This paper presents the analysis and a proof-of-concept design of the low-complexity early termination hybrid automatic repeat request (ET-HARQ) for ultra-reliable low-latency communication (URLLC). In ET-HARQ, unfit packets are flagged for retransmission prior to decoding, a process that significantly diminishes decoding complexity and facilitates swift HARQ reporting. This characteristic makes ET-HARQ well-suited for URLLC applications. We analyze the impact of ET-HARQ on the packet error rate (PER), throughput, and complexity performance in the finite block length regime, taking into consideration cyclic redundancy check (CRC) limitations. Numerical results indicate that ET-HARQ significantly reduces the decoding complexity and improves throughput with little to no loss in the PER. In addition, ET-HARQ demonstrates resilience even with a short CRC, whereas the imperfections of a short CRC significantly impact PER reliability in standard HARQ. To validate our analysis, we also design a practical early termination mechanism involving belief propagation and neural network (BP-NN) to predict the decodability of the received packet. Testing with BCH and CRC-polar codes shows that it can reach up to a 70 % ∼ 80 % prediction accuracy with packet lengths less than 128 bits encoded with high-density linear block codes. Simulation shows that the BP-NN-based ET-HARQ has significantly lower complexity at this accuracy level than the standard HARQ with similar reliability.

In this paper, we propose a novel goal-oriented method for identifying stationary Internet of Things (IoT) devices, with the performance robust to the number of inactive devices. We start by formulating a two-dimensional atomic norm minimization problem that captures the angular group-sparsity of the wireless channel. Building on this, we propose a goal-oriented optimization problem that retains only the angular information required to identify active stationary IoT devices. This problem is then reformulated as an equivalent semi-definite programming (SDP) problem, enabling efficient detection of active users. Unlike traditional methods that rely on orthogonal preambles or pilot assignments for joint active user detection and channel estimation, our approach operates without pilots, enabling blind identification of the line-of-sight angles of active stationary devices. Simulation results demonstrate that the proposed method achieves high detection accuracy and low false alarm rates, offering a scalable and robust solution for enabling massive connectivity in future wireless networks.

We investigate the performance of primitive rateless (PR) codes and introduce an enhanced ordered statistics decoder (OSD) designed for decoding them. We demonstrate that constructing PR codes using linear Boolean functions simplifies decoding to identifying dual bases over$\text{G F}\left(2^{k}\right)$. By leveraging self-dual bases over$\text{G F}\left(2^{k}\right)$, the decoding process for high-rate PR codes is simplified, contributing to a reduced complexity OSD algorithm. Through simulations, we establish that high-rate PR codes can achieve block error rates comparable to their BCH counterparts across various signal-to-noise ratios (SNRs) and code rates. The PR code can be tailored to any rate and block length, and the proposed OSD algorithm makes it well-suited for low-latency applications.

Sparse vector coding (SVC) is a promising coding technique to achieve high transmission reliability and low latency for short packet communications. However, for SVC with conventional combination-based sparse mapping, a small increase of transmitted bits may lead to excessively long sparse vectors, resulting in unsatisfactory transmission performance when coding efficiency is high. In this paper, we propose a generalized index redefinition (IR)-based SVC (GIR-SVC) to significantly enhance the efficiency of SVC. The IR mechanism enables multiple index bit streams to share position resources in SVC, with the help of constellation labels. GIR-SVC constructs the sparse vector using a hybrid IR mechanism that integrates the unlabeled IR and the pairwise-grouping-based labeled IR, which allows efficient mapping and de-mapping of index bits without requiring index tables. Consequently, the proposed GIR-SVC can be efficiently decoded without the index table using sparse recovery algorithms. Theoretical analysis is conducted to validate the block error rate (BLER) performance of GIR-SVC. Simulations show that GIR-SVC can significantly reduce the decoding delay compared to existing approaches, while maintaining the high transmission reliability.

This paper's primary focus is on designing short parallel concatenated coding schemes and list-based decoding algorithms with low complexity. We aim to design a code with a relatively large minimum Hamming distance that can be efficiently decoded through list decoding. To achieve this, we introduce a novel parallel concatenated coding scheme, where the two constituent codes are linked by a full-rank matrix instead of the interleaver, which is commonly used in Turbo codes. The proposed code structures enable us to develop codes with significantly improved minimum Hamming distances. We also demonstrate that by utilizing a convolutional code as one of the constituent codes, we can effectively employ the parallel list Viterbi algorithm to generate a list of candidate codewords. Then, we select the candidate with the lowest Euclidean distance to the overall received signal. This allows us to use a highly complex constituent code, with potentially large minimum Hamming distance, as the second constituent code without increasing the decoding complexity. Simulation results validate the superior performance of these coding schemes compared to existing candidate coding schemes for short packet communications, particularly at very low rates.

We propose real-time remote estimation of a dual-process status update system for mission-critical applications using non-orthogonal multi-access (NOMA) and orthogonal multi-access (OMA) techniques. We consider the finite block length regime so that, with OMA, the status updates of each process are transmitted using time slot sharing. Meanwhile, with NOMA, we use a power domain packet combining to allow simultaneous status updates of each process in each time slot. To compensate for the reliability loss due to short packet lengths and multi-access, we utilize packet retransmission with hybrid automatic repeat request (HARQ). Specifically, we propose OMA-HARQ and NOMA-HARQ transmission control policies, where multi-access resource sharing is jointly designed with HARQ. We propose dynamic and static scheduling policies by optimizing time-sharing or power-sharing ratios between sensors over time. The dynamic policy utilizes higher flexibility to optimize the reliability under restricted age-of-information (AoI), leading to the best estimation mean-squared-error (MSE) performance. We formulate and solve policy optimization problems, where both long-term average MSE and its variance minimization are the targets. We obtain optimal policies to minimize the composite objective function of costs of each process using the Markov decision process (MDP) framework and relative value iteration algorithm. An intensive simulation study shows significant performance improvement over existing approaches.

In this article, we consider a federated learning (FL) problem over wireless channel that takes into account the coding rate and packet transmission errors. Communication channels are modeled as packet erasure channels (PECs), where the probability of erasure is determined by block length, code rate, and signal-to-noise ratio (SNR). In spite of fluctuations in instantaneous loss of FL, we prove that the expectation of loss converges even in the presence of packet erasure. To mitigate the impact of packet erasure on FL performance, we suggest a paradigm in which the central node (CN) makes use of memory. In particular, we propose two schemes in which, in the event of packet erasure, the CN retains either the most recent local updates or the most recent global parameters. We investigate the impact of coding rate, SNR, and the CN memory on the convergence of FL. For both short- and long-packet communications, we examine a realistic scenario of a massive IoT under the assumption of error-prone transmissions. Our simulation results demonstrate that even a single memory unit has a considerable effect on the FL’s efficiency in erroneous communication.

The rateless multiple access (RMA) scheme is a promising distributed multiple access scheme to achieve simultaneous high reliability, low latency and massive connectivity. In this paper, we investigate the maximum likelihood (ML) decoding performance of the RMA scheme in an Additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) modulation. For the first time, this paper derives the ensemble weight distribution of the RMA scheme. We derive an upper bound on the decoding error performance of the RMA scheme under ML decoding in an AWGN channel with BPSK modulation. Using the derived bound as the fitness function, we adopt the continuous genetic algorithm to optimize the parameters of the RMA scheme. Simulation results show the tightness of the derived bound and the superiority of the optimized degree distribution over the conventional degree distributions.

In this paper, we design the joint decoding (JD) of non-orthogonal multiple access (NOMA) systems employing short block length codes. We first proposed a low-complexity soft-output ordered-statistics decoding (LC-SOSD) based on a decoding stopping condition, derived from approximations of the a-posterior probabilities of codeword estimates. Simulation results show that LC-SOSD has the similar mutual information transform property to the original SOSD with a significantly reduced complexity. Then, based on the analysis, an efficient JD receiver which combines the parallel interference cancellation (PIC) and the proposed LC-SOSD is developed for NOMA systems. Two novel techniques, namely decoding switch (DS) and decoding combiner (DC), are introduced to accelerate the convergence speed. Simulation results show that the proposed receiver can achieve a lower bit-error rate (BER) compared to the successive interference cancellation (SIC) decoding over the additive-white-Gaussian-noise (AWGN) and fading channel, with a lower complexity in terms of the number of decoding iterations.

In this paper, we propose a new linear-equation ordered-statistics decoding (LE-OSD). Unlike the OSD, LE-OSD uses high reliable parity bits rather than information bits to recover codeword estimates, which is equivalent to solving a system of linear equations (SLE). Only test error patterns (TEPs) that create feasible SLEs, referred to as the valid TEPs, are used to obtain codeword estimates. We introduce several constraints on the Hamming weight of TEPs to limit the overall decoding complexity. Furthermore, we analyze the block error rate (BLER) and the computational complexity of the proposed approach. It is shown that LE-OSD has a similar performance to OSD in terms of BLER, which can asymptotically approach Maximum-likelihood (ML) performance with proper parameter selections. Simulation results demonstrate that the LE-OSD has a significantly reduced complexity compared to OSD, especially for low-rate codes, that usually require high decoding order in OSD. Nevertheless, the complexity reduction can also be observed for high-rate codes. In addition, we further improve LE-OSD by applying the decoding stopping condition and the TEP discarding condition. As shown by simulations, the improved LE-OSD has a considerably reduced complexity while maintaining the BLER performance, compared to the latest OSD approaches from literature.

In this paper, we characterize the average Hamming weight distribution of subsequences of maximum-length sequences (m-sequences). In particular, we consider all possible m-sequences of dimension$k$and find the average number of subsequences of length$n$that have a Hamming weight$t$. To do so, we first characterize the Hamming weight distribution of the average dual code and use the MacWilliams identity to find the average Hamming weight distribution of subsequences of m-sequences. We further find a lower bound on the minimum Hamming weight of the subsequences and show that there always exists a primitive polynomial to generate an m-sequence to meet this bound. We show via simulations that when a proper primitive polynomial is chosen, subsequences of the m-sequence can form a good rateless code that can meet the normal-approximation benchmark.

In this article, we consider the massive nonorthogonal multiple access (NOMA) with a hybrid automatic repeat request (HARQ) for short packet communications. To reduce the latency, each user can perform one retransmission provided that the previous packet was not decoded successfully. The system performance is evaluated for both coordinated and uncoordinated transmissions. We first develop a Markov model (MM) to analyze the system dynamics and characterize the packet error rate (PER) and throughput of each user in the coordinated scenario. The power levels are then optimized for two scenarios, including the power constrained and reliability constrained scenarios. A simple yet efficient dynamic cell planning is also designed for the uncoordinated scenario. Numerical results show that both coordinated and uncoordinated NOMA-HARQ with a limited number of retransmissions can achieve the desired level of reliability with the guaranteed latency using a proper power control strategy. The results also show that NOMA-HARQ achieves a higher throughput compared to the orthogonal multiple access scheme with HARQ under the same average received power constraint at the base station.

The fifth generation (5G) of mobile standards is expected to provide ultrareliability and low-latency communications (URLLC) for various applications and services, such as online gaming, wireless industrial control, augmented reality, and self driving cars. Meeting the contradictory requirements of URLLC, i.e., ultrareliability and low latency, is considered to be very challenging, especially in bandwidth-limited scenarios. Most communication strategies rely on the hybrid automatic repeat request (HARQ) to improve reliability at the expense of increased packet latency due to the retransmission of failing packets. To guarantee high reliability and very low latency simultaneously, we enhance the HARQ retransmission mechanism to achieve reliability with guaranteed packet-level latency and in-time delivery. The proposed nonorthogonal HARQ (N-HARQ) utilizes nonorthogonal sharing of time slots for conducting retransmission. The reliability and delay analysis of the proposed N-HARQ in the finite block length (FBL) regime shows very high performance gain in packet delivery delay over conventional HARQ in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. We also propose an optimization framework to further enhance the performance of N-HARQ for single and multiple retransmission cases.

In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a primitive polynomial over$\mathbf {GF}(2)$, which can generate a potentially limitless number of coded symbols. We show that codewords of a PR code truncated at any arbitrary length can be represented as subsequences of a maximum-length sequence ($m$-sequence). We characterize the Hamming weight distribution of PR codes and their duals and show that for a properly chosen primitive polynomial, the Hamming weight distribution of the PR code can be well approximated by the truncated binomial distribution. We further find a lower bound on the minimum Hamming weight of PR codes and show that there always exists a PR code that can meet this bound for any desired codeword length. We provide a list of primitive polynomials for message lengths up to 40 and show that the respective PR codes closely meet the Gilbert-Varshamov bound at various rates. Simulation results show that PR codes can achieve similar block error rates as their BCH counterparts at various signal-to-noise ratios (SNRs) and code rates. PR codes are rate-compatible and can generate as many coded symbols as required; thus, demonstrating a truly rateless performance.

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

In this paper, a non-orthogonal hybrid automatic re-peat request (N-HARQ) packet transmission strategy is proposed for ultra-reliable delay sensitive communications. As opposed to conventional HARQ, where retransmission of the failing packet is provided in new time slots, in the proposed scheme, retransmission of the packet is served together with the next arriving packet. Using N-HARQ, we avoid the queuing delay due to retransmission and reduce the packet arrival delay. We consider the short block length regime and analyze the error rate, throughput and delay performance of N-HARQ using the Markov model. Simulation results show that the proposed scheme achieves superior performance in providing packet arrival delay guarantee in comparison to its baseline orthogonal HARQ (O-HARQ).

In this paper, a dynamic-hybrid automatic repeat request (D-HARQ) scheme with guaranteed delay performance is proposed. As opposed to the conventional HARQ that the maximum number of re-transmissions, L, is fixed, in the proposed scheme packets can be re-transmitted more times given that the previous packet was received with less than L re-transmissions. The dynamic of the proposed scheme is analyzed using the Markov model. For delay sensitive applications, the proposed scheme shows a superior performance in terms of packet error rate compared with the conventional HARQ and Fixed retransmission schemes when the channel state information is not available at the transmitter. We further show that D-HARQ achieves a higher throughput compared with the conventional HARQ and fixed re-transmission schemes under the same reliability constraint.

Real-time remote estimation is critical for mission-critical applications including industrial automation, smart grid and tactile Internet. In this paper, we propose a hybrid automatic repeat request (HARQ)-based real-time remote estimation framework for linear time-invariant (LTI) dynamic systems. Considering the estimation quality of such a system, there is a fundamental tradeoff between the reliability and freshness of the sensor's measurement transmission. We formulate a new problem to optimize the sensor's online transmission control policy for static and Markov fading channels, which depends on both the current estimation quality of the remote estimator and the current number of retransmissions of the sensor, so as to minimize the long-term remote estimation mean squared error (MSE). This problem is non-trivial. In particular, it is challenging to derive the condition in terms of the communication channel quality and the LTI system parameters, to ensure a bounded long-term estimation MSE. We derive a sufficient condition of the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system and minimizes the MSE. Also, we prove that the optimal policy has a switching structure, and accordingly derive a low-complexity suboptimal policy. Numerical results show that the proposed optimal policy significantly improves the performance of the remote estimation system compared to the conventional non-HARQ policy.

In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation- discarding technique is proposed along with the stopping rule to significantly reduce the decoding complexity without a significant performance degradation compared to ordered statistics decoding (OSD). In the proposed decoder, the list of test error patterns (TEPs) is divided into several segments according to carefully selected boundaries and every segment is checked separately during the reprocessing stage. Decoding is performed under the constraint of the discarding rule and stopping rule. Simulations results for different codes show that our proposed algorithm can significantly reduce the decoding complexity compared to the existing OSD algorithms in literature.

In this paper, we propose a fast beam tracking strategy for mobile millimeter-wave systems, where the temporal variations of the angle of departure (AoD) are considered and modeled as a discrete Markov process. In contrast to most existing works that rely on the slow-fading assumption, we consider a more practical scenario in which the AoD can vary rapidly due to blockage and other environmental obstructions. In this case, the use of narrow training beams becomes inefficient, and therefore we propose to employ multiple radio-frequency chains generating wide beams to reduce the training time. By optimizing the selected training beams, we aim to minimize the average tracking error probability (ATEP). However, since the exact expression for ATEP is difficult to obtain, we derive its upper bound in a closed form, and aim to minimize this upper bound instead. The associated training beam sequence design problem is transformed into the construction of a bipartite graph that does not contain cycles of length 4, which is implemented with the progressive edge-growth algorithm. Numerical results demonstrate significant gains of the proposed beam tracking strategy over the existing benchmark methods.

In this paper, we derive the distribution of the Hamming distance at 0-reprocessing of the ordered statistics decoding (OSD). With the assumption of decoding a random linear block code, we first find the distribution of the number of errors in any partition of the ordered channel output sequence. Then the distribution of the Hamming distance after 0-reprocessing is derived by a mixture model of two random variables. Based on the proposed statistical approach, we outline the design of high-efficiency OSD algorithm. Simulation and numerical results show that our proposed statistical approaches accurately describe the Hamming distance distributions in OSD decoding process.

Analog fountain code (AFC) is a seamless rate adaptation strategy and was recently shown to closely approach the channel capacity without the channel state information at the transmitter side. The code was mainly designed for large block lengths and therefore the design for short packet communications which is one of the communication scenarios in 5G ultra-reliable and low latency communications (URLLC), is still not clear. We tackle this problem in this work and particularly focus on the design of the precoder which is shown to significantly affects the overall performance of the AFC in the short block length regime. We consider BCH codes as the precoder, and determine the rate of the code in order to maximize the realized rate under a given block error rate constraint. Simulation is performed to investigate the effect of choices for BCH precoder on the overall performance of BCH-AFC in terms of reliability and latency. We show that by selecting the appropriate BCH code as the AFC precoder, AFC performs closely to the normal approximation benchmark. We further proposed a threshold-based decoder to reduce the decoding complexity which is of significant importance in URLLC scenarios.

In this paper, we consider a massive grant-free non-orthogonal multiple access (GF-NOMA) scheme, where devices have strict latency requirements and no retransmission opportunities are available. Each device chooses a pilot sequence from a predetermined set as its signature and transmits its selected pilot and data simultaneously. A collision occurs when two or more devices choose the same pilot sequence. Existing GF-NOMA schemes assume that a collision of at least one pair of users entails a collision for all simultaneously transmitting users, which is sub-optimal in terms of individual outage and system throughput. For that, we propose a novel framework, where collisions are treated as interference to the remaining received signals. With the aid of Poisson point processes and ordered statistics, we derive simplified expressions that can well approximate the outage probability and throughput of the system for both successive joint decoding (SJD) and successive interference cancellation (SIC). Numerical results verify the accuracy of our analytical expressions. For low data rate transmissions, results show that the performance of SIC is close to that of SJD in terms of outage probability, for packet arrival rates up to 10 packets per slot. However, SJD can achieve almost double the throughput of SIC and is, thus, far more superior.

In this paper, we propose a codebook-based beam tracking strategy for mobile millimeter-wave (mmWave) systems, where the temporal variation of the angle of departure (AoD) is considered. A closed-form upper bound of the average tracking error probability (ATEP) is derived and further optimized. We first consider a slow-varying scenario where narrow training beams implemented by single radio-frequency (RF) chain are employed. We show that the ATEP can be reduced by optimizing the power allocation strategy over these training beams, which is formulated and transformed into a second-order cone programming. The fast-varying scenario is further considered where the use of narrow training beams becomes inefficient due to the rapid variations of AoD. In order to reduce the training time, multiple RF chains generating wide beams are employed to track the AoD's variations, and the associated beam pattern design problem is shown to be a 0 - 1 nonlinear optimization problem (NLP). A sequential quadratic programming method is used to solve this binary NLP. To reduce the complexity, a progressive edge-growth algorithm is further introduced by associating the binary NLP with a bipartite graph. Numerical results demonstrate significant gains of the proposed beam tracking strategy over existing benchmarks for both scenarios.

In this paper, we propose a multi-layer grant-free non-orthogonal multiple access scheme for short packet transmissions. In every time slot, users choose a layer randomly and independently of other users. Each layer corresponds to a code book, and users in each layer utilize the same code book and perform power control such that they have the same received power level at the Access Point (AP). Users of the same layer also choose the same pilot sequence that is transmitted with their code word, together with all users from other layers. The AP uses the pilot sequences to detect the layers selected and estimate the number of users in each layer. Using this information, the AP first separates the codewords corresponding to the different layers. Then, users of the same layer are decoded jointly. Based on this, we formulate an optimization problem to find the power levels that maximize the reliability of the system, i.e., the probability that an arbitrary user is decoded successfully, subject to some power and decoding complexity constraints. The problem is found to be non-linear and very complex. We propose some approximations that allow us to use mixed-integer linear programming (MILP). Numerical results show that the multi-layer setup can support a larger load with higher power efficiency for the same reliability and decoding complexity requirements.

In this paper, we consider the design of training beam sequence for sparse millimeter wave (mmWave) multiple-input multiple-output (MIMO) tracking systems. We use Markov random walks to model the temporal variations of the beam steering angle of arrival (AoA) and angle of departure (AoD), respectively. By exploiting the MIMO virtual channel representation, the AoA/AoD tracking problem is equivalent to choosing a set of directional training beams to find the nonzero elements in a two-dimensional virtual channel matrix. Furthermore, in contrast to existing work that used each transmitting-receiving beam pair once only, we consider a more general case such that each beam pair might be adopted more than once in the tracking procedure. As the number of repetitions of each transmitting-receiving beam pair can only be integer, the training beam sequence design problem is then formulated as an integer nonlinear programming (INLP) problem. To resolve the formulated INLP problem, we derive a tractable lower bound of the successful tracking probability and then decompose it into a set of convex INLP subproblems, which are solved by implementing an iterative branch-and-bound (BB) method. Numerical results show that our proposed iterative BB algorithm significantly outperforms the benchmark schemes and achieves near-optimal tracking performance.

Many uplink grant-free non-orthogonal multiple access (NOMA) schemes have been recently proposed to solve the massive access problem of M2M communications. However, little has been done on characterizing the performance bounds for such systems. In this paper, we take a step forward in this direction. We consider an uncoordinated NOMA scheme where devices have strict latencies and no retransmission opportunities are available. Devices choose pilot sequences from a predetermined set uniformly at random. Then, each device encodes its data using the pilot as the signature and transmits its selected pilot and data simultaneously with the rest of the devices. A collision occurs when two or more devices choose the same pilot sequence. Collisions are regarded as interference to the remaining set of transmitting devices. We first show that this interference can be well-approximated by a PPP. Then, we derive the average system throughput under joint decoding and massive access for a Rayleigh fading and path loss channel model. Our numerical results verify the accuracy of our derived analytical expressions. Finally, we investigate the impact of finite block lengths on the system throughput, i.e., when the decoding error probability is strictly non-zero. We show that we can support more than 10 packets per slot when the pilot sequences are large enough.

This study considers the optimisation of multi‐edge type low‐density parity‐check (MET‐LDPC) codes to maximise the decoding threshold. The authors propose an algorithm to jointly optimise the node degree distribution and the multi‐edge structure of MET‐LDPC codes for given values of the maximum number of edge‐types and maximum node degrees. This joint optimisation is particularly important for MET‐LDPC codes as it is not clear a priori which structures will be good. Using several examples, they demonstrate that the MET‐LDPC codes designed by the proposed joint optimisation algorithm exhibit improved decoding thresholds compared with previously reported MET‐LDPC codes.

Machine-to-machine (M2M) constitutes the communication paradigm at the basis of Internet of Things vision. M2M solutions allow billions of multi-role devices to communicate with each other or with the underlying data transport infrastructure without, or with minimal, human intervention. Current solutions for wireless transmissions originally designed for human-based applications thus require a substantial shift to cope with the capacity issues in managing a huge amount of M2M devices. In this paper, we consider the multiple access techniques as promising solutions to support a large number of devices in cellular systems with limited radio resources. We focus on non-orthogonal multiple access (NOMA) where, with the aim to increase the channel efficiency, the devices share the same radio resources for their data transmission. This has been shown to provide optimal throughput from an information theoretic point of view. We consider a realistic system model and characterize the system performance in terms of throughput and energy efficiency in an NOMA scenario with a random packet arrival model, where we also derive the stability condition for the system to guarantee the performance.

We propose a novel random access (RA) scheme with the quality of service (QoS) guarantees for machine-to-machine (M2M) communications. We consider a slotted uncoordinated data transmission period during which machine type communication (MTC) devices transmit over the same radio channel. Based on the latency requirements, MTC devices are divided into groups of different sizes, and the transmission frame is divided into sub-frames of different lengths. In each sub-frame, each group is assigned an access probability based on which an MTC device decides to transmit replicas of its packet or remain silent. The base station employs successive interference cancellation to recover all the superposed packets. We derive the closed-form expressions for the average probability of device resolution for each group, and we use these expressions to design the access probabilities. The accuracy of the expressions is validated through Monte Carlo simulations. We show that the designed access probabilities can guarantee the QoS requirements with high reliability and high energy efficiency. Finally, we show that RA can outperform standard coordinated access schemes as well as some of the recently proposed M2M access schemes for cellular networks.

The focus of this paper is on the analysis and design of Raptor codes using a multi-edge framework. In this regard, we first represent Raptor codes as multi-edge type (MET) low-density parity-check codes. This MET representation gives a general framework to analyze and design Raptor codes over a binary input additive white Gaussian noise channel using MET density evolution (MET-DE). We then consider a joint decoding scheme based on the belief propagation (BP) decoding for Raptor codes in the multi-edge framework, and analyze the convergence behavior of the BP decoder using MET-DE. In joint decoding of Raptor codes, the component codes corresponding to the inner code and the precode are decoded in parallel and provide information to each other. We also derive an exact expression for the stability of Raptor codes with joint decoding. We then propose an efficient Raptor code design method using the multi-edge framework, where we simultaneously optimize the inner code and the precode. Through density evolution analysis we show that the designed Raptor codes using the multi-edge framework outperform the existing Raptor codes in literature in terms of realized rates.

Machine-to-machine (M2M) wireless systems aim to provide ubiquitous connectivity between machine-type communication (MTC) devices without any human intervention. Given the exponential growth of MTC traffic, it is of utmost importance to ensure that future wireless standards are capable of handling this traffic. In this paper, we focus on the design of a very efficient massive access strategy for highly dense cellular networks with M2M communications. Several MTC devices are allowed to simultaneously transmit in the same resource block by incorporating Raptor codes and a simple modulation scheme. This significantly reduces the access delay and improves the achievable system throughput. A simple yet efficient random access strategy is proposed to not only detect the selected preambles, but also estimate the number of devices which have chosen them. No device identification is needed in the random access phase which significantly reduces the signaling overhead. The proposed scheme is analyzed and the maximum number of MTC devices that can be supported in a resource block is characterized as a function of the message length, number of available resources, and the number of preambles. Simulation results show that the proposed scheme can effectively support a massive number of MTC devices for a limited number of available resources, when the message size is small.

In this paper, we analyze Luby Transform (LT) codes with unequal recovery time (URT-LT) and intermediate feedback. Different sets of information symbols within a message block are allocated different priorities, where the higher prioritized sets are to be recovered in a shorter time. We divide the encoding process into stages where in each stage different sets are allocated different selection probabilities. A stage ends when one of the sets' recovery times expires. We incorporate an intermediate feedback that notifies the transmitter of the recovered information symbols at the end of each stage. These recovered symbols are then excluded from future encoding. We use the AND-OR tree analysis to find the optimal selection probabilities that guarantee the sets are recovered within the required time, with a relatively small error probability. We compare the scheme to the case where the sets are encoded and transmitted separately.

The focus of this work is on the design of Raptor codes for continuous variable Quantum key distribution (CV-QKD) systems. We design a highly efficient Raptor code for very low signal to noise ratios (SNRs), which enables CV-QKD systems to operate over long distances with a significantly higher secret key rate compared to conventional fixed rate codes. The degree distribution design of Raptor codes in the low SNR regime is formulated as a linear program, where a set of optimized degree distributions are also obtained through linear programming. Simulation results show that the designed code achieves efficiencies higher than 94% for SNRs as low as −20 dB and −30 dB. We further propose a new error reconciliation protocol for CV-QKD systems by using Raptor codes and show that it can achieve higher secret key rates over long distances compared to existing protocols.

In this paper, we investigate the impact of feedback in LT codes to guarantee unequal recovery time (URT) for different message segments. We analyze the URT-LT codes using the AND-OR tree for two scenarios: complete and partial feedback. We derive the necessary conditions for these two feedback schemes to achieve the required recovery time. We validate the analysis by simulation and highlight the cases where feedback is advantageous.

We propose a capacity approaching coding strategy for additive white Gaussian noise (AWGN) channels by using multi-layer Raptor codes and superposition modulation. Each AWGN channel is divided into several binary-input AWGN (BI-AWGN) channels at a very low signal to noise ratio (SNR), where a capacity approaching Raptor code can be used to encode the message over each layer. A single capacity approaching degree distribution is then used for the Raptor codes over all the layers. A well-known multi-stage decoder is used for successive interference cancellation and decoding the multi-layer Raptor code, where each decoding stage is modeled by a BI-AWGN channel of a fixed SNR. This allows the development of a capacity approaching code for an AWGN channel at every SNR by using a single Raptor code with a fixed degree distribution as the component code.

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.

In this paper, we revisit the design of Raptor codes for binary input additive white Gaussian noise channels, where we are interested in very low signal to noise ratios (SNRs). A linear programming degree distribution optimization problem is defined for Raptor codes in the low SNR regime through several approximations. We also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum output node degree in the low SNR regime, which enables us to calculate the exact value of the fractions of output nodes of small degrees. A more practical degree distribution design is also proposed for Raptor codes in the low SNR regime, where we include the rate efficiency and the decoding complexity in the optimization problem, and an upper bound on the maximum rate efficiency is derived for given design parameters. Simulation results show that the Raptor code with the designed degree distributions can approach rate efficiencies larger than 0.95 in the low SNR regime.

We revisit random multiple access (RMAC) for wireless systems with successive interference cancellation (SIC) employed at the access point (AP). We consider an asymptotically large number of users that transmit over a large number of orthogonal sub-channels. In each transmission block, each user chooses a degree d, where d is a random variable that follows a predefined degree distribution Ω(x). Then, users transmit in d sub-channels chosen uniformly at random. Specifically, we consider signal to interference and noise ratio (SINR) based RMAC where it is assumed that a user's information can be recovered successfully at a given iteration of the SIC process when its updated SINR is above a predetermined threshold. In this paper, we develop a generalized analytical framework based on the codes-on-graph representation to track the evolution of error probabilities in each iteration of the SIC process. We compare our approach to the conventional RMAC employing SIC which assumes that only clean, interference-free transmissions can be recovered successfully. This clean packet model relies on having time slots with a single user's transmission at each iteration of the SIC process. It was shown to be analogous to the iterative recovery process of codes-on-graph for the binary erasure channel (BEC), thus, allowing the direct application of the AND-OR tree analysis. We show that the clean packet model is a special case of our more generalized tree-based analytical framework. Our numerical results show that our model can support more users under the same power requirements.

In this paper, we study a full-duplex wireless-powered communication network (FD-WPCN), which consists of one full-duplex (FD) hybrid access-point (H-AP) and one FD user. The H-AP and user are both equipped with two antennas, one for downlink wireless energy transfer (WET) from the H-AP to user and the other for uplink wireless information transfer (WIT) from the user to H-AP, where WET and WIT are performed simultaneously through the same frequency band. We consider the scenario that the role of each antenna (i.e., transmission or reception) is not predefined and propose an antenna pair selection (APS) scheme to improve the performance by optimally configuring the transmit and receive antennas at each node. The closed-form expressions for outage probability and probability density function (PDF) of the received signal-to-noise ratio (SNR) at the H-AP are derived. Based on the PDF, we then calculate the closed-form expressions of ergodic capacity, SNR moments and symbol error rate (SER). Finally, we verify the analytical results through Monte Carlo simulations.

Future machine-to-machine (M2M) communications need to support a massive number of devices communicating with each other with little or no human intervention. Random access techniques were originally proposed to enable M2M multiple access, but suffer from severe congestion and access delay in an M2M system with a large number of devices. In this paper, we propose a novel multiple access scheme for M2M communications based on the capacity-approaching analog fountain code to efficiently minimize the access delay and satisfy the delay requirement for each device. This is achieved by allowing M2M devices to transmit at the same time on the same channel in an optimal probabilistic manner based on their individual delay requirements. Simulation results show that the proposed scheme achieves a near optimal rate performance and at the same time guarantees the delay requirements of the devices. We further propose a simple random access strategy and characterize the required overhead. Simulation results show that the proposed approach significantly outperforms the existing random access schemes currently used in long term evolution advanced (LTE-A) standard in terms of the access delay.

In this paper, we focus on the sparse event detection (SED) problem in wireless sensor networks (WSNs), where a set of sensor nodes are placed in the field of interest to capture sparse active event sources. The SED problem in WSNs is represented from a coding theory perspective by using capacity approaching analog fountain codes (AFCs) and further solved with a standard belief propagation (BP) decoding algorithm. We show that the sensing process in WSNs produces an equivalent analog fountain code at the sink node, with code parameters determined based on the sensing capability of sensor nodes and channel gains. We analyze the probability of false detection of the proposed approach and show it to be negligible. Simulation results show that the proposed approach, namely sparse event detection with AFC (SED-AFC), achieves a significantly higher probability of correct detection (PCD) compared to existing literature at various SNR values, with a negligible probability of false detection (PFD). Moreover, we show that the minimum sampling ratio in high SNRs for the proposed scheme reaches the lower bound which is mainly characterized by the sensing coverage of the sensors and field dimensions.

In this paper, we propose a novel rateless code with unequal error protection (UEP) property based on recently proposed analog fountain codes (AFCs). AFCs have been originally designed and optimized to approach the capacity of a Gaussian channel in a wide range of signal to noise ratios (SNRs). In this paper, we are particularly interested in the UEP property of AFC codes, providing different levels of error protection for various sets of information symbols. In the proposed AFC code with UEP property (AFC-UEP), the whole block of information symbols is partitioned into several parts, where each part requires a certain level of error protection. Each part is then assigned with a selection probability and a code degree, which are optimized based on the error probability analysis of the AFC code to satisfy the required error protection levels of all information parts. Simulation results show that the proposed scheme can effectively provide an unequal error protection for different sets of information symbols. Moreover, various error protection requirements can be simply achieved by optimizing the code degree and the selection probability of each part; thus, achieving the desired level of error protection for each part.

In this paper, we propose a novel rateless multiple access scheme based on the recently proposed capacity-approaching analog fountain code (AFC). We show that the multiple access process will create an equivalent analog fountain code, referred to as the multiple access analog fountain code (MA-AFC), at the destination. Thus, the standard belief propagation (BP) decoder can be effectively used to jointly decode all the users. We further analyze the asymptotic performance of the BP decoder by using a density evolution approach and show that the average log-likelihood ratio (LLR) of each user's information symbol is proportional to its transmit signal to noise ratio (SNR), when all the users utilize the same AFC code. Simulation results show that the proposed scheme can approach the sum-rate capacity of the Gaussian multiple access channel in a wide range of signal to noise ratios.

In this paper, a novel cooperative transmission scheme via network coding has been proposed for Wireless Body Area Networks (WBANs) to enhance reliability and throughput. In the proposed scheme, namely Random XOR Network Coding (RXNC), each relay demodulates the received signal from each sensor node and then selects d different coded symbols amongst them and XORs them to generate a network coded symbol. We have found the optimum value of d through an analytical approach by minimizing the probability that an XOR network coded symbol is incorrectly generated. Simulation results show that the proposed RXNC scheme outperforms the no-cooperation and conventional bitwise network coding schemes in all channel signal to noise ratios (SNRs) from 0 dB to 18 dB.

In this paper, we propose a practical network coding approach for wireless body are networks (WBANs) using decode-and-forward relays. In this scheme, namely decode and forward-network coding (DF-NC), each relay linearly combines different messages from different sources to generate one message, and then transmits that message to the destination. Each relay node in DF-NC requires only one transmission time slot to forward its message. Thus, in this approach, energy usage at each relay is minimized compared to existing cooperative schemes without network coding, which require Nstime slots per relay for relay transmissions; where Nsis the number of source nodes. Simulation results show that the proposed DF-NC scheme can achieve near optimal outage probability while minimizing the number of transmissions per node, maximizing the energy efficiency of WBANs, and minimizing the delay.

In this paper, we propose an analog rateless code to achieve high spectral-efficient adaptive transmission and increase the system throughput in AWGN channels. In the proposed analog rateless coding scheme, each coded symbol is generated from a number of information bits that are selected uniformly at random and multiplied by some real values obtained randomly from a predetermined probability distribution function, called weight distribution. The analog rateless codes can be described by a weighted bipartite graph. However, unlike the conventional bipartite graph, where the combining coefficients are the binary symbols, the combining coefficients in the weighted bipartite graph of analog rateless codes are real numbers selected from a finite set. As a result, the conventional sum-product decoder cannot be directly applied. We have developed a simple decoding algorithm, called 2-Sum verification decoder, for the proposed analog rateless codes. Its performance is evaluated by using Sum-Or tree analysis. The code degree and weight distributions are optimized to maximize the error recovery probability of the 2-Sum verification decoder. Simulation results shows the proposed code can approach the channel capacity within one bit across a wide range of SNRs.

In this paper, we propose a new rateless coded cooperation scheme for a general multi-user cooperative wireless system. We develop cooperation methods based on Raptor codes with the assumption that the channels face erasure with specific erasure probabilities and transmitters have no channel state information. A fully coded cooperation (FCC) and a partially coded cooperation (PCC) strategy are developed to maximize the average system throughput. Both PCC and FCC schemes have been analyzed through AND-OR tree analysis and a linear programming optimization problem is then formulated to find the optimum degree distribution for each scheme. Simulation results show that optimized degree distributions can bring considerable throughput gains compared to existing degree distributions which are designed for point-to-point binary erasure channels. It is also shown that the PCC scheme outperforms the FCC scheme in terms of average system throughput.

In this paper, we propose a physical-layer rateless code for wireless channels. A novel rateless encoding scheme is developed to overcome the high error floor problem caused by the low-density generator matrix (LDGM)-like encoding scheme in conventional rateless codes. This is achieved by providing each symbol with approximately equal protection in the encoding process. An extrinsic information transfer (EXIT) chart based optimization approach is proposed to obtain a robust check node degree distribution, which can achieve near-capacity performances for a wide range of signal to noise ratios (SNR). Simulation results show that, under the same channel conditions and transmission overheads, the bit-error-rate (BER) performance of the proposed scheme considerably outperforms the existing rateless codes in additive white Gaussian noise (AWGN) channels, particularly at low BER regions.

This paper presents a new rateless coded cooperation (CC) scheme for the two-user cooperative multiple access channel (CMAC), where two users cooperatively communicate with a common destination. We consider two rateless CC strategies, a fully coded cooperation (FCC) scheme used in the conventional rateless cooperative schemes and a new partially coded cooperation (PCC) scheme. In FCC, each user starts coded cooperation process only after the whole block of the other user's information symbols are fully recovered. In contrast, in PCC, each user starts cooperation as soon as it receives a fraction of new message sent from the other user. The degree distribution for the PCC scheme is designed to maximize the overall system throughput. Simulation results show that the proposed PCC scheme achieves a considerably higher throughput than the conventional scheme in various scenarios.

In this paper, we propose a distributed rateless coding (DRC) scheme for a two-user cooperative system. In DRC, the overall transmission is divided into two phases, a broadcast phase and a cooperation phase. In the broadcast phase, each user keeps transmitting its rateless coded symbols to the other user and the destination until its message has been successfully decoded by the destination or the other user. In the cooperation phase, each user encodes both users' messages by using a rateless code and transmits them to the destination. A linear programming optimization problem is then formulated to find the optimal degree distribution for the proposed distributed rateless code. The performance of the proposed code is analyzed and validated by simulations.

The focus of the paper is on cross-layer transmission based on rateless coding for relay networks. In the proposed method, rateless coding is used at the packet level and a separate physical layer coding is used at the physical layer. As rateless codes are originally designed and optimized for erasure channels, using these codes at the physical layer can lead to significant performance degradation. The proposed scheme has the advantage of a cross-layer design which uses a rateless code at the packet level modeled by an erasure channel. Based on the analysis and simulation results provided in this paper, the cross-layer scheme results in earlier successful decoding at the destination.

In this paper, we introduce a new cost function for SIR-Based uplink power control algorithms that takes into account transmission power level as well as target Signal-to-Interference Ratio (SIR) deviation. Existence of Nash equilibrium point, its uniqueness and the algorithm convergence are proved in the framework of so-called standard power control schemes. As shown through simulations, the proposed method results in significant transmit power reduction while achieving almost the same average SIR level. In addition, it is shown that the new scheme results in improved overall network fairness in comparison with another algorithm.