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.

This paper proposes an improved ordered statistics decoding (OSD) algorithm, termed OSD with pre-stored systematic matrices (PSM-OSD), which completely avoids online Gaussian elimination by pre-storing multiple systematic generator matrices (SGMs) and selecting one based on the received sequence for decoding. To further improve the search efficiency, the local-constraint mechanism is combined with the PSM-OSD, resulting in the LC-PSM-OSD. We then address three critical questions for design: how many SGMs should be pre-stored, how they should be constructed, and how to select one for decoding. For the first question, we introduce the notion of maximum reliable-information coverage, which characterizes how well the pre-stored SGMs match the reliable bit positions. For construction and selection, we introduce a Reed-Muller-based design to ensure high basis diversity, and the sum-reliability strategy provides superior decoding performance among the tested selection criteria. A saddlepoint-based analytical framework is developed to estimate both the frame error rate (FER) upper bound and the average number of searches, enabling pre-stored matrix design without exhaustive decoding simulations. We also prove that, with tailored early stopping and unlimited maximum number of searches, the proposed algorithm is a non-exhaustive-search ML decoding algorithm. Numerical results and analysis demonstrate that the proposed decoding algorithms are effective across various coding schemes, including random linear codes, BCH codes, and 5G polar codes. Moreover, the results show that the proposed LC-PSM-OSD can closely approach the finite-length capacity over almost all code rates for the considered codes, and outperforms conventional OSD, guessing codeword decoding (GCD), and LC-GCD. © 2026 IEEE.

Wireless-powered Internet of Things networks face critical challenges due to the limited energy of sensor nodes and the difficulty of maintaining data freshness. To address these issues, this paper proposes a multi–unmanned aerial vehicle (UAV)-assisted data collection framework to minimize the age of information (AoI). A hierarchical multiple decision strategy (HMDS) is developed to optimize UAV hovering time by dynamically selecting non-orthogonal multiple access or orthogonal frequency division multiple access for intra-cluster transmission according to energy constraints and channel conditions. In addition, a multi-collaborative trajectory optimization (MCTO) scheme is proposed to reduce UAV flight time through joint clustering, partitioning, and trajectory planning. Specifically, radius-adaptive K-means++ clustering, load-balanced spectral partitioning, and a hybrid K-nearest neighbors and elite ant strategy are employed. Simulation results show that the proposed HMDS and MCTO significantly reduce hovering and flight times, thereby effectively improving AoI performance.

This paper proposes an enhanced guessing codeword decoding (GCD) algorithm, termed GCD with most reliable cyclic basis (MRCB-GCD), specifically tailored for BCH codes. Unlike original GCD, the proposed method selects the k consecutive bits with the highest aggregate reliability as the re-encoding basis, leveraging the cyclic structure of BCH codes. To further enhance search efficiency, a local constraint (LC) mechanism is introduced, where the extended reliable bits of length k+δ enable the algorithm to skip numerous unnecessary test error patterns (TEPs). To stop the search process, we introduce two termination criteria and prove that the proposed approach with the trivial termination criterion forms a non-exhaustive-search maximum likelihood (ML) decoding algorithm. A saddlepoint-based numerical method is developed to approximately calculate the upper bound on the performance gap to the ML decoding and estimate the average number of searches, showing the advantages of the proposed MRCB-GCD over the original GCD in terms of both decoding performance and search efficiency. Simulation results demonstrate that: 1) MRCB- GCD outperforms original GCD in both frame error rate (FER) and number of searches, 2) the LC mechanism and termination criteria further reduce the number of searches, and 3) the proposed approach achieves finite-length capacity across various code rates but without requiring Gaussian elimination.

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.

We propose in this paper to enhance the 5G low-density parity-check (LDPC) codes by transmitting the codewords in a block Markov superposition transmission (BMST) manner, resulting in a class of spatially coupled LDPC codes. We present a generalized extrinsic information transfer (EXIT) chart for performance analysis, showing that the decoding thresholds can be improved by increasing the memory size (coupled width)$m$. However, for m > 1, the receiver requires a relatively large window size for the sliding window decoding (SWD) algorithm, potentially causing unacceptable decoding latency. To address this issue, we propose an adaptive sliding window decoding (ASWD) algorithm, in which the decoding window size depends on the decoding state of the BMST system. The proposed EXIT chart analysis can also effectively guide the setting of the maximum decoding window in the ASWD algorithm, as well as the setting of the superposition fractions for the BMST-5G-LDPC system. Simulation results show that: 1) the ASWD algorithm can effectively reduce the average decoding window size in the medium to high signal-to-noise ratio (SNR) region, without the performance loss compared to the conventional SWD algorithm; 2) the proposed BMST-5G-LDPC code can achieve about 0.4, 0.5 and 1.7 dB performance gains compared to the 5G LDPC code over the AWGN channel, the fast fading channel, and the quasi-static block fading channel, respectively.

We propose a class of codes, referred to as staircase matrix codes (SMCs), which have staircase-like generator matrices or parity-check matrices. We illustrate that polar codes and Reed-Muller (RM) codes are (equivalent to) two instances of SMCs. The most distinguished feature of the SMCs is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE). Then we propose a representative ordered statistics decoding (ROSD) algorithm for the SMCs. Different from the conventional OSD, which forms the most reliable basis (MRB) by selecting reliable bits globally, the proposed ROSD forms an extended basis by selecting relatively reliable bits locally at least one from each staircase. We demonstrate by simulation that the ROSD has a similar performance to the OSD with local constraints (LC-OSD) and that the proposed random SMCs can outperform the RM codes and the polar codes. To further reduce the decoding delay and improve the performance, we propose a heuristic construction of staircase generator matrix codes (SGMCs) and analyze the ensemble weight spectrum (related to performance) and the quality of MRB (related to average number of test error patterns (TEPs)) for the heuristic construction. The simulation results show that, the proposed heuristic construction can reduce the average number of TEPs of the ROSD and provide a potential reduction in average decoding delay in the high signal-to-noise ratio (SNR) region. Furthermore, the proposed heuristic construction can approach the RCU bounds in a wide range of code rates.

In this paper, we propose a two-stage soft-decision decoding (SDD) algorithm for BCH codes. At the first stage, we search for test error patterns (TEPs) according to the reliabilities of the received bits by using the flipping pattern tree (FPT) algorithm or the ordered reliability bits (ORB) technique, with a bounded number of searches. At the second stage, traditional algebraic hard-decision decoding (HDD), say, Berlekamp-Massey (BM) algorithm, is performed for these TEPs to find codewords. The proposed algorithm, referred to as FPT-BM algorithm or ORB-BM algorithm, can achieve near-optimal performance with a significantly small number of searches (dozens to hundreds). This enables efficient parallel implementation, ensuring low decoding latency and high throughput. To justify the sufficiency of the small number of searches, we provide qualitative reasoning and quantitative evaluation (using saddlepoint approximation) to show that the transmitted codeword under the proposed FPT-BM decoding strategy is reached much earlier in the search list than that under the single stage decoding (FPT-only). To analyze the performance, we calculate the upper bound on the performance gap between the proposed algorithm and maximum likelihood (ML) decoding based on the saddlepoint approximation, showing that the proposed algorithm can effectively approach the ML lower bound for high rate BCH codes. To reduce computational complexity, we introduce a filtering criterion, where the algebraic hard-decision decoding (BM decoding) is performed only for those candidates satisfying a sufficient number of parity-check equations. To determine the key parameters, we provide an intuitive criterion for the threshold in the filtering step based on the statistical analysis and a quantitative criterion for the maximum list size based on the upper bound on the performance gap to ML decoding. Numerical results demonstrate that: 1) By introducing the filtering criterion, the proposed FPT-BM algorithm effectively reduces the number of BM calls by half, with negligible performance loss, and outperforms the Chase-BM algorithm under the same filtering criterion; 2) The proposed decoding algorithm outperforms single stage decoding (FPT only) under limited search sizes; 3) For high rate BCH codes, the proposed decoding algorithm can approach the finite-length capacity, while for medium rate regions, the proposed decoding algorithm also exhibits better performance over FPT-only and BM-only decoding algorithms.

In this paper, we present a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving over binary-input output-symmetric (BIOS) channels. In the finite-length region, we propose the generalized representative ordered statistics decoding with local constraints (LC-ROSD) algorithm for the SGMCs. The most distinguished feature of the SGMCs with LC-ROSD is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE), avoiding the serial GE of conventional OSD and supporting a potential low decoding latency, as implied from simulations. To analyze the performance of random SGMCs in the finite-length region, we derive the ensemble weight spectrum and invoke the conventional union bound. We also derive a partially random coding union (RCU) bound, which is tighter than the conventional one and is used as a criterion to design the SGMCs. Staircase-like generator matrices allow us to derive a series of (tighter and tighter) lower bounds based on the second-order Bonferroni inequality with the incremental number of codewords. The numerical results show that the decoding performance can match well with the proposed partially RCU bound for different code rates and different profiles. The numerical results also show that the tailored SGMCs with the LC-ROSD algorithm can approach the finite-length performance bound, outperforming the 5G low-density parity-check (LDPC) codes, 5G polar codes, and Reed-Muller (RM) codes.

This paper is concerned with the SCL-GCD algorithm of polar codes, which performs the successive-cancellation list (SCL) decoding algorithm for a lower rate sub-code and the guessing codeword decoding (GCD) algorithm for a higher rate sub-code. We propose to implement the GCD algorithm in a parallel way and design early stopping criteria for reducing complexity and decoding latency without sacrificing performance. Numerical results show that, when compared with the original SCL decoding algorithm, the SCL-GCD algorithm armed with the proposed early stopping criteria has lower computational complexity and decoding latency in the high signal-noise ratio (SNR) region.

In this paper, we propose a class of codes, referred to as random staircase generator matrix codes (SGMCs), which have staircase-like generator matrices. In the infinite-length region, we prove that the random SGMC is capacity-achieving over binary-input output-symmetric (BIOS) channels. In the finite-length region, we present the representative ordered statistics decoding with local constraints (LC-ROSD) for the SGMCs. The most distinguished feature of the SGMCs with LC-ROSD is that the staircase-like matrices enable parallel implementation of the Gaussian elimination (GE), avoiding the serial GE of conventional OSD and supporting a potential low decoding latency, as implied from simulations. To analyze the performance of random SGMCs in the finite-length region, we derive the ensemble weight spectrum and invoke the conventional union bound. We also derive a partially random coding union (RCU) bound, which is tighter than the conventional one and can be used as a criterion to design the SGMCs. The numerical results show that the random SGMCs with the LC-ROSD exhibit a significant decoding time improvement compared to that with the conventional OSD. They also show that the tailored SGMCs with the LC-ROSD can approach the finite-length performance bound, outperforming the 5G low-density parity-check (LDPC) codes, 5G polar codes and Reed-Muller (RM) codes.

We propose quasi ordered statistic decoding (quasi-OSD) of binary image of Reed-Solomon (RS) codes and explore the application of RS codes to joint source-channel coding (JSCC). Unlike the conventional OSD algorithms that use Gaussian elimination to obtain the systematic matrix, the proposed quasi-OSD algorithm utilizes the parallel Lagrange interpolation at the symbol level, which achieves a lower complexity and comparable performance compared with the locally constrained OSD (LC-OSD), for high-rate RS codes in the high signal-to-noise ratio (SNR) region. Additionally, we apply RS codes to the JSCC with known source statistics. At the transmitter, a new partition criterion is introduced in the classified enumerative (CE) coding to encode the source information. Then the multiple-rate RS coding transforms the variable-length codeword of the CE coding into a fixed-length transmitted codeword. At the receiver, parallel decoding is performed to recover the source. Simulation results demonstrate that the proposed JSCC scheme outperforms the double polar JSCC scheme by one dB, as expected by Gallager's JSCC bound.

In this paper, we propose a new ordered statistics decoding (OSD) algorithm called representative OSD (ROSD), specifically designed for polar codes. The generator matrices of polar codes are composed of the rows indexed by an information index set in a lower triangular matrix with ones on the diagonal. Therefore, the generator matrices of polar codes have a staircase-like structure that enables us to present the parallel implemen-tation of Gaussian elimination (GE) in ROSD avoiding the serial GE in conventional OSD. Different from the conventional OSD which forms the most reliable basis (MRB) by selecting reliable bits globally, the proposed ROSD forms an extended basis by selecting relatively reliable bits locally at least one from each staircase. Simulation results show that the ROSD has a similar performance to the LC-OSD and conventional OSD for 5G polar codes and Reed-Muller (RM) construction polar codes.

In this paper, we integrate the 5G low-density parity-check (LDPC) coded modulation systems with hybrid shaping, where the centroid-based geometric shaping is implemented to remedy the performance loss of the many-to-one probabilistic shaping. Taking into account the fact that the 5G parity-check matrices have an uneven density in different parts, we elaborately design a simple row-column interleaver for the bit-interleaved coded modulation with iterative decoding (BICM-ID) system to allocate the ambiguous bits caused by the many-to-one mapping to the sparser parity part, resulting in the hybrid shaping for BICM-ID (HS-BICM-ID) system. Numerical results have shown that the HS-BICM-ID can obtain shaping gains of about 0.5 dB and 1.4 dB compared to the constant composition distribution matching (CCDM) shaping and the geometric shaping, respectively, while it can obtain a shaping gain of about 1.7 dB compared to the scheme with uniform input. Our work has also shown that, at low and moderate spectral efficiency, the presented hybrid shaping can achieve a significant shaping gain and effectively remedy the performance loss of dyadic many-to-one probabilistic shaping.

This paper focuses on the design of dynamic quantization (DQ) and coded transmission schemes for federated learning (FL). In the conventional FL system, the updates divergences typically decrease with communication rounds as training goes on. We first study both the impact of the quantization bit-width in the error-free transmission scenario and the impact of bit error rate (BER) in the practical transmission scenario on the performance of FL. Then we propose a DQ scheme based on the fixed B-bit or 1-bit quantization scheme, where each device quantizes its local updates with dynamic bit-width according to the test accuracy of the global model and device-to-server signal-to-noise ratio (SNR). Due to the quantization bit-width is dynamic, the test accuracy (as a kind of extra data) is needed for devices to determine the bit-width, and the devices need to inform the server of the resultant bit-width (as another kind of extra data). To reliably transmit these extra data without consuming extra transmission resource, we utilize the free-ride coding, where the extra data are embedded into the low-density parity-check (LDPC) coded payload data. Numerical results show that in the practical scenario, B-bit (B > 1) quantization scheme shows fast convergence speed and high final accuracy (in high SNR region) while the L-bit quantization scheme exhibits greater robustness (in low SNR region). They also show that the proposed FL by DQ and free-ride coding not only can significantly reduce the communication overhead with a negligible performance gap to the upper bound (error-free scheme) even in low SNR region but also outperforms the fixed quantization coded transmission FL scheme in terms of accuracy and convergence speed.

This paper is concerned with the wireless video surveillance systems, which were widely deployed and now augmented by edge computing. Armed with the edge computing, on-device local intelligence algorithms like machine learning (ML) can be utilized to extract specific semantics such as events classification in terms of risk levels which are vital for downstream tasks, say video retrieval. Different from the emergent semantic communications, not only these extracted semantic features (for further use) but also the raw video (by legal requirement) need to be sent to the surveillance center. This application scenario is also different from those for the conventional edge computing. The main objective of this paper is to propose a cost-effective scheme for such extra semantic data transmission in a free-ride way that has mild impact on the existing communication link and requires neither bandwidth expansion nor extra transmission power. The basic idea is to superimpose in the binary field the extra bits on the coded payload data. Numerical results show that, with the 5G low-density parity-check (LDPC) codes, simultaneously transmitting semantic features along with the payload data delivers more reliable semantic features and has a negligible effect on the quality of the payload data.

In this paper, we propose a new joint source-channel coding (JSCC) for short-packet communications, especially for the uplink from the sensor to the base station. At the transmitter, the sensing information is first encoded by a two-stage description, referred to as classified enumerative (CE) coding, and then encoded by a random multiple-rate code. The two-stage CE coding describes a binary sequence by its type class indicator and its rank in the associated type class, which can approach the entropy for biased sources. The random multiple rate coding transforms the variable-length output of the CE coding into a fixed-length channel input, allocating lower energy to lower-rate component codes. At the receiver, the sensing information can be recovered by a trial-and-error (for type classes) decoding either serially or parallelly. The serial decoding has a low implementation complexity, while the parallel decoding has a low decoding delay. To alleviate the mis-correction probability and stop the decoding earlier, we turn to the cyclic redundancy check (CRC) coding. To predict the performance of the proposed JSCC scheme, we present the weighted random-coding union (RCU) bounds based on the conventional RCU bound. The proposed JSCC scheme is universal in the sense that it does not require knowledge of source statistics. Simulation results show that the performance matches well with the presented bounds, validating our analysis. Simulation results also show that the proposed JSCC scheme can outperform the double polar JSCC scheme (exhibiting a coding gain of up to 0.3 dB) and can approach the JSCC bounds (exhibiting a gap of less than 0.5 dB).

Free-ride coding, as an approach that admits transmission of a few extra bits over a low-density parity-check (LDPC) coded link without bandwidth expansion, is applied in this paper to construct coupled LDPC codes. Firstly, we present a syndrome channel model and derive the lower and upper bounds on its capacity (referred to as accessible capacity), indicating the feasibility of the reliable transmission of extra bits. Secondly, we present the performance evaluation on both the word error rate (WER) and the bit error rate (BER) for the free-ride codes with simple lower and upper bounds. Then we propose three applications of free-ride coding to construct coupled LDPC codes, including implicit globally-coupled LDPC (GC-LDPC) codes, partial product-LDPC codes, and terminated spatially-coupled LDPC (SC-LDPC) codes, all of which have the figure of merits that they share the same code rates with the basic component LDPC codes. Simulation results show that: 1) the proposed GC-LDPC codes can outperform the component LDPC codes, yielding a coding gain of up to 0.8 dB; 2) the proposed product codes with$(3,6)$-regular LDPC component codes of length 1024 can lower the WER from$10^{-2}$down to$10^{-6}$at the SNR around 2 dB; 3) the proposed terminated SC-LDPC codes can perform as well as the conventional terminated SC-LDPC codes but without any rate loss.

In this paper, we propose a new transmission scheme for the scenario where two nodes attempt to exchange messages and the conventional low-density parity-check (LDPC) codes are implemented for error correction. In the proposed scheme, the ACK/NACK feedback information is transmitted along with the payload data by free-ride codes, while the re-transmitted codewords are superimposed (XORed) on the current codewords, both of which cost neither extra bandwidth nor transmission power. Firstly, we present a syndrome channel model and derive its capacity (referred to as accessible capacity) with a lower bound, implying that the reliable transmission of extra bits (feedback information) is possible. Then, the performance of the extra bits is analyzed by the dependency testing (DT) bound for the syndrome channels. Moreover, motivated by the DT bound, we present a low-complexity DT-like decoder for the free-ride codes. For the superposition retransmission, we present a practical implementation, where those unsuccessfully decoded codewords are sparsely interleaved and superimposed onto the current codewords. In addition, the presented transmission scheme is combined with the conventional hybrid automatic repeat request (HARQ) protocol, resulting in a throughput-enhanced conjunction HARQ scheme. Numerical results show that the word error rate (WER) of the LDPC codes can be significantly reduced by using the presented transmission scheme, but without any extra bandwidth or transmission power. They also show that the presented conjunction HARQ schemes can achieve a throughput improvement up to 80% over fading channels in comparison with the original 5G HARQ scheme.

In this paper, we propose a new construction of product codes, where the whole information array is protected row-by-row by a low-density parity-check (LDPC) code while only a portion of the information array is protected column-by-column by an algebraic code. The most distinguished feature of the proposed product code is that, thanks to the free-ride coding technique, the additional column check bits are transmitted implicitly rather than explicitly. The constructed codes are referred to as implicit partial product-LDPC codes, which have the same rates as the row component LDPC codes. The decoding algorithm can be divided into four stages, including decoding of the free-ride codes, first-round decoding of the row codes, decoding of the column codes, and second-round decoding of the row codes by exploiting the messages associated with those successfully decoded columns. To predict the extremely low error rate of the doubly-protected (by both the row code and the column code) information bits, we derive an approximate upper bound. The simulation results show that, with a (3,6)-regular LDPC code of length 1024 as the component code, the proposed product code can lower the word error rate (WER) from 10−2down to 10−6at the SNR around 2 dB. The numerical results also show that the doubly-protected information bits are more reliable, which can have a bit error rate (BER) down to 10−15at SNR around 2.6 dB as implied by the presented approximate upper bound.

In this paper, we propose a data-aided channel estimator, which can improve the performance of the linear minimum-mean-squared-error (LMMSE) by clustering and reinforcement-learning for multiple-input multiple-output (MI-MO) systems. For clustering-based data detection, we develop a system constrained Gaussian mixture model (SCGMM), in which the a posteriori probabilities (APPs) can be calculated by the expectation-maximization (EM) algorithm. The initial centroids of the SCGMM are sensitive to the channel estimation. To obtain robust channel estimation, we design initial pilots that can reduce the estimated error of the LMMSE. To further improve the quality of channel estimation, we propose a data-aided channel estimation algorithm, which exploits the techniques of coding and reinforcement-learning to obtain soft symbol decisions. Numerical results show that the proposed method can approach the bit-error-rate (BER) performance with perfect channel state information (CSI) in the high signal-to-noise (SNR) region.

In this paper, we present a new construction of the globally-coupled LDPC (GC-LDPC) codes, referred to as implicit GC-LDPC codes, where the additional global parity-check bits are transmitted using the free-ride coding. The presented GC-LDPC codes have the same rates as the component LDPC codes, avoiding the rate reduction caused by the global parity checks for the conventional GC-LDPC codes. Moreover, the encoders of the component LDPC codes are reusable in the presented GC-LDPC codes, a distinguished feature as compared with the conventional GC-LDPC codes. The simulation results show that the proposed implicit GC-LDPC codes can improve the performance of the component LDPC codes, yielding extra coding gain of up to 0.7 dB (with (3,6)-regular LDPC codes as the component codes) and 0.5 dB (with IEEE 802.16e LDPC codes as the component codes).

This paper focuses on the real-time status update in a multiaccess vehicular network, in which multiple vehicles transmit not only the payload data (e.g., monitoring data) but also the extra data (e.g., driving intention) to a road side unit for scheduling vehicles to improve traffic efficiency and safety. A free-ride code is implemented, where the extra data is encoded by a random but fixed generator matrix and is delivered by superposition on the low-density parity-check (LDPC) coded payload data, consuming neither extra bandwidth nor extra transmit power. Considering the time slotted ALOHA random access protocol, we derive the closed-form expression for average age of information (AoI), and evaluate the AoI for both payload data and extra data. Numerical simulations demonstrate that free-ride codes can not only transmit extra data without extra transmit power, but also reduce the average AoI of extra data without affecting the average AoI of payload data.

Age of Information (AoI) is a fundamentally important metric to characterize the freshness of information in real-time Internet-of-Things (IoT) monitoring systems. Another important metric is the energy cost for information sensing and transmission. In this article, we investigate the average AoI and energy cost for low-density parity-check coded status update with and without automatic repeat request (ARQ), where the fixed redundancy scheme is employed. The non-ARQ, classical ARQ, truncated ARQ, and truncated hybrid ARQ with chase combining (HARQ-CC) schemes are analyzed and compared. By using the renewal processes theory, the expressions for the average AoI as well as the average energy cost of each considered scheme are derived. Both the lower bound of age and the upper bound of energy are provided. It is shown through simulation results that the average AoI and energy cost are mainly influenced by network parameters in the low signal-to-noise ratio (SNR) region. With short code, the smaller average AoI can be obtained at the cost of more energy consumption. Compared with other schemes, the truncated HARQ-CC achieves the best average AoI and the moderate average energy cost, which is a compromise between the age and energy.

In this paper, we present a new class of spatially coupled low-density parity-check (SC-LDPC) codes, which are constructed by sending codewords of LDPC block code (LDPCBC) in a block Markov superposition transmission (BMST) manner. Different from the conventional SC-LDPC codes, the proposed SC-LDPC codes can have encoder/decoder implemented with the basis of the hardware components of the corresponding LDPC-BCs. The proposed SC-LDPC codes are also a special class of BMST-LDPC codes. Distinguished from other types of BMST codes, BMST-LDPC codes have lower error floors even with an encoding memory of one and hence have lower decoding latency. Also different from the original BMST codes, partial superposition is implemented to alleviate error propagation. To analyze the bit error rate (BER) performance, we present the genie-aided (GA) bounds, which can be obtained by simulation or estimated from the performance of the basic code. Numerical results are presented to validate our analysis and demonstrate the performance advantage of the BMST-LDPC codes over the LDPC-BCs.

Age of information (AoI) is an important metric in real-time status update communication system to assess the freshness of information. Different from previous works, this paper focuses on the average AoI over additive white Gaussian noise (AWGN) channels. A fixed redundancy (FR) coding scheme is considered, which encodes each k-bits update as an n-bits packet by a low-density parity-check (LDPC) code. By using the renewal-reward theory, a closed-form expression of the average AoI under the FR scheme is derived. Simulation results show that the average AoI relies on Eb/N0, especially in the low Eb/N0region. For different Eb/N0, an optimal code length always exists to minimize the average AoI. In addition, the same average AoI can be achieved with different code lengths in the high Eb/N0region. Hence, in the high Eb/N0region, short codes are preferred especially when the transmission delay is taken into account.