimum mean square error and zero forcing methods for channel estimation, and the upper bounds are derived by formulating several enhanced discrete memoryless source (DMS) models. The analytical expressions are further simplified in the high signal-to-noise ratio (SNR) regime. We discover that one of the two legitimate channels should specialize in playing a role of jamming the relay or eavesdropper. We also demonstrate that the derived lower and upper bounds are tight when the eavesdropping channels are lowly or highly correlated. When the eavesdropping channels are uncorrelated, the SK and PK capacities can be determined since the corresponding upper and lower bounds are equal. Moreover, at high SNRs, a constant gap exists between the SK/PK upper and lower bounds as the correlation coefficient becomes one.

Buffer-aided relay networks provide more reliability and coverage in future wireless communications. Therefore, this paper investigates a buffer-aided cooperative relaying system with$K$relays and a direct link from the source to the destination, providing a general scenario different from other existing state-of-the-art techniques. In particular, we propose a novel link selection scheme, which adaptively coordinates the selection priorities of the direct and cooperative relay link according to the instantaneous buffer state. The performance of the proposed link selection scheme is analyzed, in terms of outage probability, average packet delay (APD) and diversity order by providing closed-form expressions. For asymptotic analysis, a theoretical framework is presented by dividing all buffer states into different sets, which verifies that the minimum buffer size is just two for achieving the full diversity order of$2K+1$. We also provide the relationship between the asymptotic APD and diversity order by adjusting predefined target queue lengths, which shows that the diversity order ranges from$K+1$to$2K+1$as the asymptotic APD ranges from 0 to$K$time slots per packet. Both theoretical and simulation results demonstrate that direct transmission significantly improves the outage and delay performance simultaneously.

Collecting users’ historical data such as movie watching and music listening, and mining frequent items from them, can improve the utility of smart services, but there is also a risk of compromising user privacy. Local differential privacy is a strict definition of privacy and has been widely used in various privacy-preserving data collection scenarios. However, the accuracy of existing locally differentially private frequent items mining methods decreases significantly with the increase in the dimensions of data to be collected. In this paper, we propose a new locally differentially private frequent item mining method for high-dimensional data, which decreases the dimension used for data perturbation by grouping the contents and improving the interference matrix generation method, so as to improve the data reconstruction accuracy. The experimental results show that our proposed method can significantly improve the accuracy of frequent item mining and provide a better trade-off between privacy and accuracy compared with existing methods.

Random interleavers are widely employed in digital communication systems to combat channel fading and burst errors. In applications such as grant-free access by Internet of Things (IoT) devices, accurately identifying a specific irregular interleaving pattern within an interleaver period is vital to both terminal recognition and data recovery. In this work, we investigate effective approaches for random interleaving pattern identification in Reed-Solomon (RS) coded data streams. We first propose an algorithm of low computational complexity to detect positions of code symbols belonging to the same RS codeword group (RSCG) under modest bit error rate. We further develop another low-complexity algorithm to successfully identify random interleaving patterns for RS code symbols within each RS codeword under moderate to high error rate applications. Our theoretical analysis and simulation results corroborate to demonstrate the effectiveness of our algorithms.

The paper proposes an improved difference-of-syndromes decoding algorithm for decoding quadratic residue codes up to half the minimum distance. Therein, soft-decision information is not essential, but it can be used to speed up the computations. The improvement over the prior art is demonstrated by simulations. Moreover, the proposed algorithm is also compared with the classic Berlekamp-Massey algorithm by taking two BCH codes as examples.

In this paper, two new decoding algorithms to decode Reed-Solomon codes during transmission over burst Rayleigh fading channels with additive white Gaussian noise (AWGN) are proposed. They only conduct error correction for coded symbols located in the pure AWGN region and conduct error and erasure correction for those symbols located in the burst fading region by treating those coded symbols that are very likely erroneous as erasures. The first algorithm does not need to know the fading locations in advance, while the second algorithm assumes that the fading locations are known. In addition, the performance of such two algorithms is studied when a pre-computed threshold is used to determine the erasures of the code. Simulation results show that our proposed algorithms not only significantly perform better than the classic Berlekamp-Messay algorithm with a comparable computational complexity but also achieve a better tradeoff between the performance and the computational complexity when compared with other existing algorithms. In particular, our algorithms exhibit excellent robustness for tested various code parameters and fading configurations. Furthermore, a more detailed mathematical analysis is also developed in this paper in order to estimate the performance of the new algorithms in the burst Rayleigh fading channels. We observe that the performance of the first algorithm can only be estimated relatively accurately when encountering burst deep-fading, whereas the performance prediction for the second algorithm is always in agreement with the simulation results for various fading cases.

The problem of blind image recovery using multiple blurry images of the same scene is addressed in this paper. To perform blind deconvolution, which is also called blind image recovery, the blur kernel and image are represented by groups of sparse domains to exploit the local and nonlocal information such that a novel joint deblurring approach is conceived. In the proposed approach, the group sparse regularization on both the blur kernel and image is provided, where the sparse solution is promoted by -norm. In addition, the reweighted data fidelity is developed to further improve the recovery performance, where the weight is determined by the estimation error. Moreover, to reduce the undesirable noise effects in group sparse representation, distance measures are studied in the block matching process to find similar patches. In such a joint deblurring approach, a more sophisticated two-step interactive process is needed in which each step is solved by means of the well-known split Bregman iteration algorithm, which is generally used to efficiently solve the proposed joint deblurring problem. Finally, numerical studies, including synthetic and real images, demonstrate that the performance of this joint estimation algorithm is superior to the previous state-of-the-art algorithms in terms of both objective and subjective evaluation standards. The recovery results of real captured images using unmanned aerial vehicles are also provided to further validate the effectiveness of the proposed method.

In this paper, an efficient decoding algorithm is developed to facilitate faster decoding of the binary systematic quadratic residue (QR) codes. It is based on the difference of syndromes (DS), and hence, is called the DS algorithm hereinafter. This new method combines the advantages of the syndrome-weight algorithm and properties of the cyclic codes. Actually, it is a natural generalization of the cyclic weight (CW) algorithm for the (47, 24, 11) QR code developed by Lin et al., and its validity of decoding any binary systematic QR code is also proved. The complexity analysis and simulation results show that the DS algorithm dramatically reduces the decoding complexity without performance loss and considerably requires less memory when compared with previous ones. Utilizing the (47, 24, 11), the (71, 36, 11), the (73, 37, 13), and the (89, 45, 17) QR codes as examples, the DS algorithm not only significantly improves the decoding efficiency, but also saves the memory evidently. When the (23, 12, 7) QR code is considered, the DS algorithm performs almost as well as the currently known best algorithm in terms of decoding efficiency and memory requirements. Thus, all QR codes of lengths less than 100 can be decoded efficiently by using the proposed algorithm. Especially, when the proposed algorithm is applied to decode the (89, 45, 17) QR code, the best one among all the QR codes of lengths less than 100, the decoding speed is raised 26 times and the memory is saved up to 76.6% in comparison with the existing fastest decoding algorithm.

In this study, a new approach is developed to facilitate faster decoding of a binary systematic (71, 36, 11) quadratic residue (QR) code. In this decoder, it simplifies the step of calculating the condition and avoids calculating the unknown syndrome, thereby yielding a fast algebraic decoder for correcting four possible errors. Moreover, while using the proposed algorithm, if uses the channel measurement information proposed by Chase to sequentially invert the bits of the received word until one of the errors is cancelled for the five‐error case and apply the new algebraic decoding algorithm mentioned above to correct the remaining four errors, the algorithm has been verified through a software simulation in C‐language. The simulation shows that the decoding scheme developed here is more efficient than the previous decoding algorithm developed for the (71, 36, 11) QR code and it is naturally suitable for software implementation.

In this paper, a new algebraic method to decode the (71, 36, 11) QR code up to five errors is proposed. It completely avoids computing the unknown syndromes, and uses the previous scheme of decoding this QR code up to three errors, but corrects four and five errors with a new different method. In the four-error case, the new algorithm directly determines the coefficients of the error-locator polynomial by eliminating unknown syndromes in Newton identities. Subsequently, the shift-search algorithm can be utilized to decode the fifth error and the concept of bit reliability is also introduced to accelerate the decoding process. In other words, a weight-five-error pattern can be decoded in terms of the four-error case by inverting an incorrect bit of the received word in ascending order of reliability. Particularly, a threshold parameter γ can be preset to limit the number of inverting bits one by one, and a corresponding upper bound of the probability that decoding fails is derived. Finally, simulation and analysis show that the proposed new decoding algorithm for the abovementioned QR code not only significantly reduces the decoding complexity in terms of CPU time but also saves a lot of memory while maintaining the same error-rate performance. Additionally, the introduction of γ achieves a better tradeoff between the decoding performance and the computational complexity.

Presents comments on the paper, "On decoding of the quadratic residue code,” (Wang, L., et al) IEEE Trans. Commun., vol. 61, no. 3, pp. 832–841, Mar. 2013.

In this paper1, a method to search the subsets I and J needed in computing the unknown syndromes for the (73, 37, 13) quadratic residue (QR) code is proposed. According to the resulting I and J, one computes the unknown syndromes, and thus finds the corresponding error-locator polynomial by using an inverse-free BM algorithm. Based on the modified Chase-II algorithm, the performance of soft-decision decoding for the (73, 37, 13) QR code is given. This result is never seen in the literature, to our knowledge. Moreover, the error-rate performance of linear programming (LP) decoding for the (73, 37, 13) QR code is also investigated, and LP-based decoding is shown to be significantly superior in performance to the algebraic soft-decision decoding while requiring almost the same computational complexity.

In this paper, a method to search the set of syndromes' indices needed in computing the unknown syndromes for the (73, 37, 13) quadratic residue (QR) code is proposed. According to the resulting index sets, one computes the unknown syndromes and thus finds the corresponding error-locator polynomial by using an inverse-free Berlekamp-Massey (BM) algorithm. Based on the modified Chase-II algorithm, the performance of soft-decision decoding for the (73, 37, 13) QR code is given. This result is new. Moreover, the error-rate performance of linear programming (LP) decoding for the (73, 37, 13) QR code is also investigated, and LP-based decoding is shown to be significantly superior in performance to the algebraic soft-decision decoding while requiring almost the same computational complexity. In fact, the algebraic hard-decision and soft-decision decoding of the (89, 45, 17) QR code outperforms that of the (73, 37, 13) QR code because the former has a larger minimal distance. However, experimental results indicate that the (73, 37, 13) QR code outperforms the (89, 45, 17) QR code with much fewer arithmetic operations when using the LP-based decoding algorithms. The pseudocodewords analysis partially explains this seemingly strange phenomenon.

We study a classic problem in wireless data communications in which receivers generally rely on training pilots for equalization of multi-path dispersive channel distortions. Traditional equalizers often require a substantial number of pilot symbols for effective channel compensation. To conserve limited channel bandwidth, we investigate novel equalization algorithms that can make more efficient use of fewer pilot symbols. We present a linear programming algorithm that takes better advantage of the QAM constellation. We further exploit the information inherent in the LDPC forward error correction codes within the linear programming framework to improve the equalization performance and convergence properties.

This work investigates the joint detection and decoding of MIMO-OFDM signals. Traditional receivers either utilize disjoint serial detector and decoder or require turbo message passing between the two functional blocks of detection and decoding. We present a novel approach that can jointly achieve detection and decoding of low density parity check (LDPC) coded multiple-input-multiple-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) signals as a unified optimization algorithm. Our receiver integrates the MIMO-OFDM signal detection and the decoding of LDPC coded data by formulating a linear programming problem regardless of affine or nonaffine quadrature amplitude modulation (QAM) mapping. The proposed joint MIMO-OFDM detector and decoder achieves substantial performance gain over existing joint detection receivers of comparable computational complexity. Furthermore, the proposed receiver also substantially outperforms the more traditional turbo receiver with only modest cost in complexity.

In this paper, Three decoding methods of the (89, 45, 17) binary quadratic residue (QR) code to be presented are hard, soft and linear programming decoding algorithms. Firstly, a new hybrid algebraic decoding algorithm for the (89, 45, 17) QR code is proposed. It uses the Laplace formula to obtain the primary unknown syndromes, as done in Lin et al.'s algorithm when the number of errors v is less than or equal to 5, whereas Gaussian elimination is adopted to compute the unknown syndromes when v ≥ 6. Secondly, an appropriate modification to the algorithm developed by Chase is also given in this paper. Therefore, combining the proposed algebraic decoding algorithm with the modified Chase-II algorithm, called a new soft-decision decoding algorithm, becomes a complete soft decoding of QR codes. Thirdly, in order to further improve the error-correcting performance of the code, linear programming (LP) is utilized to decode the (89, 45, 17) QR code. Simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with Lin et al.'s hard decoding algorithm, and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate (BER) performance. Moreover, the LP-based decoding improves the error-rate performance almost without increasing the decoding complexity, when compared with the new soft-decision decoding algorithm. It provides a coding gain of 0.2 dB at BER = 2 × 10-6.

In this work1, we present a new multiple-input-multiple-output (MIMO) receiver that integrates the MIMO signal detection and the decoding of low density parity check coded data. This joint MIMO detector and decoder utilizes linear programming and achieves about 9.0 dB gain over existing works in terms of bit error rate (BER) of 4 × 10−5with comparable computational complexity. The proposed detector also outperforms the classic turbo equalizer by achieving up to 4.0 dB improvement over turbo equalizer at frame error rate (FER) of 1 × 104. In fact, we can achieve further gain by improving the proposed joint detector through the use of redundant parity checks.

A new decoder is proposed to decode the (23, 12, 7) binary Golay-code up to five errors. It is based on the algorithm that can correct up to four errors for the (24, 12, 8) extended Golay-code proposed by Lin et al., thereby achieving the soft decoding in the real sense for the Golay-code. For a weight-2 or weight-3 error pattern decoded by the hard decoder for correcting up to three errors, one can find the corresponding 21 weight-4 or weight-5 error patterns and choose the one with the maximum emblematic probability value, which is defined as the product of individual bit-error probabilities corresponding to the non-zero locations of the error pattern as the ultimate choice. Finally, simulation results of this decoder over additive white Gaussian noise (AWGN) channels show that the proposed method provides 0.9 dB coding gain than that of Lin et al.'s algorithm at bit-error rate of 10−5.