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Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity. [ABSTRACT FROM AUTHOR]

A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is integrated into an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, efficient latency and complexity reduction schemes are introduced that virtually preserve the error-correction performance of the proposed decoder. Simulation results demonstrate that at the target frame error rate of 10−3 for the RM code of length 256 with 163 information bits, the proposed decoder reduces 6% of the computational complexity and 22% of the decoding latency of the state-of-the-art semi-parallel simplified successive-cancellation decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from the full symmetry group of RM codes, while relatively maintaining the error-correction performance and memory consumption of the semi-parallel permuted SSC-FHT decoder. [ABSTRACT FROM AUTHOR]

A novel permuted fast successive-cancellation list decoding algorithm with fast Hadamard transform (FHT-FSCL) is presented. The proposed decoder initializes $L$ $(L\geq 1)$ active decoding paths with $L$ random codeword permutations sampled from the full symmetry group of the codes. The path extension in the permutation domain is carried out until the first constituent RM code of order 1 is visited. Conventional path extension of the successive-cancellation list decoder is then utilized in the information bit domain. The simulation results show that for a RM code of length 512 with 46 information bits, by running 20 parallel permuted FHT-FSCL decoders with $L=4$ , we reduce 72% of the computational complexity, 22% of the decoding latency, and 84% of the memory consumption of the state-of-the-art simplified successive-cancellation decoder that uses 512 permutations sampled from the full symmetry group of the code, with similar error-correction performance at the target frame error rate of $10^{-4}$. [ABSTRACT FROM AUTHOR]

Polar codes are one of the most effective methods of error correction coding. Currently, these codes are used in 5G communication systems and are the main candidate for 6G. Symmetry plays an important role in coding and decoding algorithms for polar codes. Modulation and multiple access methods are the basis for a physical layer along with error correction codes. Non-Orthogonal Multiple Access (NOMA) methods are a promising technology for future telecommunication systems. They allow the increase of both spectral efficiency and the quantity of subscribers of a communication system. In this paper, we consider a communication system with polar codes, traditional orthogonal multiple access (OMA), and NOMA. The channel with multipath propagation, which can be defined by the Rayleigh channel model, is especially difficult to transmit. We propose a method for adapting signals with polar codes to a channel state based on the analysis of channel matrix and permutation of logical subchannels. The results obtained demonstrate efficiency compared to classical solutions and do not really increase the computational complexity of signal processing and decoding. [ABSTRACT FROM AUTHOR]

Soft-Input Soft-Output (SISO) polar decoding algorithms, such as Belief Propagation (BP) and Soft Cancellation (SCAN) polar decoding, offer iteration capability for facilitating turbo-style detection. However, at lower Signal-to-Noise Ratios (SNRs), the performance of the BP and SCAN decoders is about 1.5 dB and 0.5 dB worse than that of the state-of-the-art hard-decision Successive Cancellation List (SCL) decoding algorithm, respectively, despite iteratively exchanging information with a Multiple Input Multiple Output (MIMO) detector. Motivated by this gap, we conceive a novel G-SCAN polar decoder, which generates both soft-decision and hard-decision outputs. This is achieved by intrinsically amalgamating a list decoder with a novel SISO decoder. These soft-decision outputs may be used for turbo-detection, but they also support the hard-decision outputs of the SCL algorithm for achieving superior block error rate (BLER) performance. As a result of these benefits, the proposed G-SCAN algorithm using a list size of $L = 2$ offers around 1 dB BLER gain compared to the conventional hard-decision SCL decoder relying on $L = 32$. Furthermore, we have carried out its Extrinsic Information Transfer (EXIT) chart analysis, and characterized the performance vs. the complexity of the proposed G-SCAN algorithm, and compared it to various soft- and hard-decision output benchmarks for a wide variety of different rate-matching modes and block lengths. Furthermore, in order to reduce the complexity of the proposed algorithm, a novel Cyclic Redundancy Check (CRC)-aided G-SCAN algorithm is also proposed, which facilitates early termination and improves the BLER performance. [ABSTRACT FROM AUTHOR]

Recently, technologies based on neural networks (NNs) and deep learning have improved in different areas of Science such as wireless communications. This study demonstrates the applicability of NN-based receivers for detecting and decoding sparse code multiple access (SCMA) codewords. The simulation results reveal that the proposed receiver provides highly accurate predictions based on new data. Moreover, the performance analysis results of the primary optimization algorithms used in machine learning are presented in this study. [ABSTRACT FROM AUTHOR]

Ultra-reliable and low-latency communications (URLLC) partakes a major role in 5 G networks for mission-critical applications. Sparse vector coding (SVC) appears as a strong candidate for future URLLC networks by enabling superior performance in terms of bit error rate (BER). SVC exploits the virtual digital domain (VDD) and compressed sensing (CS) algorithms to encode and decode its information through active symbol indices. In this paper, first, a clever encoding/decoding algorithm is proposed for the SVC scheme, which allows the use of all possible activation patterns (APs) resulting in increasing spectral efficiency. Second, a novel solution is proposed to convey additional information bits by further exploiting index modulation (IM) for the codebooks of the SVC scheme. Computer simulation results reveal that our low-complexity algorithm and novel IM solution provide not only a superior BER performance but also an increase in the number of bits conveyed by IM compared to the ordinary SVC approach. [ABSTRACT FROM AUTHOR]

The interest in polar codes has been increasing significantly since their adoption for use in the 5th generation wireless systems standard. Successive cancellation (SC) decoding algorithm has low implementation complexity, but yields mediocre error-correction performance at the code lengths of interest. SC-Flip algorithm improves the error-correction performance of SC by identifying possibly erroneous decisions made by SC and re-iterates after flipping one bit. It was recently shown that only a portion of bit-channels are most likely to be in error. In this paper, we investigate the average log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, and develop the Thresholded SC-Flip (TSCF) decoding algorithm. We also replace the LLR selection and sorting of SC-Flip with a comparator to reduce the implementation complexity. Simulation results demonstrate that for practical code lengths and a wide range of rates, TSCF shows negligible loss compared with the error-correction performance obtained when all single-errors are corrected. At matching maximum iterations, TSCF has an error-correction performance gain of up to 0.45 dB compared with SC-Flip decoding. At matching error-correction performance, the computational complexity of TSCF is reduced by up to 40% on average and requires up to $5\times $ lower maximum number of iterations. [ABSTRACT FROM AUTHOR]

In order to improve the performance of non-binary low-density parity check codes (LDPC) hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA) and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes' (VN) magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF) algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER) of 10-5 over an additive white Gaussian noise (AWGN) channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced. [ABSTRACT FROM AUTHOR]

Full-duplex communication enables simultaneous transmission from both ends of a communication link, thereby promising significant performance gains. Generally, it has been shown that the throughput and delay gains of full-duplex communication are somewhat limited in realistic network settings, leading researchers to study other possible applications that can accord higher gains. The potential of full-duplex communication in improving the physical-layer security of a communication link is investigated in this contribution. We specifically present a thorough analysis of the achievable ergodic secrecy rate and the secrecy degrees of freedom with full-duplex communication in the presence of a half-duplex eavesdropper node, with both single-user decoding and multi-user decoding capabilities. For the latter case, an eavesdropper with successive interference cancellation and joint decoding capabilities is assumed. Irrespective of the eavesdropper capabilities and channel strengths, the ergodic secrecy rate with full-duplex communication is found to grow linearly with the log of the direct channel signal-to-noise-ratio (SNR) as opposed to the flattened out secrecy rate with conventional half-duplex communication. Consequently, the secrecy degrees of freedom with full-duplex is shown to be two as opposed to that of zero in half-duplex mode. [ABSTRACT FROM AUTHOR]

Multi-input multi-output (MIMO) transmission schemes have become the techniques of choice for increasing spectral efficiency in bandwidth-congested areas. However, the design of cost-effective receivers for MIMO channels remains a challenging task. The maximum likelihood detector can achieve excellent performance—usually, the best performance—but its computational complexity is a limiting factor in practical implementation. In the present work, a novel MIMO scheme using a practically feasible decoding algorithm based on the phase transmittance radial basis function (PTRBF) neural network is proposed. For some practical scenarios, the proposed scheme achieves improved receiver performance with lower computational complexity relative to the maximum likelihood decoding, thus substantially increasing the applicability of the algorithm. Simulation results are presented for MIMO-OFDM under 5G wireless Rayleigh channels so that a fair performance comparison with other reference techniques can be established. [ABSTRACT FROM AUTHOR]