To meet the stringent high-throughput demands of enhanced mobile broadband (eMBB), low-density parity-check (LDPC) decoding is limited to few iterations. This constraint usually degrades error-correcting performance, rousing a critical need for puncturing towards algorithmic enhancements. However, existing puncturing methods lack modulation and rate compatibility, converging to local optima due to greedy search strategies. To this end, this paper proposes a modulation and rate compatible puncturing (MrcPunc) for 5G LDPC codes. It incorporates three key techniques: 1)a revised protograph-based extrinsic information transfer (PEXIT) analysisfor accurate performance prediction, 2)a progressive multi-path search (PMPS) algorithmto avoid local optima, and 3)a compatibility optimizationsupporting various modulations and code rates. The MrcPunc yields up to 0.6 dB gain over the 5G standard puncturing under few-iteration condition without extra decoding complexity. It is noted that MrcPunc guarantees robustness against both larger iteration counts and mismatched modulations, alongside reducing the average number of decoding iterations.

Batched network codes (BNCs) are a low-complexity solution for communication through networks with packet loss. Although their belief propagation (BP) performance is proved to approach capacity in the asymptotic regime, there is no evidence indicating that their BP performance is equally good in the finite-length regime. In this paper, we propose a protograph-based construction for BNCs, referred to as protograph-based BNCs (P-BNCs), which significantly differs from existing BNCs in three aspects: 1) The vast majority of existing construction methods mainly focus on the degree distribution of check nodes (CNs), whereas P-BNCs not only specify the degree distributions of CNs and variable nodes (VNs) but also partially constrain the connectivity between CNs and VNs. 2) Traditional BNCs use a fixed degree distribution to generate all batches, making their performance highly sensitive to channel conditions, but P-BNCs achieve good performance under varying channel conditions due to their rate-compatible structures. 3) The construction of P-BNCs takes into account joint BP decoding with a sparse precode, whereas traditional constructions typically do not consider a precode, or assume the presence of a precode that can recover a certain fraction of erasures. Due to these three improvements, P-BNCs not only have higher achievable rates under varying channel conditions, but more importantly, their BP performance is significantly improved at practical lengths.

Batched sparse (BATS) codes were proposed as a reliable communication solution for networks with packet loss. In the finite-length regime, the error probability of BATS codes under belief propagation (BP) decoding has been studied in the literature and can be analyzed by recursive formulae. However, all existing analyses have not considered precoding or have treated the BATS code and the precode as two separate entities. In this paper, we analyze the word-wise error probability of finite-length BATS codes with a precode under joint decoding, including BP decoding and maximum-likelihood (ML) decoding. The joint BP decoder performs peeling decoding on a joint Tanner graph constructed from both the BATS and the precode Tanner graphs, and the joint ML decoder solves a single linear system with all linear constraints implied by the BATS code and the precode. We derive closed-form upper bounds on the error probability for both decoders. Specifically, low-density parity-check (LDPC) precodes are used for BP decoding, and any generic precode can be used for ML decoding. Even for BATS codes without a precode, the derived upper bound for BP decoding is more accurate than the approximate recursive formula, and easier to compute than the exact recursive formula. The accuracy of the two upper bounds has been verified by many simulation results. Based on the two upper bounds, we formulate an optimization problem to optimize the degree distribution of LDPC-precoded BATS codes, which improves BP performance, ML performance, or both. In our experiments, to transmit 128 packets over a line network with packet loss, the optimized LDPC-precoded BATS codes reduce the transmission overhead to less than 50% of that of standard BATS codes under comparable decoding complexity constraints.

Non-rectangular QAM can achieve better bit error rate performance in the face of different channel characteristics, and finding the constellation distribution that best matches the channel characteristics has always been a topic of discussion. The NVI$D$IA/Sionna open-source library provides a scheme of end-to-end transmission comprised of trainable constellation and deep neural network detection to achieve accurate information transfer. However, this application has a high computational complexity in the detection part, which contains dense layers that involve intensive and massive matrix multiplication operations. This study considers using an approximate matrix multiplication (AMM) algorithm based on table lookup, Multiply-ADDitioN-lESS (MADDNESS), to replace the accurate multiplication calculations in the DNN-Based detection and achieves a significant reduction in overall computational complexity at the cost of certain storage.

The minimum mean-squared error (MMSE) detector is widely used in massive multiple-input multiple-output communication systems for its suboptimal performance and simple deployment. However, the computational complexity of the MMSE detector is extremely high due to its matrix calculation when the number of antennas increases. In this paper, a learning vector quantization method is introduced to significantly accelerate specific matrix multiplication at the expense of acceptable performance decay and memory cost. Specifically, exact matrix multiplication is replaced by a series of simple operations involving comparison, querying the lookup table (LUT) and integer additions. The LUT saving the results of vector multiplication is constructed offline. When performing matrix multiplication online for signal detection, received signals are encoded into address indices for querying the LUT. Numerical results prove that the proposed method can achieve similar performance compared to exact matrix calculation for the MMSE detector with much lower computational complexity and acceptable memory cost.

Phase noise introduced by imperfect oscillators can degrade the performance of multiple-input multiple-output (MIMO) systems. To address the issue, this paper investigates a joint estimation of channel and phase noise algorithm by taking advantage of the soft output of the decoder. Specifically, a novel criterion is proposed to select the most reliable symbols as virtual pilots to refine the channel amplitude. Furthermore, we develop a decoding-aided extended Kalman filter (EKF) to track the phase variation. Numerical results demonstrate that the proposed approach can effectively improve the accuracy of the channel and phase noise estimation, thereby enhancing the bit error rate (BER) performance of the MIMO system.

In this paper, we study a class of staircase codes (SCCs), which is constructed by algebraic and single-parity-check component codes. These codes are referred to as mixed-component SCCs (MC-SCCs). We propose a low-complexity ternary message passing decoding algorithm for MC-SCCs, where error-and-erasure decoding plays a core role and soft reliability is reconstructed by hard decisions and channel log-likelihood ratios. We develop the density evolution analysis that is applicable to both binary and non-binary algebraic codes to optimize the decoder. By properly selecting mixed components, we can construct low-error-floor MC-SCCs with a smaller size of decoding window (proportional to component lengths) and a faster speed of convergence compared with the conventional SCCs. Moreover, we verify that for various requirements of overhead and decoding window size, MC-SCCs can outperform the conventional SCCs with both BCH components in terms of both error-rate performance and decoding complexity.

This paper presents a product coding scheme based on binary images of Reed-Solomon (RS) codes and single-parity-check (SPC) codes for high-speed communications. Utilizing the special selection of components, we propose hybrid soft- and hard-decision iterative decoding (ID) algorithms for these codes, during which many RS component decoders can be early terminated. The proposed hybrid ID only exchanges ternary messages between component decoders and early stops the RS component decoders satisfying a proposed stopping criterion, thus low hardware and computational complexities are guaranteed. The hybrid ID of RS-SPC product codes not only performs comparable to the soft-decision decoding of low-density parity-check (LDPC) codes and block turbo codes (BTCs), but also takes much lower computational complexity and smaller decoder data flow. We also propose semi-analytical methods to estimate the waterfall and error-floor performances of the proposed scheme, which yield relatively accurate estimated results. The simulation results and error-floor estimations indicate that some good RS-SPC product codes have very low error floors that satisfy the requirements of optical systems.

This paper presents a ternary message passing (TMP) decoding algorithm for product codes constructed from binary image Reed-Solomon (RS) codes and single-parity-check (SPC) codes. All exchanged messages among component decoders in TMP decoding take value from a ternary alphabet {–1, 0, +1}, which gives a potential for designing fast decoders. In particular, intersymbol interference (ISI) channels are considered due to their applications in many high-speed systems. Moreover, we propose the density evolution (DE) analysis for RS-SPC product codes over AWGN and ISI channels. The DE analyses and simulation results show RS-SPC product codes under TMP decoding performs well in various channels.

In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.

In this paper, we propose a modified adaptive belief propagation (ABP) algorithm, which is referred to as the random ABP (R-ABP) algorithm, for decoding short channel codes adopted in the fifth generation (5G) New Radio (NR) wireless systems. Based on the cyclic redundancy check (CRC) concatenation structure of 5G channel codes, we can take partial or even all CRC bits into iterative R-ABP decoding to improve the error correction performance, while the error detection capability can still be guaranteed by the remaining CRC bits and a proposed threshold-based acceptance criterion. We call this improved R-ABP decoding the threshold-and-CRC-aided R-ABP (TCA-R-ABP) decoding. The simulation results show that our proposed TCA-R-ABP algorithm outperforms the state-of-the-art decoding algorithms for many 5G low-density parity-check (LDPC) and polar codes. Moreover, the proposed TCA-R-ABP algorithm leads to a unified decoder for LDPC and polar codes, which has the potential to be a lower-complexity decoder over the combination of the belief propagation (BP) and CRC-aided successive cancellation list (CA-SCL) decoders.

This paper presents a generalized construction of RS-SPC product codes. A low-complexity joint-decoding scheme is proposed for these codes, in which a BP-based iterative decoding is performed based on the binary expansion of the whole parity-check matrix. Various powerful RS codes can be used as the component codes for RS-SPC product codes, which gives a good performance for local decoding (decode a single component codeword). The proposed BP-based iterative decoding is a global decoding, and it achieves an error-correcting capability compa-rable to codes of large blocklengths. This two-phase decoding scheme preserves the low decoding latency and complexity of the local decoding while achieves high reliability through the global decoding. The complexity of the proposed iterative decoding is discussed, and the simulation results show the proposed scheme offers a good trade-off between the complexity and the error performance.

This is the demonstration description for a cloud- based cell-free distributed massive MIMO system, which is based on our already published work. Distributed massive MIMO antennas will result in design and implementation challenges regarding synchronization, calibration, real-time baseband processing, and so on. The contributors propose a cloud-based cellfree distributed massive MIMO system, which cannot only meet 5G NR requirements but also can be easily extended to different application scales. For this demostration, a 128 × 128 distributed MU-MIMO system with frequency 100 [email protected] GHz is given. Test results show that 10.185 Gbps throughput and more than 100 bps/Hz spectrum utilization can be obtained. On-site applications such as HD video transmission and virtual reality (VR) are offered for visitor experiences and interacts.

In this paper, a deep learning (DL) approach for enhancing the bit-interleaved coded modulation (BICM) receiver is designed to mitigate the clipping distortion in the low-density parity-check (LDPC) coded direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) systems. This work aims to combine the neural network (NN) with the physical layer communications by using a model-driven DL architecture. We first develop a non-iterative NN-aided BICM (NN-BICM) receiver, where the NN is trained with the loss function of cross-entropy to output the modified conditional probability through the softmax activation function, thereby assisting in a log-likelihood ratio (LLR) improvement. Then, we propose two iterative NN-BICM receivers for iterative demapping and decoding. The single iterative design feeds the soft decisions from the LDPC decoder back to the demapper only, while the joint iterative design feeds the soft decisions back to the demapper and NN jointly. By adopting the iteration-wise pre-training strategy, the joint iterative design has been improved by representing the intractable relationship between the conditional probability and the a priori probability with a deeper NN architecture. We further investigate an efficient bit loading algorithm for DCO-OFDM systems employing the NN-BICM receiver. Both NN-BICM receivers and iterative schemes can obtain remarkable performance gains over the existing benchmarks.

In visible light communications (VLC), a neural network-aided bit-interleaved coded modulation (NN-BICM) receiver is designed to mitigate the clipping distortion for the LDPC coded DC biased optical orthogonal frequency division multiplexing (DCO-OFDM) systems. Taking the cross-entropy as loss function, the feed forward network is trained by backprop-agation algorithm to output the condition probability through the softmax activation function, thereby assisting in a modified log-likelihood ratio (LLR) improvement. This feed-forward network simplifies the input layer with a single symbol and the corresponding Gaussian variance instead of focusing on the inter-carrier interference over multiple subcarriers. To achieve a further gain, a staked NN-BICM (S-NN-BICM) iterative receiver is proposed by calculating the condition probability with the aid of apriori probability that derived from the extrinsic LLRs in the LDPC decoder at the previous iteration. Both NN-BICM and S-NN-BICM schemes achieve significant performance gains over the existing counterparts, especially more than 0.8 and 1.4 dB in the case of 16-QAM and 511 occupied subcarriers.

In this paper, we propose a coding scheme for distributed matrix-vector multiplication that builds upon the Luby transform (LT) codes with feedback. The ideal soliton distribution is utilized in our LT coding scheme to encode the sub-matrices. Besides, the belief propagation (BP) decoding algorithm is modified to cooperate with the feedback information. Compared with other coded distributed computations with straggling servers, our approach achieves lower computation latency when the overall delay incurred by the encoding, mapping and decoding process is considered. Furthermore, we compare the storage loads of different schemes and show that the LT coding with feedback has a strong comparative advantage in these straggler-tolerant computation scenarios.

In this paper, we propose a practical deep neural network for OFDM symbol equalization and demonstrate its advantages in combating large Doppler Shift. In particular, a novel zero-forcing initialized neural architecture named Cascaded Net (CN) is proposed for equalization, where deep trainable network is cascaded behind a zero-forcing preprocessor to prevent the network getting stuck in a saddle point or a local minimum point. In addition, we propose a sliding equalization approach to detect those OFDM symbols with large number of subcarriers. We also evaluate this novel equalizer, as well as the sliding algorithm, using Rayleigh fading channel with large Doppler shift. The numerical results show this novel equalizer can achieve better performance than zero-forcing equalizer and classical ICI cancellation methods in SISO scenario. Thanks to proper training methods, this equalizer is relatively robust to traditional methods when channel estimation is inaccurate or Doppler shift changes.

A novel iterative receiver for polar-coded massive multiuser multiple-input-multiple-output (MU-MIMO) systems is proposed. In the receiver, the feedbacks of the polar decoder, including the correctly decoded data and the soft outputs generated using Pyndiah's Chase algorithm, are available to the detector and the channel estimator, respectively. Moreover, interference cancellation (IC) schemes are employed to improve the overall performance and reduce the computation complexity. Simulation results show that the proposed receiver with polar codes can bring about considerable performance gains through iterations and can always outperform the one with LDPC codes.

In this study, the authors propose a parallel concatenated decoding (PCD) scheme for short non‐binary low‐density‐parity‐check (NB‐LDPC) codes. It consists of a reduced trellis extended min‐sum (R‐TEMS) algorithm which efficiently reduces the check node updating complexity over high‐order Galois fields and a low complexity ordered statistic decoding aided by partial cyclic redundancy check bits. The R‐TEMS algorithm has a negligible performance loss and noticeable reduction in decoding complexity with respect to the trellis‐based EMS (TEMS) algorithm. Besides, the PCD shows a close error‐correction performance when compared with other concatenated decoding schemes for NB‐LDPC codes. It achieves a coding gain about 0.5 dB with reasonable complexity contrasted with the Q‐ary sum–product algorithm for high‐rate short NB‐LDPC codes over GF(256).

Pulse blanking is a common approach for impulsive interference mitigation in orthogonal frequency division multiplexing (OFDM) systems. The blanking threshold that decides whether a received signal is blanked or not, shows a crucial effect on the mitigation performance. Considering the influence of error correcting codes, we investigate the threshold optimization of pulse blanking for low-density parity-check (LDPC) coded OFDM systems. The protograph based extrinsic information transfer (PEXIT) charts and system simulations are used to tackle the optimization problem of blanking threshold with various LDPC coding schemes, which include different proto-graph structures, code lengths, code rates and the number of iterations. The simulation results show that the optimal blanking threshold changes with the code rate, whereas it remains the same regardless of the protograghs, code lengths and decoding iterations.

To obtain a robust physical‐layer network coding (PLNC) for two‐way relaying system, the authors propose a low‐density parity‐check (LDPC) coded PLNC scheme with phase pre‐rotation to combat the carrier phase asynchronous in the multiple access stage. At two users, each modulation symbol is rotated according to a predefined incremental phase without the knowledge of carrier phase difference. Decoding simulation and numerical analysis are carried out to evaluate this joint LDPC and PLNC scheme with phase pre‐rotation. Simulation results show that this strategy can achieve a significant improvement and a good trade‐off between performance and complexity. Protograph‐based extrinsic information transfer analysis demonstrates the proposed scheme is robust, which is consistent with the simulation results.

Chinese next generation broadcast wireless (NGB-W) systems are aimed to provide high-speed, ubiquitous, and secure broadcast services and tri-play services to massive users. New terrestrial broadcast techniques are needed to support these services in NGB-W systems. In this paper, a new set of quasi-cyclic (QC) low density parity check (LDPC) codes with a moderate code length and a wide operation range are proposed for NGB-W systems. It is shown by simulations that the perfor-mance of the proposed LDPC codes is much better than that of the LDPC codes used in the second generation television broad-cast of digital video broadcasting (DVB-T2/NGH) systems.

The authors study the optimisation of the rate-compatible (RC)-irregular-repeat-accumulate (IRA) codes for asymmetric Slepian–Wolf coding to deal with flexible correlated sources. By assuming two different additive white Gaussian noise channels, the authors formulate a non-uniform extrinsic information transfer method to optimise the degree distribution of RC-IRA codes. The parity check matrices of RC-IRA codes are constructed from a mother matrix by combining puncturing and check-splitting, which achieves a good trade-off between the lowest-rate codes and the highest-rate codes. Simulation results show that the optimised non-uniform error-correcting code performs very close to the Slepian–Wolf limit over the target compression rate range and outperforms the prior results.

Physical layer secret key can be extracted from wireless fading channels based on channel quantization with guardband (CQG). In this paper, we analyze the key generation efficiency of the CQG protocol. Analytical closed-form expressions of bit error rate (BER) and key generation efficiency are derived for the CQG protocol. In order to further improve the key generation efficiency, we concatenate the CQG protocol with reconciliation. And then, we present a upper bound of key generation efficiency, which can be maximized by careful selecting the guardband region and LDPC codes. The key generation efficiency is also analyzed by considering the attacks in the case of an unauthenticated wireless channel.

In this paper, we show how to compute the Slepian-Wolf lower bound for the reconciliation of physical layer secret keys between two radio terminals. Two coding approaches, including the syndrome method and the parity method, have been proven to require the same number of bits exchanged between two terminals for the reconciliation in the noiseless environment. We also present a practical coding approach based on LDPC codes, and the gap between the practical approach and the Slepian-Wolf bound is given.

A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-sum decoding, one can find that its WBF algorithm is the algorithm proposed by Jiang et al. For BP decoding, we propose a new WBF algorithm and show its performance advantage. The proposed WBF algorithms are parallelized to achieve rapid convergence. Two efficient simulation-based procedures are proposed for the optimization of the associated thresholds.

The queued-code based on low-density parity-check (LDPC) codes, which exploit both the near Shannon-limit performance LDPC codes and the instantaneous channel state information (CSI), can provide excellent performance in the block fading channels. The existing work utilized the conventional random puncturing and repetition operation, which may lead to considerable performance loss due to the changed intrinsic connections of parity-check matrix (PCM) for the receiver. In this paper, we present a reversed sequential puncturing (RSP) scheme and a construction method with modified dual-diagonal structure for the LDPC coded queued-code. The consecutive puncturing pattern in reversed direction can ensure the uniform row-weight distribution of the punctured PCM. The modified dual-diagonal form and the RSP scheme can ensure no more than one punctured symbol involved in each check-sum equation. The simulation results demonstrate that our proposed scheme can achieve noticeable performance gains.

The clustering of cycles to form stopping sets are first observed by T. Tian and et al. As the determination of stopping sets of minimum size is NP-hard, we propose to consider clustering of cycles to avoid the stopping sets of small sizes. In particular, the clustering of two cycles are considered for an improved version of progressive edge-growth construction of LDPC codes.

In this paper, a modification to the weighted bit- flipping (WBF) decoding algorithm for low-density parity-check (LDPC) codes is proposed. This modification, based on the adjustment in reliabilities of the check sums during iterative decoding, can be applied to various WBF algorithms. Our studies show that the modification can be achieved with a small increase in complexity, but leads to an appealing improvement in error performance.

Orthogonal frequency division multiplexing (OFDM) is sensitive to carrier frequency offset (CFO), which destroys the orthogonality and causes inter-carrier interference (ICI). In this paper, we investigate the average error probability of OFDM systems impaired by CFO over frequency selective Rayleigh fading channels. By exploiting the Beaulieu series, the effects of CFO on the symbol error rate (SER) and bit error rate (BER) performance, which depend strongly on the statistical characteristics of the fading channels, are expressed as the sum of an infinite series in terms of the characteristic function (CHF) of the ICI. We only consider OFDM systems modulated with BPSK, QPSK, 8-PSK and 16-QAM, and the Gray-coded mapping are employed for the evaluation of BER performance.

A natural relationship between weighted bit-flipping (WBF) decoding and message-passing decoding is explored. This understanding can help us develop a dual WBF decoding algorithm from one type of message-passing decoding algorithm and vice versa. For min-sum decoding, one can find that its dual WBF algorithm is the algorithm proposed by Jiang et al. For belief-propagation (BP) decoding, we propose a new WBF algorithm and show its performance advantage. For some high-rate low-density parity-check (LDPC) codes of large row weight, it is shown that the WBF algorithm proposed by Liu and Pados performs extraordinarily well. However, its dual message- passing decoding does not work well. Furthermore, we propose a parallel implementation framework for various WBF algorithms. Compared to serial implementations, various WBF algorithms in their parallel form converge significantly faster and often perform better.