Faster-than-Nyquist (FTN) signaling is a classic signaling scheme for improved spectral efficiency compared to the conventional Nyquist signaling at the cost of increased complexity. In this paper, we investigate the FTN transmission with Nyquist receiver sampling (a.k.a. FTN-NR transmission), in order to simplify the receiver processing. Particularly, we derive a closed-form expression on the achievable rates of the FTN-NR transmission with arbitrary shaping pulses and Gaussian constellations. Our analysis reveals that this achievable rate relates closely to both the folded spectrum and folded squared spectrum of the pulse, which incorporate the folding effect of the signal spectrum due to the receiver sampling. Furthermore, we prove that the achievable rate of FTN-NR transmission is no better than that of Nyquist signaling despite the pulse shapes, when Gaussian constellation is applied. However, we then provide a numerical study on the rate with finite-alphabet constellations, and verify that FTN-NR transmission can outperform Nyquist signaling in terms of the achievable rate, especially when the modulation order is low. Our numerical results confirm our conclusions and report a noticeable achievable rate improvement of the FTN-NR transmission compared to Nyquist signaling under QPSK signaling.

This paper focuses on the design and performance analysis of faster-than-Nyquist (FTN) signaling employing enhanced 5G low-density parity-check (LDPC) codes, oriented toward the requirements of future 6G systems. We propose the extrinsic information transfer (EXIT) chart analysis for the LDPC-coded FTN system based on the Ungerboeck observation model, where the input-output mutual information function of the detector is approximated using least squares fitting. With the proposed EXIT chart analysis, we explore the thresholds and decoding performance of different LDPC codes (regular codes, irregular codes and protograph codes) in both Nyquist and FTN systems, revealing two important observational findings for FTN signaling: 1) Unlike Nyquist systems, where certain 5G New Radio (NR)-like information puncturing can enhance the decoding threshold and performance, we observe that in the FTN setting considered in this paper such puncturing leads to performance degradation; 2) Unlike Nyquist systems, the paritycheck matrix of LDPC codes optimized for FTN signaling tends to be relatively sparser within comparable ensembles, due to the intentionally introduced inter-symbol interference (ISI). Based on these findings, we develop tailored LDPC codes for FTN signaling by applying the masking operation to the base matrix of the standard 5G LDPC codes, aiming to achieve a lower decoding threshold and thereby better decoding performance. Moreover, the raptor-like structure and rate compatibility are preserved in the proposed LDPC codes, and the encoder and decoder are reused with only minor modifications. Numerical results show that: 1) All simulation results align with the decoding thresholds obtained by the proposed EXIT chart analysis, confirming the effectiveness of the analysis; 2) For the FTN system, the tailored LDPC codes outperform standard 5G LDPC codes, achieving over 0.4 dB coding gain and approaching (slightly exceeding) the constrained Nyquist capacity; 3) Under the same spectral efficiency, FTN with tailored LDPC codes performs better than standard 5G LDPC codes with Nyquist signaling, demonstrating a coding gain of up to 0.6 dB; 4) The proposed LDPC codes with the FTN signaling achieve better performance compared to existing high-performance codes specifically designed for FTN signaling.

In order to achieve rate-compatible RM codes, two most effective ways are puncturing and shortening. In this paper, puncturing schemes are studied. Different from the existing spherical puncturing, puncturing schemes which do no change the Plotkin structure of RM codes are proposed, enabling existing decoding techniques be readily accessible. The proposed puncturing schemes are based on Hamming weights of column indices of the generator matrix of RM codes. When Hamming weights of column indices (also determining the column weights, CW) are the same, different strategies are proposed, producing four different puncturing strategies, called CW-IV, CW-LSB, CW-MSB, and CW-MSB-Sym, respectively. Analysis is performed to show the union bound on error performance of RM codes with puncturing. Theoretically, it also shows that the punctured first 1st-order subcode can have potentially better performance than the non-puncturing case if puncturing is properly designed. Simulation results show that the proposed puncturing strategies outperform random and quasi-uniform puncturing (QUP) schemes in terms of block error rate (BLER). Union bound results also confirm that the first 1st-order subcode shows better performance than the original non-puncturing case. This fact indicates a more efficient transmission scheme of RM codes: transmitting part of the original codeword to increase the spectrum efficiency while achieving a better BLER performance under recursive list decoding.

Based on a recently proposed fast Fourier transform by Lin, Chung, and Han, this paper presents two fast erasure decoding algorithms for Reed–Solomon (RS) codes over binary extension fields of lengthNand dimensionK. The first algorithm applies to low-rate RS codes (i.e.,K/N≤ 0:5) and achieves a complexity ofO(N log K). The second algorithm applies to high-rate RS codes (i.e.,K/N≥ 0:5) and achieves a complexity ofO(N log(N–K)). Compared to recent state-of-the-art algorithms, both proposed algorithms achieve the best complexity, resulting in significant throughput improvements in Single Instruction Multiple Data (SIMD) based simulations. Besides yielding new fast algorithms for RS codes, this paper also presents a new interpolation formula, as well as related results, which may be of independent interest.

Recently, index modulated orthogonal time frequency space modulation combined with multi-input and multi-output (MIMO-OTFS) has been introduced to get superior bit error rate (BER) performance than conventional MIMO-OTFS schemes. In this paper, we propose a novel transmission scheme called generalized space-delay-Doppler index modulated OTFS (GSDDIM-OTFS) to further utilize the multi-domain resources and explore the potential benefits of the index modulated MIMO-OTFS. In this scheme, additional information bits are transmitted through the combined space-delay-Doppler resource units. We also derive the analytical expressions of average bit error probability (ABEP) to evaluate the performance of the proposed scheme. For multi-domain index modulation schemes, the traditional detection suffers a supreme complexity with a large size of look-up table. To address this issue, we propose a coarse-to-fine (CTF) network for the GSDDIM-OTFS detection, called the CTFIM detector. In the proposed detector, the characteristic of the transmit constellation of index modulated schemes is fully utilized and we explore the coarse-to-fine strategy to capture the general features more efficiently from different dimensions. Specifically, the coarse module is used to capture features based on the index pattern and the fine classification to establish the global relationships in each GSDDIM-OTFS subblock. Furthermore, we also employ feature fusion to increase the feature dimensions. Simulation results demonstrate the enhanced performance of the GSDDIM-OTFS over doubly-selective fading channels and the proposed DL-based detectors under perfect and imperfect channel conditions.

Recently, the application of deep learning (DL) technologies to communication systems has garnered significant attention. The Mamba architecture can adaptively adjust the model parameters based on the dynamic changes of the sequence, effectively capturing complex dependencies in long sequences. Furthermore, Mamba provides similar modeling capabilities to Transformers while ensuring near-linear scalability with respect to sequence length. In this paper, we propose a Mambabased detector for orthogonal time frequency space with index modulation (OTFS-IM), termed as MambaIM, that can extract features and establish the global input-output relations from the received signal. Simulation results demonstrate that the proposed MambaIM detector outperforms current DL-based detectors in terms of bit error rate (BER) performance.

In this paper, we present a fast Chinese remaindering transform (FCRT) over finite fields by exploring Lin-Chung-Han (LCH)-FFT. We take a new approach to LCHFFT by formulating it as a procedure to compute a remainder tree. It is demonstrated that by adopting the Cantor basis for the underlying field$\mathbb{F}_{2} Q$of LCH-FFT, a special set of moduli$\left\{M_{i}(x): 0 \leq i \leq n-1\right\}$, termed “FFT-moduli”, can be picked from the remainder tree, satisfying that they reside in a subfield$\mathbb{F}_{2^{q}}$, specifically$M_{i}(x) \in \mathbb{F}_{2^{q}}[x]$, and that their degrees sum up to$N=\sum_{i=0}^{n-1} \operatorname{deg} M_{i}(x)=2^{Q}$. The FCRT is defined as taking a polynomial$f(x) \in \mathbb{F}_{2^{q}}[x]$of degree less than$N$as input and computing the remainders$\left\{f(x) \bmod M_{i}(x): 0 \leq i \leq n-1\right\}$as output. Since the FCRT realizes a subfield subtree within LCH-FFT, it requires$O(N \log N)$operations over$\mathbb{F}_{2 q}$. Potential applications in coding and secret sharing are also discussed.

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding. The existence of such lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

This paper focuses on the analysis and design of improved 5G low-density parity-check (LDPC) codes for faster-than-Nyquist (FTN) signaling. We first propose the protograph-based extrinsic information transfer (PEXIT) chart analysis for the LDPC-coded FTN system using the sum-product algorithm (SPA) based on the Ungerboeck observation model, where the distribution of the output mutual information from the detector is approximately derived using least squares fitting. With the proposed PEXIT chart analysis, we then design the improved LDPC codes for the coded FTN signaling aiming to achieve a lower decoding threshold and thereby better error performance. The proposed codes are optimized based on the raptor-like structure of the 5G LDPC codes and also support rate compatibility. The proposed codes reveals two distinct LDPC code design criteria for FTN signaling, i.e., 1) no information bits should be punctured; 2) columns with high column weights should be removed in the base graph. The advantages of the proposed codes are explicitly verified by our numerical results, where noticeable coding gains compared to existing codes and coded Nyquist systems can be observed.

Recently, Huang and Zhang [1], [2] introduced the derivative as a fundamental structure of cyclic codes, based on which the derivative decoding was further presented. It is well known that some cyclic codes constructed based on finite geometries form a special class of low-density parity-check (LDPC) codes, which perform well under the sum-product algorithm. In this paper, we study the derivative structure of Euclidean geometry (EG) codes, with a special interest in EG-LDPC codes. It is proved that for µ = m −2, the derivative ascendant of the extended (µ,s)th-order EG code of length 2msis the extended (µ+1,s)th-order twofold EG code of length 2ms. As a subcode of EG-LDPC code, the derivative descendant of the extend (1,s)th-order twofold EG code is characterized in terms of the roots of the generator polynomial. The new code relationship suggests that the twofold EG code can leverage the sum-product decoding of the derivative descendant for its derivative decoding.

Polar codes have been proven to be capable of achieving the optimal rate for the lossless compression problem. However, their finite-length performance is not satisfactory due to the insufficient polarization effect. In this work, we combine source polarization with several entropy coding techniques to improve the compression efficiency while keeping the additional complexity negligible. In our framework, the standard encoding of polar codes can be treated as a pre-transform on the source data, and only a small proportion of the transformed data needs further compression thanks to the source polarization. We show that our framework is compatible with the mainstream entropy coding schemes such as Huffman coding, arithmetic coding, and asymmetric number system (ANS). To optimize performance, an iterative algorithm is proposed for the set partitioning of the transformed data. Simulation results show that the improved scheme is superior to the original polar source coding.

In this paper, we consider the design of polar codes for point-to-point (P2P) MIMO-OFDM system with channel sparsity. We first adopt singular value decomposition (SVD) precoding to obtain a parallel symbol-wise fading channel with different effective signal-to-noise ratios (SNRs) on different subchannels due to the frequency selectivity. After a detailed evaluation on the effective SNRs, we show that the received symbols not only are corrupted by channel noise but also suffer from, effectively, channel erasure since some subchannels are in deep fade. Therefore, we propose the Reed Muller (RM)-channel degradation construction based on the statistical SNRs in achieving the balance between erasure correction and error correction abilities of polar codes via adjusting a tunable parameter. Numerical results show that a noticeable coding gain can be achieved by the proposed construction comparing with 5G polar codes.

In this paper, a point-to-point (P2P) orthogonal time frequency space (OTFS)-based multiple-input multiple-output (MIMO-OTFS) transmission scheme is devised for millimeter wave (mmWave) channels. The proposed transmission scheme relies on a low-complexity hybrid digital-analog beamforming (HBF) scheme that exploits the delay-Doppler (DD) domain channel properties, where detailed design criteria for different channel conditions are presented, including the case where paths are indistinguishable by angles. Thanks to the proposed HBF scheme, approximate path-wise interference-free transmission of multiple data streams is achieved, and consequently, only little pre-equalization is required for combating the residual channel impairments. The achievable rate of the proposed scheme is studied and compared with the orthogonal frequency-division multiplexing (OFDM) counterpart. In particular, we unveil that the condition number of the effective angular domain matrix for OTFS is smaller than that for OFDM, due to the enhanced path separability in the DD domain. As a result, the proposed MIMO-OTFS transmission scheme demonstrates superior performance over the MIMO-OFDM transmission scheme. Our numerical results corroborate our theoretical analysis and show a near-optimal rate performance with significantly reduced complexity compared to the optimal singular value decomposition (SVD) precoding method.

In this paper, we investigate the fundamental tradeoff between computation and communication for the full-duplex (FD) wireless MapReduce distributed computing network. Specifically, a coded interference alignment and neutralization (CIAN) scheme is proposed to significantly reduce the achievable normalized delivery time (NDT) for any given computation load, which jointly exploits both the coding and interference management technologies. In particular, a novel coding strategy is designed to create the coded message desired by multiple nodes, thereby providing the coded multicasting gain. Furthermore, the Shuffle phase is molded as a special cooperative X-multicast network. For this network, a novel IAN scheme is proposed to improve the achievable sum degree of freedom (SDoF), thereby providing the IAN gain. In the proposed CIAN scheme, the fundamental tradeoff between the coded multicasting gain and IAN gain is characterized, and the achievable NDT is minimized by carefully optimizing these two gains. Furthermore, a tight information-theoretic lower bound on the NDT is derived, demonstrating the optimality of the CIAN scheme in some cases. In other cases, the achievable NDT of the CIAN scheme and the lower bound are within a multiplicative gap of 2. Theoretical analysis and numerical results indicate the superior performance of the CIAN scheme compared to existing schemes, particularly by providing additional coded multicasting gain and improved IAN gain.

In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity. Moreover, this code can achieve zero-error capacity when the symbols in a vertex with degree one are the same. We further apply our method to the one-edge graphs representing the binary channels with two memories. There are 28 possible graphs, which can be organized into 11 categories based on their symmetries. The code constructed by our method is proved to achieve the zero-error capacity for all these graphs except for the two graphs in Case 11.

Matroidal entropy functions are entropy functions in the form h = logv·rM, wherev≥ 2 is an integer and rMis the rank function of a matroidM. They can be applied into capacity chracterization and code construction of information theory problems such as network coding, secret sharing, index coding and locally repairable code. In this paper, by constructing the variable strength orthogonal arrays of some matroid operations, we characterize matroidal entropy functions induced by regular matroids and some matroids with the same p-characteristic set as uniform matroidU2,4.

This paper presents new variants of the Welch-Berlekamp algorithm that are favorable to hardware implementation. First, we derive the parallel Welch-Berlekamp (PWB) algorithm in a constructive manner based on the properties of solutions to the rational interpolation problem. The algorithm features the simultaneously performed discrepancy computation and polynomial update. Second, we explore the early-termination mechanism of the PWB algorithm for decoding of Reed-Solomon (RS) codes. By introducing the concept of incomplete error locator polynomial, we show that if$e \leq t$(whereeis the number of errors andtis the error correction capability), the PWB algorithm can be terminated at latest at the completion of the$(t+ e)$-th iteration. This leads to the early-terminating PWB (EPWB) algorithm. Finally, we develop frequency-domain versions of the PWB and EPWB algorithms, namely, FPWB and FEPWB. The key point toward the two algorithms is to replace the update of polynomial coefficients with the update of polynomial evaluations. It is worth noting that the FEPWB algorithm applies only to shortened RS codes. Furthermore, an efficient systolic architecture for the FPWB algorithm is designed, which is easily adapted for the FEPWB algorithm.

In this paper, we present an efficient decoding algorithm for a class of Reed-Solomon (RS) codes over Fermat field$\mathbb{F}_{2^{r}+1}$. We show that the Fermat number transform can be used to speed up the syndrome computation and the Chien search. The implementation architectures are designed for the two blocks. The key equation is then derived. When using the RS code in practice, there arises the issue that a$(2^{r}+1)$-ary symbol is less efficiently represented by a tuple of$(r+1)$bits. We present a nested coding scheme based on RS code and single parity-check (SPC) code to harness the inefficiency. A modified Wagner algorithm is proposed for decoding the inner (nonlinear) code and is proved to be an ML decoding over the BPSK-modulated AWGN channel. Simulation results show that the proposed RS-SPC nested coding scheme yields a considerable performance gain compared to the stand-alone RS coding scheme.

This paper aims to build a bridge between the probabilistic shaping and the geometric shaping for lattice codes from the perspective of polar lattices. We prove that when performing the lattice Gaussian shaping on polar lattices, a shaping lattice As which is good for the so-called discrete additive white Gaussian noise (AWGN) channel is constructed indeed, and the shaping process is equivalent to the modulo As operation within a multi-level decoding manner. To achieve the power-constraint AWGN channel capacity or the rate distortion bound of the i.i.d. Gaussian source, one classical approach is to construct two nested lattices where the fine lattice takes care of the Gaussian noise or the target distortion, and the coarse lattice is responsible for the boundary of the lattice codewords. Another approach is to construct a single lattice and then perform the lattice Gaussian shaping. The former approach falls into the category of geometric shaping, while the latter one is regarded as a type of probabilistic shaping. This work proposes a unified perspective of these two approaches, and provides new evidence on why they are both able to achieve the optimal performance of Gaussian channel coding and source coding problems.

In this paper, we present a Reformulated Euclidean Algorithm (REA) and its optimized architecture for Reed-Solomon decoding. Through algorithm transformations on a modified Euclidean algorithm by Berlekamp et al., the REA is derived, featuring free of inversion operations. It has a fixed number 2$t$of iterations (t is the error-correction capability), and owns a very simple description. By generalizing the Horiguchi-Koetter formula and exploring the early termination mechanism, we present the optimized reformulated Euclidean algorithm (OREA). The derivative architecture is a systolic one, consisting of 2t + 1 processing elements (PEs) with the critical path of one multiplier and one adder. Complexity comparisons show that the proposed OREA saves 30% resources over sDCMEA, the state-of-art architecture based on Euclidean algorithm, and has almost the same (actually slight lower) complexity as ePIBMA, the state-of-art architecture based on Berlekamp-Massey algorithm. Thus this work fills an important gap for the hardware implementation between two RS decoding algorithms.

This paper begins a systematic study of the zeroerror capacity problem of broadcast channels, where the message sent can be decoded by each receiver with zero error. A graph set is used to represent the broadcast channel. We particularly consider a set of two graphs, where each graph in the set contains only one edge. The corresponding zero-error capacity is determined in this paper.

The Berlekamp-Massey algorithm is a primary algorithm for decoding Reed-Solomon codes. As an inherent property of the algorithm, the early termination can effectively reduce the latency and power of decoding. It has been known that the algorithm can be terminated at the completion of the$(t+e)$-th iteration (where$e$is the number of errors and$t$is the error-correction capability of the code). In this paper, we explore a new mechanism for the early termination. Specifically, assuming$e\leq t$, we present a detection method that can identify the$2e$-th iteration. Since the error locator polynomial will have been found at the completion of the$2e$-th iteration, we can terminate the algorithm at this point based on the proposed method. As an application, a hardware-friendly algorithm variant, dubbed Reformulated Early-Terminating Parallel Inversionless Berlekamp-Massey (RETPIBM) algorithm, is presented, which yields a systolic architecture. The derivative architecture consists of$3t+1$processing elements (PEs) and has the critical path of one multiplier and one adder. To the best of the authors' knowledge, this is literally the first architecture that achieves the early termination for Berlekamp-Massey algorithm.

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach$\frac{1}{2\pi e}$as the dimension of lattices increases. It has been predicted by Zamir et al. [1] that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work [2], we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e.$q$bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of$q$bits but only$i$bits,$1 \leq i

A ring-based constant composition distribution matcher (R-CCDM) is designed for shaping rotationally symmetrical two-dimensional (RS-2D) constellations. The procedure of distribution matching can be divided into two steps. First, nonuniformly distributed rings are generated by CCDM to approach a probability distribution calculated from that of modulation symbols. Second, a uniform mapping is performed to select one amplitude signal point from each ring. Compared with CCDM, the proposed DM contains multiple amplitude compositions, and hence achieves less rate loss. Numerical results show that, at moderate spectral efficiency, probabilistic shaping with R-CCDM outperforms that with CCDM by about $0.2 \sim 0.3 \mathrm{~dB}$ for different modulation formats.

With application of a novel user-centric architecture, cell-free massive MIMO (CF-mMIMO) significantly improves the user experienced rate, thereby addressing the issue of constrained interference in dense cell networks. In this technology, high-precision joint over-the-air (OTA) calibration plays an essential role in ensuring the performance of CF-mMIMO networks. However, the large number of remote antenna units (RAUs) in CF-mMIMO, coupled with their spatial independence, introduces considerable complexity for scalable calibration solutions. To address this challenge, this paper proposes a dynamic RAUs clustering and self-healing calibration topology construction algorithm, designed to operate within the constraints of the minimum required signal-to-noise ratio (SNR) and coherence time. Furthermore, to minimize the time overhead of calibration, a calibration timing mechanism for both intra-cluster and inter-cluster of RAUs is devised. Finally, a RIS-aided and scalable OTA calibration algorithm is developed, which can achieve phase alignment for an arbitrary number of RAUs. Simulation results show that the proposed calibration algorithm exhibits low calibration errors and demonstrates excellent performance, resulting in a notable 9.5% increase in spectral efficiency.

In this paper, we propose a low-latency probabilistically shaped multilevel polar coded modulation (PS-MLPCM) scheme for 6G called parallel PS-MLPCM. The proposed scheme achieves parallel encoding by disregarding the relationship between different bit levels when profiling shaping bits, while the conventional PS-MLPCM scheme has to perform encoding level by level. Additionally, we have found a suitable mapping scheme for the spiral constellations to ensure that the spiral constellations based parallel PS-MLPCM scheme can approach the capacity of additive white Gaussian noise (AWGN) channels. We perform numerical simulation for 64-Spiral and 64-QAM based schemes under both successive cancellation (SC) decoder and cyclic redundancy check aided SC-list (CA-SCL) decoder. The results show that the 64-Spiral based scheme achieves more than 0.8dB shaping gain at high signal-to-noise ratio (SNR). Meanwhile, the 64-Spiral based scheme can outperform the 64- QAM based scheme, especially when SNR is high or CA-SCL decoder is used.

This paper investigates the generalized linear system (GLS), widely employed to evaluate the impact of nonlinear preprocessing on wireless transceivers. Two state-of-the-art signal recovery algorithms, namely generalized approximate message passing (GAMP) and generalized orthogonal/vector AMP (GOAMP/GVAMP), are comparatively studied. They have demonstrated Bayesian optimality for independently and identically distributed (IID) Gaussian matrices and unitary matrices, respectively. However, Bayesian optimality does not inherently guarantee error-free signal recovery. For coded GLS, the information-theoretic (i.e., achievable rate) limit of GAMP remains unknown, and there are still no analytical comparisons between GAMP and GOAMP/GVAMP in terms of the mean-square error and information-theoretic limit. To address these issues, we present the achievable rate analysis and optimal coding principle for GAMP with IID Gaussian matrices, as well as provide comprehensive comparisons with GOAMP/GVAMP with unitary matrices. Specifically, based on the celebrated I-MMSE lemma and the preconditions for state evolution (SE) to hold, the simplified variational SEs of GAMP and GOAMP/GVAMP are derived, leveraging the IID and unitary matrix properties to analyze the achievable rate and optimal coding principle, respectively. On this basis, it is proven that GOAMP/GVAMP outperforms GAMP in terms of asymptotic MSE and maximum achievable rate while requiring less complexity. Furthermore, two common nonlinear functions, clipping and quantization, are used as examples to demonstrate the theoretical comparisons and practical low-density parity-check (LDPC) code design for GAMP and GOAMP/GVAMP. Numerical results show that GAMP and GOAMP/GVAMP with optimized LDPC codes can approach the theoretical limits within 0:3 dB and overcome the decoding deterioration and even divergence of the existing state-of-the-art methods, particularly under low-resolution quantization.

In this paper, we study the pulse shaping for delay-Doppler (DD) communications. We start with constructing a basis function in the DD domain following the properties of the Zak transform. Particularly, we show that the constructed basis functions are globally quasi-periodic while locally twisted-shifted, and their significance in time and frequency domains are then revealed. We further analyze the ambiguity function of the basis function, and show that fully localized ambiguity function can be achieved by constructing the basis function using periodic signals. More importantly, we prove that time and frequency truncating such basis functions naturally leads to approximate delay and Doppler orthogonalities, if the truncating windows are periodic within the support. Motivated by this, we propose a DD Nyquist pulse shaping scheme considering signals with periodicity. Finally, our conclusions are verified by using various strictly or approximately periodic pulses.

This paper presents an early-termination method for the Welch-Berlekamp algorithm. Specifically, if e ≤ t (where e is the number of errors and t is the error correction capability), the Welch–Berlekamp algorithm can be terminated at latest at the completion of the (t + e)-th iteration. Based on the early-termination mechanism, a new variant of the Welch–Berlekamp algorithm called eFDMA is presented, and a systolic architecture is designed for the eFDMA algorithm. This provides an efficient implementation for the key equation solver for a new class of Reed–Solomon codes recently proposed by Lin et al. [9].

Multicarrier faster-than-Nyquist (MFTN) signaling achieves spectral-efficient transmissions through simultaneous compression in the time and frequency domains. However, it brings the problem of high peak-to-average power ratio (PAPR). In this study, we propose a novel scheme by element-wise phase rotations (EPR) and subcarrier-wise phase rotations (SPR) to reduce the PAPR of MFTN signal. Specifically, the EPR applies phase rotations to different elements (symbols) on subcarriers, while the SPR introduces different phase terms among different subcarriers. Such a simple scheme is motivated by the fact that introducing additional phase terms in the summation will be likely to decrease the sum value. Numerical results indicate that the proposed EPR-SPR combined scheme improves the PAPR performance of MFTN signaling.

Recently, index modulated orthogonal time frequency space modulation with multi-input and multi-output (MIMO-OTFS) has been introduced to achieve better bit error rate (BER) performance than conventional MIMO-OTFS. To further utilize the multi-domain resources, in this paper, we present a transmission scheme called generalized space-delay-Doppler index modulated OTFS (GSDDIM-OTFS) to explore the potential advantages of the high dimensional index modulation, in which additional information bits are carried through the combined space-delay-Doppler resource units. Furthermore, the analytical expressions of average bit error probability (ABEP) are derived to evaluate the performance of the proposed scheme. Simulation results demonstrate the enhanced performance of the proposed scheme over doubly-selective fading channels.

In this paper, an orthogonal time frequency space modulation-based point-to-point multiple-input multiple-output (MIMO-OTFS) transmission is devised. Specifically, we propose a low-complexity hybrid digital-analog beamforming (HBF) scheme for MIMO-OTFS transmissions, in which symbols can be transmitted in an interference-free manner. In particular, the designed HBF scheme exploits the delay-Doppler (DD) domain path separability, which gives rise to a low-complexity DD domain precoding that can obtain a near-optimal rate performance facilitated by a path-wise power allocation. Simulation results demonstrate that the proposed HBF scheme achieves near-optimal rate and improved error performance in comparison to the singular value decomposition (SVD) precoding benchmark.

In this paper, we investigate two important issues of faster-than-Nyquist (FTN) signaling, namely, reduced-complexity detection and code design. Different from previous works, we consider these two issues jointly by designing a scheme that increases the minimum squared Euclidean distance of FTN signaling via repetition coding at a cost of an increased complexity. Furthermore, to reduce the rate loss of the repetition, we adopt the idea of spatially-coupling from coding theory to FTN signaling, and the resultant signaling scheme is therefore referred to as spatially-coupled faster-than-Nyquist (SC-FTN) signaling. The signal of SC-FTN signaling is generated in a continuous manner by interleaving and repeating the coded FTN signals and a graph-based iterative sliding-window detector is applied for signal detection. Both bounding and extrinsic information transfer chart analysis are provided to study the error-floor and convergence performances of SC-FTN signaling. These analyses unveil the intrinsic relationship between error floor, decoding threshold, and detection/decoding complexity, which provides guidelines for the designs of practical systems. Simulation results show that the promising error performance can be achieved with a simple FTN detection, where the bit error rate performance of coded SC-FTN signaling outperforms that of state-of-the-art coded FTN systems and the capacity of Nyquist signaling.

In this paper, we characterize matroidal entropy functions, i.e., entropy functions in the form h = log v • r, where v ≥ 2 is an integer and r is the rank function of a matroid M. By constructing the variable strength arrays of some matroid operations, we characterized matroidal entropy functions induced by regular matroids and some matroids with the same p-characteristic set as uniform matroid U2,4.

A spatially-coupled faster-than-Nyquist (SC-FTN) signaling is proposed in this paper. The signal of SC-FTN signaling is generated continuously by interleaving and repeating the coded FTN signals and a graph-based iterative sliding-window detector can be applied for signal detection. Both bounding and extrinsic information transfer chart analysis are provided to study the error performance of SC-FTN signaling, where performances of both error floor and convergence are considered. Those analyses unveil the intrinsic relationship between error floor, decoding threshold, and detection/decoding complexity, which provides guidelines for the designs of practical systems. Numerical results show that the promising error performance can be achieved with a simple FTN detection, where the bit error rate of coded SC-FTN signaling outperforms both state-of-art coded FTN systems and the BPSK capacity of Nyquist signaling.

Faster-than-Nyquist (FTN) signaling aided non-orthogonal multiple access (NOMA) is conceived and its achievable rate is quantified in the presence ofrandomlink delays of the different users. We reveal that exploiting the link delays may potentially lead to a signal-to-interference-plus-noise ratio (SINR) gain, while transmitting the data symbols at FTN rates has the potential of increasing the degree-of-freedom (DoF). We then unveil the fundamental trade-off between the SINR and DoF. In particular, at a sufficiently high symbol rate, the SINR gain vanishes while the DoF gain achieves its maximum, where the achievable rate is almost$(1+\beta)$times higher than that of the conventional synchronous NOMA transmission in the high signal-to-noise ratio (SNR) regime, with$\beta $being the roll-off factor of the signaling pulse. Our simulation results verify our analysis and demonstrate considerable rate improvements over the conventional power-domain NOMA scheme.

In this paper, we propose a novel integrated sensing and communication (ISAC) transmission framework based on the spatially spread orthogonal time frequency space (SS-OTFS) modulation by considering the fact that communication channel strengths cannot be directly obtained from radar sensing. We first propose the concept of SS-OTFS modulation, where the key novelty is the angular domain discretization enabled by the spatial spreading/de-spreading. This discretization gives rise to simple and insightful effective models for both radar sensing and communication, which results in simplified designs for the related estimation and detection problems. In particular, we design simple beam tracking, angle estimation, and power allocation schemes for radar sensing, by utilizing the special structure of the effective radar sensing matrix. Meanwhile, we provide a detailed analysis on the pair-wise error probability (PEP) for communication, which unveils the key conditions for both precoding and power allocation designs for communication. Based on those conditions, we design a symbol-wise precoding scheme for communication based only on the delay, Doppler, and angle estimates from radar sensing, without thea prioriknowledge of the communication channel fading coefficients, and also propose a suitable power allocation. Furthermore, we notice that radar sensing and communication requires different power allocations. Therefore, we discuss the performances of both the radar sensing and communication with different power allocations and show that the power allocation should be designed leaning towards radar sensing in practical scenarios. The effectiveness of the proposed ISAC transmission framework is verified by our numerical results, which also agree with our analysis and discussions.

In this paper, we concentrate on one algebraic-based quasi-cyclic low-density parity-check (QC-LDPC) code constructed from two subsets of a finite field and generalize it to propose a class of variable-rate QC-LDPC (VR-QC-LDPC) codes, whose parity-check matrices are nested horizontally and have constant number of rows. Thus the proposed codes are significant at least in terms of storage complexity and can be simply implemented. The constructed codes also inherit the original algebraic-based QC-LDPC codes and their exponent matrices can be obtained from two subsets of the given finite field. We hereby analyze the structural properties from the isomorphism perspective, and present some rules to significantly prune the size of search space and determine the non-isomorphic exponent matrices. By distinguishing the smaller quantities of non-isomorphic matrices with cycle property metric, we can easily construct a series of nested exponent matrices with better cycle distributions and obtain the VR-QC-LDPC codes. Numerical results demonstrate that the constructed codes have better iterative decoding performance within a range of code rates and decoding iterations.

Non-orthogonal multiple access (NOMA) has been widely recognized as a promising multiple access scheme for realizing next generation wireless communications. Unlike existing NOMA schemes assuming perfectly time synchronized user's signals received at the base station (BS), in this paper, we investigate the achievable rates of uplink NOMA with asynchronized transmission. By invoking Szegö's Theorem, we derive both the upper- and lower-bounds of the achievable rates of asynchronized NOMA (aNOMA) systems. In particular, we reveal that the derived lower-bound is essentially the achievable rate for conventional synchronized NOMA systems, which indicates that the asynchronization is not necessarily a foe. More specifically, we show that aNOMA systems are superior to conventional NOMA systems in terms of the achievable rates with non-sinc shaping pulses. Important insights are also unveiled based on the derived bounds. Simulation results confirm the validity of our derived analysis and demonstrate considerable achievable rates gains of aNOMA systems over conventional NOMA systems.

To provide reliable transmissions with flexible rates for satellite communications, this paper presents a novel method of constructing multi-rate quasi-cyclic low-density parity-check (LDPC) codes. The basic idea is to generate low-rate codes from a high-rate mother code by combining shortening and extending, which ensures that the generated code family owns the same code length, in order to maintain the same frame structure. The code construction involves the design of base matrices and exponent matrices for the designed codes. A progressive row elimination and addition algorithm is proposed for designing the code base matrices from a high rate to low rates. This algorithm leads to the nested and systematic structure of the parity-check matrices, which are desirable for practical implementations of their encoders and decoders, while ensuring the optimal decoding thresholds. In addition, we construct a circulation coefficient matrix based on finite fields and select the optimal rows in this matrix to construct exponent matrices while considering of cycle structures. We demonstrate that the designed codes achieve better performance for all the code rates than the LDPC codes in DVB-S2X standards. In addition, the proposed codes do not exhibit error floors for their block error rates down to 10−5.

Orthogonal time frequency space (OTFS) modulation is a recently developed multi-carrier multi-slot transmission scheme for wireless communications in high-mobility environments. In this paper, the error performance of coded OTFS modulation over high-mobility channels is investigated. We start from the study of conditional pairwise-error probability (PEP) of the OTFS scheme, based on which its performance upper bound of the coded OTFS system is derived. Then, we show that the coding improvement for OTFS systems depends on the squared Euclidean distance among codeword pairs and the number of independent resolvable paths of the channel. More importantly, we show that there exists a fundamental trade-off between the coding gain and the diversity gain for OTFS systems, i.e., the diversity gain of OTFS systems improves with the number of resolvable paths, while the coding gain declines. Furthermore, based on our analysis, the impact of channel coding parameters on the performance of the coded OTFS systems is unveiled. The error performance of various coded OTFS systems over high-mobility channels is then evaluated. Simulation results demonstrate a significant performance improvement for OTFS modulation over the conventional orthogonal frequency division multiplexing (OFDM) modulation over high-mobility channels. Analytical results and the effectiveness of the proposed code design are also verified by simulations with the application of both classical and modern codes for OTFS systems.

In this paper, a novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where a special type of convolutional codes is used to absorb the channel memory. In contrast to conventional schemes, the proposed CCS algorithm performs joint detection and decoding (JDD) based only on the code trellis by exploiting the code structure. Therefore, the proposed CCS algorithm provides a new view for channel shortening (CS) techniques, i.e., absorbing the channel memory by using channel codes. According to the code structure, we derive the path metric of the proposed CCS algorithm. Furthermore, we introduce a design of self-concatenated convolutional codes (SECCCs) for FTN signaling based on the CCS algorithm. Simulation results show that with a 16-states BCJR algorithm for JDD, the bit error rate (BER) performance of the designed SECCC incorporated with FTN signaling is only around 0.75 dB away from the Shannon limit of the shaping pulse, and the required signal-to-noise ratio (SNR) is below the BPSK capacity limit of Nyquist signaling.

In this paper, we present an improved belief propagation list (BPL) decoding algorithm for polar codes. Rather than getting L factor graphs (FGs) at random and cyclic shift permutation, we use the upper bounds on the block error propability of polar codes with different FGs as the metric to choose the best L FGs. By observing the bounds of different FGs, we propose a heuristic method to reduce search complexity. Simulation results show that there is only a gap of 0.2 dB between the frame error rate (FER) performance of the improved BPL decoder using RM16-GA construction and that of length-1024 5G polar code decoded by SCL with the same list size of 32 at FER =10-4. Moreover, with the proposed FG selection method, BPL decoding can reduce clock cycles by 97.74% compared with the SCL decoding.

A novel low-density parity-check (LDPC) coded Gaussian minimum shift keying (GMSK) scheme is proposed for wireless communications subject to low SNRs, limited power and spectrum resources. We first design a non-recursive GMSK modulator to alleviate the impact of error propagation. Then, a pilot-aided quasi-coherent demodulation algorithm (PA-QCDA) is derived, where a modified BCJR-based detection is used to produce the soft-output with initial and ending trellis-states being determined using the overhead-limited pilot. We choose proper parameters for the non-recursive GMSK signaling according to the trade-off of the power and spectral efficiency. Simulation results show that the proposed non-recursive GMSK system with the PA-QCDA can achieve performance similar to the LDPC coded BPSK system and can also work well in the presence of large frequency and phase offsets or burst errors.

A novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where special convolutional codes are used to absorb the channel memory. These convolutional codes have a special type of generator matrix that allows previous code symbols to be determined by the current code trellis state and thus been referred to as output-retainable convolutional codes (ORCCs). Different from conventional schemes, the CCS algorithm performs joint detection and decoding (JDD) based only on the code trellis by exploiting the ORCC structure. Therefore, it provides a new view for channel shortening techniques, i.e., absorbing the channel memory by using channel codes. Properties of ORCCs are discussed. Based on these properties, we derive the bit error rate (BER) bound for the CCS algorithm. According to the bound, a code search algorithm is proposed to facilitate the code design. Furthermore, two concatenated codes based on ORCCs are designed. Simulation results show that with a 16-states BCJR algorithm for JDD, the BER performance of the designed self-concatenated convolutional code incorporated with FTN signaling is only 0.75 dB away from the Shannon limit of the shaping pulse, and the required signal-to-noise ratio is below the BPSK limit of Nyquist signaling.

In this paper, we introduce a novel method, called doubly-recursive block Markov superposition transmission (DrBMST), to construct high-performance spatially coupled codes. An important characteristic of DrBMST codes is that the degrees of the constraint nodes in their normal graphs are at most three. As a result, DrBMST codes can be decoded with low complexity. We first prove that the error probability of an enlarged DrBMST code ensemble can be made arbitrarily small under windowed maximum-likelihood decoding (MLD) by increasing the decoding window size. This result partially explains the superior performances of DrBMST codes. Then we propose to use the extrinsic information transfer (EXIT) chart analysis to estimate the iterative windowed decoding thresholds of DrBMST codes. The EXIT chart analyses show that, with such a simple structure, DrBMST codes are comparable to BMST codes with large encoding memories in terms of decoding thresholds. Finally, we carry out comparisons to validate the advantages of DrBMST codes in terms of error performances and decoding complexities. In particular, for a decoding latency of 20,000 bits, the DrBMST code performs better than the (4, 8)-regular spatially coupled low-density parity-check (SC-LDPC) code, but with lower computational complexity. Hence, DrBMST codes can be used in communication systems with limited computational resources. In addition, we show that DrBMST can be used to construct multiple-rate codes.

We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER) performance at small to moderate frame length. Here, we consider a sliding window decoder in the context of large frame length or one that continuously outputs blocks in a streaming fashion. In this case, decoder error propagation, due to the feedback inherent in BCCs, can be a serious problem. To mitigate the effects of error propagation, we propose several schemes: a window extension algorithm where the decoder window size can be extended adaptively, a resynchronization mechanism where we reset the encoder to the initial state, and a retransmission strategy where erroneously decoded blocks are retransmitted. In addition, we introduce a soft BER stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm, resynchronization mechanism, and retransmission strategy, the BER performance of BCCs can be improved by up to four orders of magnitude in the signal-to-noise ratio operating range of interest, and the soft BER stopping rule can be employed to reduce computational complexity.

In this paper, we consider the sparse code multiple access (SCMA) for low earth orbit (LEO) satellite communications to achieve high user capacity and provide technical support for satellite-based Internet of Things (IoT) applications. Note that Doppler shift in the LEO satellite link can not be ignored and the message passing algorithm (MPA) extensively utilized by SCMA is quite time-consuming due to high complexity. Thus we propose a coherent iterative receiver with low complexity for SCMA-based LEO satellite communication systems. First, we design a data-aided carrier synchronization scheme using multiple disjoint pilot blocks to estimate the Doppler shift precisely. Then, a soft-out approximate message passing (SO-AMP) algorithm with linear complexity is derived from the first-order approximation of MPA based on a novel framework of SCMA mapper. Further, a damping method is introduced into the SO-AMP detector developing a damped SO-AMP (DSO- AMP) to improve the overall performance. Numerical results show that the designed receiver can achieve excellent performance close to ideal performance with no Doppler shift while maintaining low complexity.

This paper presents a new type of globally-coupled low-density parity-check (GC-LDPC) codes whose base matrix has a cyclic structure in the global part. Therefore, the resulting codes are referred to as tail-biting GC-LDPC (TB-GC-LDPC) codes. We propose two methods to construct TB GC quasi-cyclic LDPC (TB-GC-QC-LDPC) codes. For the first method, we extract a replicated version of a constructed base matrix and mask it with a designed masking matrix. Compared to the conventional construction methods, this method provides more flexibility in code length for TB-GC-QC-LDPC codes. The second method is based on designing the incidence matrix of a special type of packings. Examples show that the constructed TB-GC-QC-LDPC codes perform well over the additive white Gaussian noise channel (AWGNC) and the binary erasure channel (BEC). The asymptotic performance of TB-GC-LDPC ensembles over BECs are also analyzed by resorting to density evolution. Moreover, numerical results show that TB-GC-LDPC ensembles can achieve better flooding-schedule decoding (FSD) thresholds than the corresponding GC-LDPC ensembles with a similar structure. With sufficient decoding iterations in the global phase, the local/global two-phase iterative decoding (TPD) thresholds of the TB-GC-LDPC ensembles significantly outperform those of the corresponding GC-LDPC ensembles as well.

In this paper, we design a generalized pilot symbol assisted modulation (G-PSAM) format and study its relevant optimization problem to serve unsynchronized wireless communication systems with small pilot overhead. Based on the prototype of the PSAM format, we design a generalized PSAM format and derive corresponding data-aided Cramer-Rao bound (DA CRB) and data-aided & non-data-aided CRB (DA&NDA CRB). Then taking the DA CRB for frequency offset estimation as a criterion and adopting control variable method, we solve GPSAM format optimization problem and rebuild two “good” GPSAM formats. Theoretical analysis and simulation results show that the two G-PSAM formats can achieve better performance than the existing special PSAM formats (including the classical preamble-postamble (PP) format); and an unbiased frequency offset estimator using the two G-PSAM formats will tend more possibly to employ easier DA processing rather than DA&NDA processing without significant performance loss.

In this paper, we study sliding window decoding of braided convolutional codes (BCCs) in the context of a streaming application, where decoder error propagation can be a serious problem. A window extension algorithm and a resynchronization mechanism are introduced to mitigate the effect of error propagation. In addition, we introduce a soft bit-error-rate stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm and resynchronization mechanism, the error performance of BCCs can be improved by up to three orders of magnitude with reduced computational complexity.

We study a class of finite geometry codes referred to as finite hyperplane codes, which are constructed based on hyperplanes and flats of a lower dimension in a finite geometry over the finite field F2s. We will determine the minimum distance for this class of codes and reveal a special property of them. In particular, we will show that for a finite geometry code based on flats of two non-consecutive dimensions, the error-correction capability guaranteed by Rudolph's one-step majority-logic decoding algorithm is less than or equal to that guaranteed by Reed-Massey's multi-step majority-logic decoding algorithm, with equality if and only if the code is a finite hyperplane code. In addition, both decoding algorithms can achieve the error-correction capability of finite hyperplane codes.

In this paper we consider the generalization of binary non-uniformly coupled low-density parity-check (LDPC) codes to that over Galois field GF (2m). We will perform an iterative decoding threshold analysis for this class of non-uniformly coupled LDPC ensembles formed by randomly coupled and protograph-based coupled ensembles, respectively. By optimizing the coupling among spatial positions, we can construct codes having excellent thresholds and small rate-loss. Moreover, we propose a list-aided windowed decoding (list-aided WD) scheme for nonbinary SC-LDPC codes with low decoding latency. Numerical results show that the list-aided WD which outperforms conventional WD can perform better performance and lower decoding latency than the flooding-schedule decoding at low SNRs on the additive white Gaussian noise channel.

In this paper, we introduce the doubly recursive block Markov superposition transmission (DrBMST) of short code. An important characteristic of DrBMST codes is that the degrees of the constraint nodes in their normal graphical realizations are at most three. As a result, DrBMST codes can be decoded with low complexity. We propose to use an enlarged code ensemble to analyze the performance of DrBMST under windowed maximum likelihood decoding. Further, the extrinsic information transfer (EXIT) chart analysis is used to study the iterative decoding thresholds of DrBMST code ensembles. The EXIT analysis shows that the iterative decoding thresholds of DrBMST code ensembles are comparable to those of the BMST codes. We have also compared the error performance and the decoding complexity of finite-length DrBMST codes with regular spatial-coupled low-density parity-check (SC-LDPC) codes under equal decoding latency. The comparison results show that the DrBMST code performs about 0.1 dB better than a (4, 8)-regular SC-LDPC code, but with lower computational complexity.

With the development of the high-speed trains (HST), high spectral efficiency and low latency in high mobility scenarios have become an urgent demand. In this paper, we consider bandwidth-efficient multilevel coding (MLC) based on polar codes under high mobility scenarios. Since the use of a lot of binary coding levels and large list sizes will lead to a high latency for polar decoding, we first introduce a new kind of nonbinary polar codes based on multiplicative repetition method. Then, we employ the proposed codes as component codes for MLC scheme, and optimize the design for high mobility scenarios with low latency. Simulation results show that nonbinary polar coded MLC scheme (with less coding levels) outperform LTE turbo codes with high-order modulations, and can exhibit similar performance of binary polar coded bit-interleaved coded modulation scheme but with a smaller list size (reflecting low latency) over HST channels.

In this paper, we consider the detection of faster-than-Nyquist (FTN) signaling. By noticing that the whitening filter for FTN signaling cannot be directly derived when the symbol rate exceeds the signal bandwidth, we propose a new reduced-complexity M-algorithm BCJR (M-BCJR) algorithm based on the Ungerboeck observation model. By taking some “future” symbols into account, the proposed algorithm is able to select the M best states in the maximum a posteriori sense. We further simplify the above algorithm by choosing the key path from each possible state, which successfully reduces the complexity while maintaining a good bit error rate performance. Simulation results show that, with the use of the proposed methods, great gains can be obtained in terms of spectral efficiency (up to 186%) or signal-to-noise ratio (up to 4.5 dB) compared with the Nyquist signaling.

Extensive studies have demonstrated the effectiveness and the flexibility of constructing capacity-approaching codes by block Markov superposition transmission (BMST). However, to achieve high performance, BMST codes typically require large encoding memories and large decoding window sizes, which result in high decoding complexity and high decoding latency. To address these issues, we introduce the recursive BMST (rBMST), in which the block-oriented feedback convolutional code is used instead of the block-oriented feedforward convolutional code of BMST. We propose to use a modified extrinsic information transfer chart analysis, which relates the mutual information to the bit error rate, to study the convergence behaviors of rBMST codes. On one hand, rBMST code shares most merits of BMST code, including near-capacity performance, low-complexity encoding, and flexible construction. On the other hand, compared with BMST code, rBMST code requires a smaller encoding memory, hence a lower decoding complexity, to approach the capacity. In particular, both analytical and simulation results show that rBMST code with encoding memory three reveals a lower error floor than the BMST code with encoding memory twelve. Furthermore, we show by analysis and simulations that rBMST with fixed encoding memory (m = 3 ) and fixed decoding delay (d = 12 ) can be used to construct capacity-approaching multiple-rate codes. Finally, the comparison between rBMST codes and spatially coupled low-density parity-check codes is carried out, which shows the advantages of rBMST codes in terms of performances and decoding complexities.

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. The information sequence is partitioned equally into blocks and transmitted directly, while their replicas are interleaved and transmitted in a block Markov superposition manner. By taking into account that the codes are systematic, we derive both upper and lower bounds on the bit-error-rate (BER) under maximum a posteriori decoding. The derived lower bound reveals connections among BER, encoding memory and code rate, which provides a way to design good systematic BMST-R codes and also allows us to make trade-offs among efficiency, performance, and complexity. Numerical results show that: 1) the proposed bounds are tight in the high signal-to-noise ratio region; 2) systematic BMST-R codes perform well in a wide range of code rates; and 3) rate 1/2 systematic BMST-R codes outperform the considered (3,6)- and (4,8)-regular spatially coupled low-density parity-check codes under an equal decoding latency constraint.

This paper presents a nonbinary low-density parity-check (LDPC) coded spatial modulation (CSM) for multiple-input multiple-output communication systems, in which the information bits for choosing active transmit antennas and the bits for choosing constellation signals are protected by a nonbinary LDPC code. We apply a many-to-one mapping known as Gallager mapping to signal constellation, resulting in an improved constellation design for the CSM system. Furthermore, we propose a Gallager mapping-based scheme to solve the design problem of the CSM system with arbitrary transmit antennas, in which Gallager mapping is used to map the index information bits to the active antenna, thus an integer-bit transmission can be achieved for any number of transmit antennas. With the use of nonbinary LDPC codes, a non-iterative receiver is able to recover the undistinguished information caused by the many-to-one mapping. Several communication scenarios are studied and simulation results show that the proposed scheme can offer substantial performance gains with design flexibility over the Rayleigh fading channel.

A structure of faster‐than‐Nyquist (FTN) signaling combined with superposition coded modulation (SCM) is considered. The so‐called FTN‐SCM structure is able to achieve the constrained capacity of FTN signaling and only requires a low detection complexity. By deriving a new observation model suitable for FTN‐SCM, we offer the power allocation based on a proper detection method. Simulation results show that, at any given spectral efficiency, the bit error rate (BER) curve of FTN‐SCM lies clearly outside the minimum signal‐to‐noise ratio (SNR) boundary of orthogonal signaling with a larger alphabet. The achieved data rates are also close to the maximum data rates of the certain shaping pulse.

This paper presents a family of rate‐compatible (RC) globally coupled low‐density parity‐check (GC‐LDPC) codes, which is constructed by combining algebraic construction method and graph extension. Specifically, the highest rate code is constructed using the algebraic method and the codes of lower rates are formed by successively extending the graph of the higher rate codes. The proposed rate‐compatible codes provide more flexibility in code rate and guarantee the structural property of algebraic construction. It is confirmed, by numerical simulations over the AWGN channel, that the proposed codes have better performances than their counterpart GC‐LDPC codes formed by the classical method and exhibit an approximately uniform gap to the capacity over a wide range of rates. Furthermore, a modified two-phase local/global iterative decoding scheme for GC‐LDPC codes is proposed. Numerical results show that the proposed decoding scheme can reduce the unnecessary cost of local decoder at low and moderate SNRs, without any increase in the number of decoding iterations in the global decoder at high SNRs.

We consider the degree distribution design of the low-density parity-check (LDPC) code ensembles for symmetric Gaussian multiple-access channels (GMAC). To characterize the probability density function (PDF) of the message passing in the process of joint decoding, we propose a new scheme to construct the associated Gaussian mixture (GM) distribution, where each GM component is assigned according to the corresponding signal group transmitted by the users. By tracking the variation of the GM components in the iterative decoding process, more accurate mutual information can be obtained for the extrinsic information transfer (EXIT) chart analysis. Simulation results show that the performance of our proposed LDPC codes is better than that of the existing methods.

This paper proposes a two-stage decoding algorithm (called BP-LED) for short nonbinary low-density parity-check (LDPC) codes. It consists of the classical belief propagation (BP) decoder and a list erasure decoder (LED). Simulation results show that, for the (16, 8) LDPC code over GF(256) in the CCSDS standard, our proposed BP-LED algorithm can achieve a coding gain of 0.6 dB with respect to the FFT-QSPA. By choosing the parameters suitable for the proposed algorithm, it has a negligible performance loss with lower decoding complexity compared with the BP-MRB (most reliable basis) algorithm in [10].

Extensive studies have demonstrated the effectiveness of constructing capacity-approaching codes by block Markov superposition transmission (BMST). However, to achieve high performance, BMST codes typically require large encoding memories and large decoding window sizes, which result in increased decoding complexity and decoding latency. To address this issue, we introduce the recursive BMST (rBMST), in which block-oriented feedback convolutional code is used instead of the block-oriented feedforward convolutional code. We propose to use a modified extrinsic information transfer (EXIT) chart analysis to study the convergence behavior of rBMST codes. On one hand, rBMST code shares most merits of BMST code, including near-capacity performance, low-complexity encoding, and flexible construction. On the other hand, compared with BMST code, rBMST code requires a smaller encoding memory, hence a lower decoding complexity, to approach the capacity. In particular, analytical results show that, rBMST code ensemble with encoding memory three reveals a lower error-floor than the BMST code ensemble with encoding memory twelve.

With the development of high-speed trains (HST), efficient and reliable communication services in high mobility scenarios have become an urgent demand. As one of the strong candidates in 5G wireless system, polar codes along with its optimized design should also be investigated under high mobility scenarios. In this paper, a scheme of hash-concatenated polar codes is proposed to reduce the false alarm rate, which is a key performance in 5G enhanced mobile broadband control channel. Then, for data channels, hash-based cyclic redundancy check (CRC)-aided polar codes with a joint successive cancellation list decoding method is introduced to improve the error-correcting performance. Simulation results show that the hash-concatenated polar codes can achieve both the lower false alarm rate and better error-correcting performance than conventional CRC-aided polar codes in both the AWGN and high mobility channels. Furthermore, with the joint decoding approach, hash-based CRC-aided polar codes perform better than LTE turbo codes for high-order modulations in terms of the frame error rate over the HST channel.

In this paper, we investigate the application of nonbinary LDPC codes to spatial modulation, and a nonbinary LDPC coded spatial modulation (NBLDPC- SM) system is proposed. In the system, the symbols for choosing the active antennas and the symbols for choosing constellation signals are protected by a nonbinary LDPC code. Furthermore, we combine the NBLDPC-SM system with Gallager mapping, a method of constellation shaping, to improve the system spectral efficiency. We demonstrate that such NBLDPC-SM system can achieve low probability of bit error at near SM capacity. Several communication scenarios are investigated to verify good performance of the proposed system and simulation results are also given to provide substantial performance gains in different channel conditions.

Sparse code multiple access (SCMA) is a promising technique to meet the requirements for massive capacity in 5G communications. In this paper, a nonbinary LDPC- coded SCMA system with a turbo receiver is proposed. We also provide a heuristic approach based on Cartesian product and Euclidean distance to construct the SCMA codebook, which greatly reduces the detection complexity and can be easily extended to large-size constellations. Furthermore, the codebook design for large SCMA systems is presented, and the sparse structure is optimized via the construction of matrices with optimized cycle distribution. Simulation results show that the nonbinary LDPC-coded SCMA system is much more compatible with high-order modulation than its binary counterpart, and the proposed design outperforms the original SCMA codebook design in both the error probability and complexity even in large loading situations.

Spinal codes, a new class of rateless codes, have received considerable attention for their capacity‐approaching performance over noisy channels. Hash function is the core of a spinal encoder to generate infinite coded symbols, which has higher hardware complexity. In this study, the authors propose a multiplicative repetition‐based method instead of the hash function to generate innumerable symbols with low encoding complexity. Furthermore, both frozen‐aided and cyclic redundancy check‐aided decoding methods are proposed to improve the spectral efficiency. Simulation results show that the proposed spinal codes have lower computational complexity and can achieve higher spectral efficiency in the high signal‐to‐noise ratio region compared with the conventional ones over both additive white Gaussian noise and Rayleigh fading channels.

In this paper, we present a novel sliding window decoding scheme based on iterative Bahl-Cocke-Jelinek-Raviv decoding for braided convolutional codes, a class of turbo-like codes with short constraint length component convolutional codes. The tradeoff between performance and decoding latency is examined and, to reduce decoding complexity, both uniform and nonuniform message passing schedules within the decoding window, along with early stopping rules, are proposed. We also perform a density evolution analysis of sliding window decoding to guide the selection of the window size and message passing schedule. Periodic puncturing is employed to obtain rate-compatible code rates of 1/2 and 2/3 starting from a rate 1/3 mother code and a code rate of 3/4 starting from a rate 1/2 mother code. Simulation results show that, with nonuniform message passing and periodic puncturing, near capacity performance can be maintained throughout a wide range of rates with reasonable decoding complexity and no visible error floors.

In this paper, we propose systematic block Markov superposition transmission of repetition (BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional (RCPC) codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. By taking into account that the codes are systematic, the performance of systematic BMST-R codes under maximum a posteriori (MAP) decoding can be analyzed with a simple lower bound and an upper bound with the help of partial input-redundancy weight enumerating function (IRWEF). Numerical results verify our analysis and show that systematic BMST-R codes perform well in a wide range of code rates.

This paper presents a new superposition transmission method, called multiplicative repetition based superposition transmission (MRST). It is based on multiplicative repetition and superposition of nonbinary codes. For the encoding process, we use a short nonbinary code as basic code, and superimpose the multiplicatively repeated codewords of the basic code. Two decoding algorithms, the joint decoding algorithm and sliding-window decoding algorithm are proposed. Simulation results show that MRST with joint decoding algorithm is able to achieve to good performance. Compared with block Markov superposition transmission (BMST), MRST with sliding-window decoding algorithm can achieve better performance with less memory order. An improved transmission scheme, which is referred to as punctured multiplicative repetition based superposition transmission (P-MRST), is also proposed to increase the code rate of MRST. Simulation results show that the performance of P-MRST with sliding-window decoding algorithm can be improved by increasing memory order or decoding delay.

In the paper, a class of LDPC coded continuous phase modulation (CPM) systems is proposed for reliable communication over burst-error channels. A series of binary LDPC codes with code rates 1/4, 1/2 and 2/3 are chosen for binary and quaternary CPM schemes. A non-recursive decomposition of CPM is incorporated to eliminate the error propagation caused by burst errors. To reduce the complexity, an improved demodulation algorithm for noncoherent soft in soft out (N-SISO) is considered. Simulation results show that the proposed LDPC coded CPM offers a better error performance and is abler to recover the transmitted information under severe burst errors than current systems.

In this paper, a two-stage phase-increment-based frequency estimator with a general pilot-symbol-assisted- modulation (PSAM) structure is proposed for burst-mode communications. We derive the true Cramer-Rao bounds (CRBs) under the general PSAM structure for pure data-aided (DA) estimator. The proposed phase increment-based estimator is a pure DA estimator and implemented via two stages. In the first stage, a joint auto-correlation with one-symbol delay (AC-1) and simplified L&R (S-L&R) estimator is employed for the coarse estimation. In another stage, a two-step simplified cross-correlation algorithm with three disjoint pilot blocks is proposed for the fine estimation, where the problem of phase ambiguity is solved in the first stage such that wide estimation range as large as half of symbol rate can be guaranteed, and the fine estimation improves overall estimation accuracy. It is shown that the proposed estimator exhibits wide operating range while providing both high accuracy and moderate complexity, and efficient pilot utilization.

In this paper, we propose a simple procedure to construct (decodable) good codes with any given alphabet (of moderate size) for any given (rational) code rate to achieve any given target error performance (of interest) over additive white Gaussian noise channels. We start with constructing codes over groups for any given code rates. This can be done in an extremely simple way if we ignore the error performance requirement for the time being. Actually, this can be satisfied by repetition (R) codes and uncoded (UN) transmission along with time-sharing technique. The resulting codes are simply referred to as RUN codes for convenience. The encoding/decoding algorithms for RUN codes are almost trivial. In addition, the performance can be easily analyzed. It is not difficult to imagine that the RUN code usually performs far away from the corresponding Shannon limit. Fortunately, the performance can be improved as required by spatially coupling the RUN codes via block Markov superposition transmission (BMST), resulting in the BMST-RUN codes. Simulation results show that the BMST-RUN codes perform well (within around 1 dB away from Shannon limits) for a wide range of code rates and outperform the BMST with bit-interleaved coded modulation scheme.

This paper studies an extension and improvement of the joint detection-decoding algorithm for nonbinary LDPC-coded modulation systems. The iterative joint detection-decoding (IJDD) algorithm in [1] combines nonbinary LDPC decoding with signal detection based on the hard-message passing strategy, resulting in significantly reduced decoding complexity. However, it applies only to majority-logic decodable nonbinary LDPC codes with high column weight. For nonbinary LDPC codes with low column weight, a noticeable performance loss will be incurred. To handle this problem, we propose a reliability-based iterative joint detection-decoding (also termed improved IJDD) algorithm, which combines the accumulated reliability of symbols based on the one-step majority-logic decoding (MLGD) algorithm and a Chase-like local list decoding algorithm. Simulation results show that the improved IJDD algorithm outperforms the IJDD algorithm by about 0.3 dB using nonbinary LDPC codes with high column weight, and by about 3 dB using nonbinary LDPC codes with low column weight (dv= 4), while maintaining the low complexity of decoding. Compared to the FFT-QSPA, the proposed algorithm has a performance degradation of 0.5 dB in the high column weight regime, and about 1 dB in the low column weight regime.

This paper focuses on the design and performance analysis of single user detectable multiuser systems based upon continuous phase modulation. This problem is formulated as a special application of mismatched receiver theory, where a closed-form expression for achievable Euclidean distance can be derived. This expression inspires the constructions of two classes of spectrally efficient multiuser designs: nonorthogonal and orthogonal designs. They are both confirmed to offer strong robustness against nonlinear hardware impairment in downlink and uplink transmissions, but differ in spectral efficiency, complexity and achievable minimum Euclidean distance. Moreover, the proposed designs are able to reduce the convergence threshold in serially concatenated multiuser systems. As a general approach to constructing orthogonal and near-orthogonal signals, the proposed techniques find potential applications in multiantenna systems, and full-duplex communications. Compared with existing continuous phase modulated multiuser designs, the proposed techniques offer improved spectral efficiency and significantly reduced detection complexity.

Kite codes are a class of rateless FEC codes designed for the noisy channel. In this paper, we propose a new ensemble of nonbinary rate-compatible (RC) LDPC codes, which is constructed based on Kite codes. The proposed nonbinary RC codes (nonbinary Kite codes, for simplicity) possess coding rate varying “continuously” from 0.3 to 0.9. Moreover, the degree distribution varies with the incremental redundancy. Simulation results show that the nonbinary Kite codes outperform their binary counterparts with the BPSK modulation in a wide range of coding rates over the AWGN channel. We also examine the application of nonbinary Kite codes to fountain communications. Numerical results show that the average throughput achievable with nonbinary Kite codes can be close to the capacity within a wide region of SNRs.

A (v,g)-cage is a (not necessarily unique) smallest v-regular graph of girth g. On such a graph, a nonbinary (2,v)-regular low-density parity-check (LDPC) code can be defined such that the Tanner graph has girth 2g and the code length achieves the minimum possible. In this paper, we focus on two aspects of this class of codes, structural property and code optimization. We find that, in addition to those found previously, many cages can be used to construct structured LDPC codes. We show that all cages with even girth can be structured as protograph-based codes, many of which have block-circulant Tanner graphs. We also find that four cages with odd girth can be structured as protograph-based codes with block-circulant Tanner graphs. For code optimization, we develop an ontology-based approach. All possible inter-connected cycle patterns that lead to low symbol-weight codewords are identified to put together the ontology. By doing so, it becomes handleable to estimate and optimize distance spectrum of equivalent binary image codes. We further analyze some known codes from the Consultative Committee for Space Data Systems recommendation and design several new codes. Numerical results show that these codes have reasonably good minimum bit distance and perform well under iterative decoding.

In this paper, we investigate the performance of a wireless relay network with multiple transmission sessions, in which multiple groups of source nodes communicate with their respective destination nodes via a shared wireless relay network. A multiple transmission session model with network code division multiplexing (NCDM) scheme is proposed to remove the inter-session interference at each destination. The fundamental idea of the NCDM scheme takes advantage of the property of G Θ HT= 0 of the low-density generator matrix (LDGM) codes. Based on the analysis of the NCDM scheme, we investigate the relationship among the equivalent received signal vector, the number of sessions and the column weight of the generator matrix. New code design criteria for the construction of the generator matrix is proposed. We further evaluate the multiple transmission session model with the proposed NCDM scheme in terms of throughput and complexity. Our evaluation demonstrates that the proposed scheme not only has a linear computational complexity, but also shows a similar error performance in the AWGN case and a considerable throughput improvement compared with its counterpart, which is referred to as a serial session scheme, where groups of source nodes communicate with their respective destinations in a time division manner.

This paper focuses on the design and performance analysis of continuous phase modulated orthogonal multiple access systems. The multiuser interference is firstly derived in the context of single user detection, which reveals that the interference is determined by the modulation format. Therefore, the interference can be successfully suppressed by carefully chosen modulation parameters. Based on this observation, a class of orthogonal multiple access schemes is proposed. It is shown that the proposed strategy not only facilitates simple detection at the receiver side but also offers improved sum rate.

The performance analysis of single user detection of continuous phase modulated multiuser systems is presented in this paper. The discussion is formulated in the context of a mismatched receiver and the performance of single user detection is analyzed in terms of Euclidean distance. Taking the modulation parameters into consideration, a closed-form expression for the performance evaluation is obtained. Principles of designing the transceiver for spectrally-efficient systems are proposed. Numerical and analytical results show that properly designed spectrally efficient multiuser systems can be successfully detected by the presented detector with low complexity.

This paper concerns with the design of spectrally-efficient Frequency-Division-Multiple-Access (FDMA) multiuser systems based on Continuous-Phase-Modulation (CPM). A class of FDMA-CPM is proposed to accommodate multiple users in a subchannel and therefore admits significantly improved spectral-efficiency. Phase spacing is incorporated into the system to improve the Euclidean distance property, especially for FDMA-CPM systems with small frequency spacing. The impacts of the phase spacing and frequency spacing are then evaluated in terms of the distance property, which shows that the proposed FDMA-CPM systems have a comparable error performance to the single user systems. The proposed strategy is exemplified by systems having spectral-efficiency varying from 1.67 bits/s/Hz to 12 bits/s/Hz, which shows significantly improved spectral efficiency is obtained comparing with existing systems given the same signal to noise ratio.

In this paper, we apply the precoding technique developed by Abbasfar et al. for ARA codes to the original rate-compatible LDPC codes introduced in [1] to obtain an improved ensemble of variable-rate LDPC codes, which perform universally well over the AWGN channel in the low to high code-rate region. The proposed codes will be named precoded Kite codes. The Extrinsic Information Transfer (EXIT) chart is used to optimize the code performance. Numerical results show that the precoded Kite codes can achieve a coding gain of up to 0.3 dB over the codes in [1]. A performance comparison is also made between the proposed codes and the Raptor codes over the AWGN channel. It is shown that the proposed codes outperform the Raptor codes universally in a wide code rate range over AWGN channels. Extensive simulation results confirm that precoded Kite codes perform close to capacity within a range of code rates from 0.1 to 0.9.

This paper concerns developing a low complexity detector for spectrally-efficient Frequency-Division-Multiple-Access (FDMA) multiuser systems based on Continuous-Phase-Modulation (CPM). A class of tree-trellis-search based algorithms is proposed for joint/iterative detection and the complexity is further reduced employing a state-reduction technique based on mismatched filters. The proposed detector is evaluated in terms of minimum achievable Euclidean distance. Analytical and simulated results reveal that the proposed detector offers near optimum performance with significantly reduced complexity.

In this study, the authors consider designing low‐density parity‐check (LDPC) coded modulation systems to achieve unequal error protection (UEP). They propose a new UEP approach by partial superposition transmission (PST) called UEP‐by‐PST. In the UEP‐by‐PST system, the information sequence is distinguished as two parts, the more important data (MID) and the less important data (LID), both of which are coded with LDPC codes. The codeword that corresponds to the MID is superimposed on the codeword that corresponds to the LID. The system performance can be analysed by using discretised density evolution. Also proposed in this study is a criterion from a practical point of view to compare the efficiencies of different UEP approaches. Numerical results show that, over both additive white Gaussian noise channels and uncorrelated Rayleigh fading channels, (i) UEP‐by‐PST provides higher coding gain for the MID compared with the traditional equal error protection approach, but with negligible performance loss for the LID; and (ii) UEP‐by‐PST is more efficient with the proposed practical criterion than the UEP approach in the digital video broadcasting system.

In this study, the authors present a low‐complexity iterative joint detection–decoding algorithm for majority‐logic decodable non‐binary low‐density parity‐check (LDPC) coded modulation systems. In the proposed algorithm, a hard‐in–hard‐out decoder is combined with a hard‐decision signal detector in an iterative manner. Each iteration consists of five phases. Firstly, the detector makes hard decisions based on the iteratively updated ‘received’ signals; secondly, these hard decisions are distributed via variable nodes to check nodes; thirdly, check nodes compute hard extrinsic messages; fourthly, each variable node counts hard extrinsic messages from its adjacent check nodes and feeds back to the detection node the symbol with the most votes as well as the difference between the most votes and the second most votes; finally, these feedbacks are used to shift each ‘received’ signal point along an estimated direction to possibly reduce noise. The proposed algorithm requires only integer operations and finite field operations and consequently can be implemented with simple combinational logic circuits in practical systems. Simulation results show that the proposed algorithm performs well and hence serves as an attractive candidate for trading off performance against complexity for majority‐logic decodable non‐binary LDPC codes.

For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatially coupling the generator matrix of the basic code. This paper presents a systematic design methodology for BMST systems to approach the channel capacity at any given target bit error rate (BER) of interest. To simplify the design, we choose the basic code as the Cartesian product of a short block code. The encoding memory is then inferred from the genie-aided lower bound according to the performance gap of the short block code to the corresponding Shannon limit at the target BER. In addition to the sliding-window decoding algorithm, we propose to perform one more phase decoding to remove residual (rare) errors. A new technique that assumes a noisy genie is proposed to upper bound the performance. Under some mild assumptions, these genie-aided bounds can be used to predict the performance of the proposed two-phase decoding algorithm in the extremely low BER region. Using the Cartesian product of a repetition code as the basic code, we construct a BMST system with an encoding memory 30 whose performance at the BER of 10-15can be predicted within 1 dB away from the Shannon limit over the binary-input additive white Gaussian noise channel.

In this paper, we consider the performance-optimized nonbinary low-density parity check code over general linear group, i.e.,$\bar{\cal C}$. A new methodology for constructing the binary representation [generalized binary representation (GBR)] of$\bar{\cal C}$is proposed, which can be optimized with regard to both degree distributions and girth. As to the decoding of the GBR, we develop a low-complexity hybrid parallel decoding process. It is shown that the decoding performance of the GBR under the proposed binary decoding process could closely approach the decoding performance of its mother code$\bar{\cal C}$under nonbinary belief propagation decoding. A simple code optimization algorithm for the GBR is also provided. Simulations show the comparative results and justify the advantages of the proposed constructions.

A new problem formulation is presented for the Gaussian interference channels with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement under the assumption that no interference exists from other users. In the scenario when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as accessible capacity) at which secondary users can communicate reliably without affecting the error performance requirement by the primary users under the constraint that the primary encoder (not the decoder) is kept unchanged. By modeling the primary encoder as a generalized trellis code (GTC), we are then able to treat the secondary link and the cross link from the secondary transmitter to the primary receiver as finite state channels. Based on this, upper and lower bounds on the accessible capacity are derived. The impact of the error performance requirement by the primary users on the accessible capacity is analyzed by using the concept of interference margin. In the case of nontrivial interference margin, the secondary message is split into common and private parts and then encoded by superposition coding, which delivers a lower bound on the accessible capacity. For some special cases, these bounds can be computed numerically by using the BCJR algorithm. Numerical results are also provided to gain insight into the impacts of the GTC and the error performance requirement on the accessible capacity.

This paper is concerned with the design and performance of nonbinary LDPC-coded differential modulation systems. A low-complexity joint detection/decoding method for noncoherent demodulation is proposed, in which the hard-message-passing strategy is used for a joint factor graph. It combines trellis-based differential detection aided with channel prediction and the reliability-based decoding of nonbinary LDPC codes introduced in [1]. The Max-Log-MAP algorithm with soft-in hard-out is used for the differential detection. Simulation results show that the proposed method can offer good performances with a greatly reduced complexity.

In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial rings. The computational complexity is dominated by the complexity of the trellis. In addition, we show that these new enumerating functions can be used to improve existing performance bounds on the maximum likelihood decoding.

In this paper, we focus on network coding design for the wireless sensor networks (WSNs), where multiple source nodes communicate with a common destination node with the help of multiple relay nodes in a two-hop fashion. Specifically, we propose an unequal error protection (UEP) distributed network-channel coding (DNCC) scheme based on Luby-transform (LT) codes. We analyse three properties of the proposed UEP DNCC scheme, i.e. effective weights, turning points, and thresholds of the source nodes' number. Also, we derive the upper and lower bit error rate (BER) bounds for the proposed UEP DNCC scheme over Rayleigh fading channels under maximum-likelihood (ML) decoding. Based on the analysis, it is observed that the proposed UEP DNCC scheme can achieve all protection levels required when the number of source nodes is large enough. Simulation results show that our UEP DNCC scheme can provide desirable UEP to all source nodes.

This study is concerned with the application of non‐binary low‐density parity‐check (NB‐LDPC) codes to binary input inter‐symbol interference channels. Two low‐complexity joint detection/decoding algorithms are proposed. One is referred to as max‐log‐MAP/X‐EMS algorithm, which is implemented by exchanging soft messages between the max‐log‐MAP detector and the extended min‐sum (EMS) decoder. The max‐log‐MAP/ X ‐EMS algorithm is applicable to general NB‐LDPC codes. The other one, referred to as Viterbi/GMLGD algorithm, is designed in particular for majority‐logic decodable NB‐LDPC codes. The Viterbi/GMLGD algorithm works in an iterative manner by exchanging hard‐decisions between the Viterbi detector and the generalised majority‐logic decoder (GMLGD). As a by‐product, a variant of the original EMS algorithm is proposed, which is referred to as µ ‐EMS algorithm. In the µ ‐EMS algorithm, the messages are truncated according to an adaptive threshold, resulting in a more efficient algorithm. Simulations results show that the max‐log‐MAP/ X ‐EMS algorithm performs as well as the traditional iterative detection/decoding algorithm based on the BCJR algorithm and theQ‐ary sum–product algorithm, but with lower complexity. The complexity can be further reduced for majority‐logic decodable NB‐LDPC codes by executing the Viterbi/GMLGD algorithm with a performance degradation within one dB. These algorithms provide good candidates for trade‐offs between performance and complexity.

For cyclic LDPC codes, we propose to use their automorphism groups to improve the iterative decoding performance. The basic idea is to construct nonequivalent parity-check matrices via column permutations. Three types of iterative decoders are devised to take advantage of the code's automorphism group. In this paper we focus on cyclic LDPC codes defined by a circulant parity-check matrix and consider two known subgroups of the automorphism group of a cyclic code. For the large class of idempotent-based cyclic LDPC codes in the literature, we show that the two subgroups only provide equivalent parity-check matrices and thus cannot be harnessed for iterative decoding. Towards exploiting the automorphism group of a code, we propose a new class of cyclic LDPC codes based on pseudo-cyclic MDS codes with two information symbols, for which nonequivalent parity-check matrices are obtained. Simulation results show that for our constructed codes of short lengths, the automorphism group can significantly enhance the iterative decoding performance.

In this paper, new techniques are presented to either simplify or improve most existing upper bounds on the maximum-likelihood (ML) decoding performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly, the recently proposed union bound using truncated weight spectrum by Ma et al. is re-derived in a detailed way based on Gallager's first bounding technique (GFBT), where the "good region" is specified by a sub-optimal list decoding algorithm. The error probability caused by the bad region can be upper-bounded by the tail-probability of a binomial distribution, while the error probability caused by the good region can be upper-bounded by most existing techniques. Secondly, we propose two techniques to tighten the union bound on the error probability caused by the good region. The first technique is based on pair-wise error probabilities. The second technique is based on triplet-wise error probabilities, which can be upper-bounded by the fact that any three bipolar vectors form a non-obtuse triangle. The proposed bounds improve the conventional union bounds but have a similar complexity since they involve only the Q-function. The proposed bounds can also be adapted to bit-error probabilities.

This letter is concerned with a class of nonbinary low-density parity-check (LDPC) codes, referred to as column-scaled LDPC (CS-LDPC) codes, whose parity-check matrices have a property that each column is a scaled binary vector. The CS-LDPC codes, which include algebraically constructed nonbinary LDPC codes as subclasses, admit fast encoding and decoding algorithms. Specifically, for a code over the finite field F2p, the encoder can be implemented with p parallel binary LDPC encoders followed by a series of bijective mappers, while the decoder can be implemented with an iterative decoder in which no message permutations are required during the iterations. In addition, there exist low-complexity iterative multistage decoders that can be utilized to trade off the performance against the complexity. Simulation results show that the performance degradation caused by the iterative multistage decoding algorithms is relevant to the code structure.

In this paper, we analyse the performance of distributed network-channel coding (DNCC) with multiple destinations executing a code nulling (MDCN) process. By analysing the formulation deduced from DNCC with the MDCN process, we find that some unstable zero elements and additional noise are generated after right multiplying the parity-check matrix. These unstable zero elements and additional noise are the reasons to degrade BER performance in the two groups of source nodes and two destination nodes (TSTD) network model. Theoretical bit error ratio (BER) curves are drawn according to the calculated equivalent received signal-to-noise ratio (SNR). The analysis results are consistent with the theoretical curves. A design principle for the generator matrix of the DNCC scheme is proposed to solve the BER performance degradation problem. Simulation results show that the problem caused by the MDCN process can be managed effectively and the BER performance can be improved significantly by using the proposed design principle.

The performance of maximum likelihood detection of a coded modulation scheme over an additive white Gaussian noise channel can be predicted precisely by its Euclidean distance spectrum. In this paper, three algorithms are developed to generate the Euclidean distance spectra. The first algorithm is an exhaustive tree-search algorithm which is simplified by exploiting the correspondence between a code tree and the trellis. This algorithm is then modified to incorporate the A* algorithm and results in two heuristic algorithms. Moreover, the technique of trellis minimization is further developed for the multi user case and employed to reduce the complexity and memory requirements. Numerical results confirm that the proposed algorithms can generate the distance spectra of all systems with lower complexity relative to previous methods and are particularly suited for multi user CPM systems.

This paper is concerned with general interference channels characterized by a sequence of transition (conditional) probabilities. We present a general formula for the capacity region of the interference channel with two pairs of users. The formula shows that the capacity region is the union of a family of rectangles, where each rectangle is determined by a pair of spectral inf-mutual information rates. Although the presented formula is usually difficult to compute, it provides us useful insights into the interference channels. For example, the formula suggests us that the simplest inner bounds (obtained by treating the interference as noise) could be improved by taking into account the structure of the interference processes. This is verified numerically by computing the mutual information rates for Gaussian interference channels with embedded convolutional codes.

In this paper, we presented three approaches to improve the design of Kite codes (newly proposed rateless codes), resulting in an ensemble of rate-compatible LDPC codes with code rates varying “continuously” from 0.1 to 0.9 for additive white Gaussian noise (AWGN) channels. The new ensemble rate-compatible LDPC codes can be constructed conveniently with an empirical formula. Simulation results show that, when applied to incremental redundancy hybrid automatic repeat request (IR-HARQ) system, the constructed codes (with higher order modulation) perform well in a wide range of signal-to-noise-ratios (SNRs).

Based jointly on idempotents and modular Golomb rulers, we construct a class of nonbinary cyclic low-density parity-check (LDPC) codes. The defining parity-check matrix is a sparse circulant, on which we put two constraints: 1) the characteristic polynomial is an idempotent, 2) the nonzero elements of the first row are located on a modular Golomb ruler. We show that the second constraint forms a necessary and sufficient condition for the Tanner graph to have no cycles of length 4. The minimum distance of the code is proved equal to the column weight of the parity-check matrix plus one. A search algorithm is presented, with which we obtain some high rate codes with large minimum distances. The issue of code equivalence is also discussed. Simulation results show that the obtained codes perform well under iterative decoding.

The extended min-sum (EMS) algorithm is redescribed as a reduced-search trellis algorithm (called M-EMS algorithm). Two variants of the M-EMS algorithm, called T-EMS algorithm and D-EMS algorithm, are presented. Simulation results show that, these three algorithms (referred to as X-EMS algorithms for convenience), combined with factor correction techniques, perform almost as well as the Q-ary sum-product algorithm (QSPA) but with a much lower complexity.

Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm. We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP algorithm. In our feedback procedure, we exploit much of the information from stabilizers, not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel. Our algorithm does not increase the measurement overhead compared to the previous method, as the extra information comes for free from the requisite stabilizer measurements.

This paper introduces a new class of rate less forward error correction codes named semi-random Kite (SR-Kite) codes, which can be described by a sparse semi-random parity-check matrix in systematic form. SR-Kite codes have not only rate less property, but also low error floors. We present a simulation-based greedy optimization algorithm to design the degree distribution of SR-Kite codes for independent Rayleigh fading channels. The performances of SR-Kite codes under maximum likelihood decoding are analyzed for both AWGN and independent Rayleigh fading channels via union bound. Both the analysis and simulation results show that the proposed codes perform well over AWGN and fading channels within a wide range of signal-to-noise-ratios.

In this paper, we consider user selection algorithms for Multi-user MIMO systems with perfect or partial channel state information at the transmitter (CSIT). A novel user selection algorithm based on chordal distance is proposed. The basic principle is to serve the user subset in which one is approximately orthogonal to the others. Since the chordal distance relies only on the channel direction information, the proposed algorithm has a low computational complexity, and can be extended straightly to the limited feedback system. Analysis and simulations verify the effectiveness of the proposed method.

High complexity of frequency-hopping (FH)/spread- spectrum(SS) sequence is of great importance to high-security multiple-access communication systems, for it makes FH/SS sequence difficult to be analyzed. In this paper, a new complexity metric to evaluate the unpredictability of FH/SS sequence based on the Fuzzy Entropy(FuzzyEn) is presented. Simulation and analytical results show that, the proposed FuzzyEn works can effectively discern the changing complexities of the FH/SS sequences, and are compared with complexity metric based on the Approximate Entropy(ApEn). The FuzzyEn scheme has obvious advantages in the robustness to resolution parameter, the dependence to observation length and the sensitivity to vector dimension.

A new problem formulation is presented for the Gaussian interference channels (GIFC) with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement (EPR) under the assumption that no interference exists. In the case when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as accessible capacity) at which secondary users can communicate reliably without affecting the EPR under the constraint that the primary encoder (not the decoder) is kept unchanged. The relation of the accessible capacity to the capacity region of the GIFC is revealed. By modeling the primary encoder as a generalized trellis code (GTC), we are able to treat the secondary links as finite state channels. Then upper and lower bounds on the accessible capacity are derived and computed by using the BCJR algorithm. The numerical results show us either expected or interesting facts.

In this paper, two techniques are presented to either simplify or improve most of the existing upper bounds on the maximum-likelihood decoding (MLD) performance of the binary linear codes over additive white Gaussian noise (AWGN) channels. Firstly, the recently proposed union bound using truncated weight spectra by Ma et al is re-derived in a detailed way based on Gallager's first bounding technique (GFBT). Secondly, we propose using triplet-wise error probabilities instead of pair-wise error probabilities to improve the union bound. In doing so, we prove that any three codewords form a non-obtuse triangle, which can be utilized to upper-bound the triplet-wise error probability. The proposed bounds improve the conventional union bounds but have a similar complexity since they involve only the Q-function. The proposed bounds can also be adapted to bit-error probabilities.

Kite codes, which were originally defined over the binary field, are generalized to arbitrary abelian groups in this paper. Kite codes are a special class of prefix rateless codes over groups, which can generate potentially infinite (or as many as required) random-like parity-check symbols. In this paper, we consider four kinds of Kite codes, which are binary Kite codes, Kite codes over one-dimensional lattices, Kite codes over M-PSK signal constellations and Kite codes over multi-dimensional lattices. It is shown by simulations that the proposed codes perform well over additive white Gaussian noise channels.

A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M)RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M)RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.

In this paper, we first propose a general framework for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on a two-dimensional (2-D) maximum distance separable (MDS) code. Two classes of QC-LDPC codes are defined, whose parity-check matrices are transposes of each other. We then use a 2-D generalized Reed-Solomon (GRS) code to give a concrete construction. The decoding parity-check matrices have a large number of redundant parity-check equations while their Tanner graphs have a girth of at least 6. The minimum distances of the codes are very respectable as far as LDPC codes are concerned. We further show that many existing constructions of QC-LDPC codes based on finite fields in the literature can be unified under this construction. Experimental studies show that the constructed QC-LDPC codes perform well with the sum-product algorithm (SPA).

In this paper, we present a low-complexity joint detection-decoding algorithm for nonbinary LDPC coded-modulation systems. The algorithm combines hard-decision decoding using the message-passing strategy with the signal detector in an iterative manner. It requires low computational complexity, offers good system performance and has a fast rate of decoding convergence. Compared to the q-ary sum-product algorithm (QSPA), it provides an attractive candidate for practical applications of q-ary LDPC codes.

This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.

For real-time wireless communications, short forward error-correcting (FEC) codes are indispensable due to the strict delay requirement. In this paper we study the performance of short FEC codes. Reed-Solomon (RS) codes and concatenated zigzag (CZ) codes are chosen as representatives of classical algebraic codes and modern simple iterative decodable codes, respectively. Additionally, we use random binary linear codes as a baseline reference for comparison. Our main results (demonstrated by both simulation and ensemble distance spectrum analysis) are as follows: 1) Short RS codes are as good as random binary linear codes; 2) Carefully designed short low-density parity-check (LDPC) codes are almost as good as random binary linear codes when high decoding complexity can be tolerated; 3) Low complexity belief propagation decoders incur considerable performance loss at short coding lengths.

This letter concerns the performance assessment of cascade trellis-block space-time codes. We focus on the case where the 2/spl times/2 orthogonal block space-time code is used as the inner code. Either bounding or hybrid bounding/simulation techniques can be used. The proposed work provides some insights into the properties of such codes.

This paper presents a family of concatenated two-state trellis-coded modulation (CT-TCM) schemes. Compared with the existing turbo-type bandwidth-efficient coded modulation schemes, the proposed codes have significantly reduced complexity without sacrificing performance. A joint design strategy for all component codes is established. This leads to so-called asymmetrical and time-varying trellis structures, which possess good Hamming and Euclidean distance distributions. The performance of the proposed codes is demonstrated by simulation results.

We report the progress in concatenated tree (CT) codes and related schemes, including low rate codes for CDMA applications and bandwidth efficient coded modulation schemes. It is shown that CT codes provide efficient solutions for various situations. Near capacity performances (within about 0.5 dB) can be achieved at significantly reduced decoding costs.