The industrial Internet of things (IIoT) is revolutionizing industrial processes by facilitating massive machinetype communications among countless interconnected devices. To efficiently handle the resulting large-scale and sporadic traffic, grant-free random access protocols-especially coded random access (CRA)-have emerged as scalable and reliable solutions. At the same time, advancements in wireless hardware, including extremely large-scale MIMO arrays and high-frequency communication (e.g., mmWave, Terahertz), are pushing network operations into the near-field propagation regime, allowing for dense connectivity and enhanced spatial multiplexing. This paper proposes an innovative approach that combines near-field spatial multiplexing with the interference mitigation capabilities of CRA, utilizing an extremely large aperture array at the access point. This integration improves reliability and reduces access latency, offering a robust framework for IIoT connectivity in next-generation 6 G networks.

Energy efficiency maximization for given traffic and target packet loss probability is a main design goal for grant-free protocols supporting massive connectivity. This paper investigates the performance limits of a class of coded slotted ALOHA (CSA)based protocols over the Gaussian channel. Assuming a multipacket reception decoder with perfect estimation of the number of packets in a slot and ideal error detection, we present a novel asymptotic analytical framework that allows deriving the minimum packet loss probability limits, the conditions for an$E_{b} / N_{0}$limits. Numerical results show that CSA schemes have energy efficiency limits within few dB from the random coding bounds, with 1-2 dB improvement to irregular repetition slotted ALOHA (IRSA) ones.

Ultra-reliable low-latency communications (URLLC) demand decoding algorithms that simultaneously offer high reliability and low complexity under stringent latency constraints. While iterative decoding schemes for LDPC and Polar codes offer a good compromise between performance and complexity, they fall short in approaching the theoretical performance limits in the typical URLLC short block length regime. Conversely, quasi-ML decoding schemes for algebraic codes, like Chase-II decoding, exhibit a smaller gap to optimum decoding but are computationally prohibitive for practical deployment in URLLC systems. To bridge this gap, we propose an enhanced Chase-II decoding algorithm that leverages a neural network (NN) to predict promising perturbation patterns, drastically reducing the number of required decoding trials. The proposed approach combines the reliability of quasi-ML decoding with the efficiency of NN inference, making it well-suited for time-sensitive and resource-constrained applications.

An extension of the frame-asynchronous coded slotted ALOHA (FA-CSA) protocol for grant-free access, based on packet fragmentation and fragment erasure coding, is investigated. In the analyzed scheme, active users employ maximum distance separable erasure codes at fragment level and transmit encoded fragments on orthogonal subcarriers. Fragment decoding errors at physical layer, even in absence of collisions, are included in the analysis. Asymptotic load threshold values approaching the upper limit are obtained by density evolution over a large efficiency range. At finite frame length, FA-CSA configurations with a very good reliability versus scalability tradeoff are obtained, together with accurate error floor estimation.

We investigate the packet collision probability among uncoordinated devices, in the uplink of Direct-to-Satellite Internet of Things (DtS-IoT). Both the satellite spot shape and its motion along its orbital path are considered in the analysis. We analyze the probability of no uplink collision under two DtS-IoT settings: 1) unconfirmed ALOHA over a single channel, e.g., long-range wide-area network (LoRaWAN) class A with long-range chirp spread spectrum (LoRa-CSS) modulation and 2) unconfirmed ALOHA with frequency-hopping compliant with LoRaWAN class A with long-range frequency-hopping spread spectrum (LR-FHSS). A closed-form solution is derived for the former, while an upper bound is found for the latter. The analytical results are validated by comparison with the outcomes of extensive simulations, showing that the obtained closed-form expressions accurately predict the probability of no collision. Moreover, the upper bound for the frequency-hopping case is proven to be tighter when there are less than 35 hopping channels. Finally, we provide a concise performance comparison between LoRa-CSS and LR-FHSS in DtS-IoT, showing that LR-FHSS significantly increases the number of devices that can simultaneously transmit during a satellite pass, thereby enhancing uplink capacity.

Massive machine-type communications are transforming the Industrial Internet of Things (IIoT) by enabling seamless connectivity among a vast number of devices. To efficiently manage the resulting sporadic and large-scale traffic, grant-free random-access protocols, particularly coded random access (CRA), have emerged as scalable and reliable solutions. Meanwhile, advancements in extremely large-scale MIMO and high-frequency communications (e.g., mmWave, THz) are pushing networks into the near-field regime, enhancing spatial multiplexing and connectivity. In this paper, we propose a novel coded spatial random access (CSRA) scheme that leverages an extremely large aperture array (ELAA) at the access point (AP) to exploit near-field spatial multiplexing for grant-free massive access in IIoT systems. Unlike conventional approaches, CSRA eliminates the need for complex channel estimation by integrating CRA with successive interference cancellation and the spatial multiplexing capabilities of the near-field regime. This enables improved reliability and scalability, making CSRA a promising solution for next-generation wireless networks.

We introduce a massive multiple access scheme designed to meet different trade-offs between reliability, scalability, and latency. To maximize the number of successfully decoded users, the scheme builds upon coded random access, incorporating both grant-free and grant-based procedures, along with a massive acknowledgment phase conducted at the base station. The main design premise is the establishment of two distinct latency deadlines: the first one guaranteeing high reliability (e.g., between 99% and 99.99%), and the second one enforcing ultra-high reliability, even above 99.9999%. This dual-latency approach, supplemented with massive MIMO, enables the system to support a higher number of active users per frame while meeting stringent reliability requirements. Throughout the paper, we present a theoretical analysis and derive performance bounds to guide and support effective system design. The approach opens the door for the development of critical services that bridge the gap between massive machine-type communication (mMTC) and ultra-reliable and low-latency communication (URLLC), providing a more flexible and efficient framework for next-generation systems.

In this paper, feedback-aided coded random access (CRA) protocols for grant-free massive access, with and without exploitation of the power domain, are investigated. The developed schemes can support non-instantaneous acknowledgment messages, along with their time resources, with very little penalty in terms of the achieved tradeoff between scalability, reliability, and latency. The new CRA-type protocols rely on waiting slots introduced between consecutive transmissions from the same device to pipeline the feedback reception without degrading the throughput. Their performance can be further enhanced by exploitation of the power domain, in particular by introduction of a deterministic power selection scheme designed for transmission of different packet replicas over a short time window. The system performance is investigated assuming a realistic wireless channel model, a massive MIMO base station, and a realistic processing, via simulation and analysis. The achieved results show that the realistic feedback-aided protocols with deterministic power selection can support 12.8 grant-free users per slot guaranteeing a packet loss rate of 10−4while a massive MIMO base station equipped with 128 antennas is employed

Orthogonal time frequency space (OTFS) modulation is gaining recognition for its potential to facilitate integrated sensing and communication (ISAC) within future mobile networks. However, computing the sensing channel matrix in orthogonal time frequency space (OTFS), a crucial step for accurate target parameter estimation, presents significant challenges due to its high dimensionality. Therefore, this study introduces an innovative method to reduce such computational complexity by combining two ingredients. First, through algebraic operations, we decompose the sensing channel matrix into four lower-dimensional matrices whose elements can be associated with a Dirichlet kernel. Second, we formulate an analytical criterion, independent of system parameters, that leverages the properties of the Dirichlet kernel and identifies the most informative elements of these matrices that deserve computation. To demonstrate the effectiveness of our approach, we assess the computational complexity of this distilled channel matrix in terms of the number of elementary operations required. Numerical results indicate that our technique markedly decreases receiver complexity by up to three orders of magnitude without compromising sensing performance.

Cell-free massive MIMO (CF-mMIMO) networks leverage seamless cooperation among numerous access points to serve a large number of users over the same time/frequency resources. This paper presents a novel multi-task learning approach aimed at mitigating inter-user interference and enhancing spectral efficiency, particularly in scenarios where the number of users far exceeds the available orthogonal pilots. Our proposed method entails the design and unsupervised training of a deep neural network (DNN), employing a custom loss function specifically tailored to perform joint power control and pilot assignment. Numerical results demonstrate that our algorithm outperforms existing power control and pilot assignment strategies in terms of achievable network throughput, minimum user rate, and per-user energy consumption.

This work proposes a maximum likelihood-based parameter estimation framework for a multistatic millimeter wave integrated sensing and communication system using energy-efficient hybrid digital-analog arrays. Due to the typically large arrays used in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field (NF) regime. To address this, we propose a two-step estimation process. Initially, we consider far-field (FF) propagation assumptions, followed by refined estimation based on NF assumptions, enhancing accuracy when the target is within the NF of the arrays. In particular, when operating in the NF of the transmitter (Tx), we select beamfocusing array weights designed to achieve constant gain over an extended spatial region. Subsequently, we re-estimate target parameters at the receivers (Rxs). The effectiveness of the proposed framework is evaluated over various scenarios through numerical simulations. In particular, the impact of customdesigned flat-gain beamfocusing codewords in improving both communication and sensing performance when the target is in the NF of the Tx is demonstrated. Additionally, the benefit of considering a correct NF channel model when the target is located near an Rx is shown.

This paper considers a direct-to-satellite Internet of Things system where nodes on ground contend to deliver data packets to a low Earth orbit satellite, during its pass. In this framework, the paper focuses on the collision probability between the packets transmitted by the uncoordinated contending devices. An exact and closed-form expression for this probability is derived that considers both the satellite velocity and the different contention time widows the devices may have, depending on their positions on ground. The analytical expression, valid for a wide range of different shapes of the satellite spot, is validated by comparison with numerical simulations. Usage of the developed expression to upper bound the packet loss probability over realistic channels is discussed.

This paper elaborates on the idea of building grant-free channel access schemes from non-orthogonal multiple access ones, and proposes an explicit such scheme based on sparse code multiple access (SCMA). In the designed protocol, SCMA codebooks and pilots are chosen by users in a fully uncoordinated fashion, with multiple pilots associated with the same codebook to aid codebook detection. A modified two-stage SCMA decoder is proposed, where a low-complexity collision resolution algorithm, working on a super-constellation, and an SCMA message passing detector are iteratively applied. Numerical results, integrated by analysis in the high signal-to-noise ratio regime, highlight a potential for the proposed scheme in the context of massive uncoordinated machine-type uplink.

In this paper, grant-free uplink communication from a large number of machine-type devices in CF-mMIMO networks is explored. A novel approach that leverages coded random access, on the device side, with combining of signals received at properly selected AP and cooperative successive interference cancellation, on the network side, is presented. Initially, an analytical framework based on stochastic geometry is developed to investigate performance of AP cooperation through signal combining under diverse AP cluster compositions. The potential gain from AP signal combining is then assessed by evaluating a genie-aided scheme, guiding the network in cluster selection for each active device. Subsequently, two practical AP selection algorithms that operate in grant-free conditions (i.e., do not require prior information regarding the active users) are proposed. Numerical results show how AP cooperation through signal combining and distributed interference cancellation can bring tangible benefits even without prior information about active users, under different SNR regimes, closing in some cases the gap to the genie-aided approach. Additionally, the results prove that AP cooperation can be used to reduce the devices’ energy consumption and the number of AP that have to be deployed by the service providers to achieve specific performance levels.

A framework for the analysis of synchronous grant-free massive multiple access schemes based on the irregular repetition slotted ALOHA (IRSA) protocol and operating over the Gaussian multiple access channel is presented. IRSA-based schemes are considered here as an instance of the class of unsourced slotted random access codes, operating over a frame partitioned in time slots, and are obtained by concatenation of a medium access control layer code over the entire frame and a physical layer code over each slot. In this framework, an asymptotic analysis is carried out in presence of both collisions and slot decoding errors due to channel noise, which allows the derivation of density-evolution equations, asymptotic limits for minimum packet loss probability and average load threshold, and a converse bound for threshold values. This analysis is exploited as a tool for the evaluation of performance limits in terms of minimum signal-to-noise ratio required to achieve a given packet loss probability, and also provides convergence boundary limits that hold for any IRSA scheme with given physical layer coding scheme. The tradeoff between energy efficiency and spectrum efficiency is numerically evaluated comparing some known coding options, including those achieving random coding bounds at slot level. It is shown that IRSA-based schemes have a convergence boundary limit within few dB from the random coding bound when the number of active transmitters is sufficiently large.

This work proposes a maximum likelihood (ML)- based parameter estimation framework for a millimeter wave (mmWave) integrated sensing and communication (ISAC) system in a multistatic configuration using energy-efficient hybrid digital-analog (HDA) arrays. Due to the typically large arrays deployed in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field (NF) regime. The proposed parameter estimation in this work consists of a two-stage estimation process, where the first stage is based on far-field (FF) assumptions, and is used to obtain a first estimate of the target parameters. In cases where the target is determined to be in the NF of the arrays, a second estimation based on NF assumptions is carried out to obtain more accurate estimates. In particular, when operating in the near-filed of the transmitter (Tx), we select beamfocusing array weights designed to achieve a constant gain over an extended spatial region and re-estimate the target parameters at the receivers (Rxs). We evaluate the effectiveness of the proposed framework in numerous scenarios through numerical simulations and demonstrate the impact of the custom-designed flat-gain beamfocusing codewords in increasing the communication performance of the system.

In this paper, we consider a joint sensing and communication (JSC) network in which multiple base stations (BSs) cooperate through a fusion center (FC) to detect and track the objects present in a supervised area. Every BS acts as a monostatic sensor capable of scanning the environment and sensing the targets while simultaneously communicating with user equipments (UEs). In particular, each BS generates range-angle maps, which are shared with a FC for data fusion and tracking via particle filter (PF) and multi-hypothesis tracker (MHT) algorithms. The performance of the proposed solutions is evaluated by varying the fraction of power and time devoted to sensing to manage the network overhead and offer a sensing/communication trade-off. Numerical results show that the proposed algorithms can successfully track multiple targets with different sizes and behavior in a vehicular scenario, ensuring, e.g., a root mean squared error (RMSE) of the estimated position of a pedestrian less than 50 cm when considering three BSs.

In this paper, new coded random access schemes for massive IoT, capable of accommodating a non-instantaneous feedback from the receiver, are developed. The proposed schemes are based on the introduction of waiting slots between any two consecutive replicas transmitted by the same active device. The waiting window can be exploited by the device to receive acknowledgment messages that, otherwise, would consume uplink resources with a consequent performance degradation. The achievable performance of the developed schemes is investigated, by analysis and simulation, over a realistic wireless channel model and realistic signal processing at the base station, showing negligible losses with respect to previously proposed coded random access systems with idealized instantaneous feedback.

In this work, we consider a multistatic joint sensing and communication network composed of a transmitter and multiple receivers capable of estimating the position of a target in the monitored area. In particular, the system consists of a transmitter equipped with multiple antennas (typically a base station) and several receivers that can act as sensors with a single antenna. The transmitter adopts multiple beams to accommodate the communication towards the user equipment and the sensing functionality, with the ability to split the power between the two beams to adjust the sensing/communication trade-off. Processing of target echoes by the sensors produces a bistatic distance estimate or soft maps, which are combined by the fusion center. We then propose two sensor data fusion strategies, least square and soft maps fusion; the former has a negligible impact on the network overhead, while the latter always provides better performance in terms of root mean squared error of target position estimation when considering a small fraction of power devoted to sensing. Finally, we highlight the benefits of cooperation offered by the multistatic configuration, compared to the bistatic one, in terms of power saving for sensing.

This work proposes a low-complexity estimation approach for an orthogonal time frequency space (OTFS)-based integrated sensing and communication (ISAC) system. In particular, we first define four low-dimensional matrices used to compute the channel matrix through simple algebraic manipulations. Secondly, we establish an analytical criterion, independent of system parameters, to identify the most informative elements within these derived matrices, leveraging the properties of the Dirichlet kernel. This allows the distilling of such matrices, keeping only those entries that are essential for detection, resulting in an efficient, low-complexity implementation of the sensing receiver. Numerical results, which refer to a vehicular scenario, demonstrate that the proposed approximation technique effectively preserves the sensing performance, evaluated in terms of root mean square error (RMSE) of the range and velocity estimation, while concurrently reducing the computational effort enormously.

In next generation Internet-of-Things, the overhead introduced by grant-based multiple access protocols may engulf the access network as a consequence of the unprecedented number of connected devices. Grant-free access protocols are therefore gaining an increasing interest to support massive access from machine-type devices with intermittent activity. In this paper, coded random access (CRA) with massive multiple input multiple output (MIMO) is investigated as a solution to design highly-scalable massive multiple access protocols, taking into account stringent requirements on latency and reliability. With a focus on signal processing aspects at the physical layer and their impact on the overall system performance, critical issues of successive interference cancellation (SIC) over fading channels are first analyzed. Then, SIC algorithms and a scheduler are proposed that can overcome some of the limitations of the current access protocols. The effectiveness of the proposed processing algorithms is validated by Monte Carlo simulation, for different CRA protocols and by comparisons with developed benchmarks.

Grant-free access schemes are candidates to support future massive multiple access applications owing to their capability to reduce control signaling and latency. As a promising class of grant-free schemes, coded random access schemes can achieve high reliabilities also with uncoordinated transmissions and therefore in presence packet collisions. In this paper, an analysis tool for coded random access, based on density evolution, is proposed and exploited for system design and optimization. In sharp contrast with the existing literature, where such tools have been developed under simplified channel assumptions, the proposed tool captures not only MAC layer features, but also the physical wireless fading channel and a realistic physical layer signal processing based on multiple antennas and randomlychosen orthogonal pilots. Theoretical results are validated by comparison with symbol-level Monte Carlo simulations.

Systems that combine sensing and communication functionalities are gaining interest for several possible applications related to the internet of things (IoT) and the upcoming 6G mobile radio networks. Studies have recently been proposed to find the optimal tradeoff between sensing and communication performance. However, these studies assume continuous transmission and thus consider that the time available for estimation can always be large enough to achieve some desired accuracy. Moreover, in line with this assumption, communication performance is measured via the well-known Shannon capacity, which implicitly assumes indefinitely long error correction codes. However, in the case of short packet transmissions, such as the case in several IoT applications, the above assumption is unrealistic, as the length of the transmitted packet limits that of the error correction code and the observation time for parameter estimation. Therefore, this paper aims at investigating the optimal tradeoff between the data transmission and the target localization capabilities in a finite block-length regime, by making use of some typical metrics of the finite length information theory. In particular, the optimal beamforming, which minimizes the Cramér Rao bound of target localization, is derived under a constraint over the block error probability for given packet length values.

The design of highly scalable multiple access schemes is a main challenge in the evolution towards future massive machine-type communications, where reliability and latency constraints must be ensured to a large number of uncoordinated devices. In this scenario, coded random access (CRA) schemes, where successive interference cancellation algorithms allow large improvements with respect to classical random access protocols, have recently attracted an increasing interest. Impressive performance can be potentially obtained by combining CRA with massive multiple input multiple output (MIMO). In this paper we provide an analysis of such schemes focusing on the effects of imperfect channel estimation on successive interference cancellation. Based on the analysis we then propose an innovative signal processing algorithm for CRA in massive MIMO systems.

An information-theoretic approach to irregular repetition slotted ALOHA (IRSA) is proposed. In contrast with previous works, in which IRSA analysis is conducted only based on quantities that are typical of collision models such as the traffic, the new approach also captures more fundamental quantities. Specifically, a suitable codebook construction for the adder channel model is adopted to establish a link with successive interference cancellation over the multi-packet reception channel. This perspective allows proving achievability and converse results for the average sum rate of IRSA multiple access schemes.

This work investigates a multibeam system for joint sensing and communication (JSC) based on multiple-input multiple-output (MIMO) 5G new radio (NR) waveforms. In particular, we consider a base station (BS) acting as a monostatic sensor that estimates the range, speed, and direction of arrival (DoA) of multiple targets via beam scanning using a fraction of the transmitted power. The target position is then obtained via range and DoA estimation. We derive the sensing performance in terms of probability of detection and root mean squared error (RMSE) of position and velocity estimation of a target under line-of-sight (LOS) conditions. Furthermore, we evaluate the system performance when multiple targets are present, using the optimal sub-pattern assignment (OSPA) metric. Finally, we provide an in-depth investigation of the dominant factors that affect performance, including the fraction of power reserved for sensing.

Massive multiple access schemes, capable of serving a large number of uncoordinated devices while fulfilling reliability and latency constraints, are proposed. The schemes belong to the class of grant-free coded random access protocols and are tailored to massive multiple input multiple output (MIMO) base station processing. High reliability is obtained owing to an intra-frame spatial coupling effect, triggered by a simple device access protocol combined with acknowledgements (ACKs) from the base station. To provide system design guidelines, analytical bounds on error floor and latency are also derived. The proposed schemes are particularly interesting to address the challenges of massive machine-type communications in the framework of next generation massive multiple access systems.

Multiple radar systems represent an attractive option for target tracking because they can significantly enlarge the area coverage and improve both the probability of trajectory detection and the localization accuracy. The presence of multiple extended targets or weak targets is a challenge for multiple radar systems. Moreover, their performance may be severely deteriorated by regions characterized by a high clutter density. In this paper, an algorithm for detection and tracking of multiple targets, extended or weak, based on measurements provided by multiple radars in an environment with heavily cluttered regions, is proposed. The proposed method features three stages. In the first stage, past measurements are exploited to build a spatio-temporal clutter map in each radar; a weight is then assigned to each measurement to assess its significance. In the second stage, a track-before-detect algorithm, based on a weighted three-dimensional Hough transform, is applied to obtain target tracklets. In the third stage, a low-complexity tracklet association method, exploiting a lion reproduction model, is applied to associate tracklets of the same target. Three experiments are presented to illustrate the effectiveness of the proposed approach. The first experiment is based on synthetic data, the second one on actual data from a radar network with two homogeneous air surveillance radars, and the third one on actual data from a radar network with four different marine surveillance radars. The results reveal that the proposed method can outperform competing approaches.

Owing to the extremely narrow beams, a main issue in optical deep space communications is represented by miss-pointing errors, which may severely degrade the system performance and availability. In this paper, we address pointing losses in the case in which both the receiver and the transmitter are affected by angular errors. Pointing losses are evaluated through two approaches. The first approach is deterministic and only requires knowledge of a maximum angular error. The second approach requires knowledge of the angular error statistical distribution and tackles the problem from an outage probability viewpoint. These tools are then applied to analyze the impact of pointing losses in deep space optical links in which both terminals suffer from miss-pointing effects. The antenna gains are first optimized to maximize the effective system gain. The optimum antenna gains are then applied to evaluate maximum achievable ranges and to perform link design by means of optical link budgets.

In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i) the standard Raptor code construction, (ii) a multi-edge type construction, (iii) a construction where the Raptor code is nonbinary but the generator matrix of the LT code has only binary entries, (iv) a combination of (ii) and (iii). The latter construction resembles the one employed by RaptorQ codes, which at the time of writing this article represents the state of the art in fountain codes. The bounds are shown to be tight, and provide an important aid for the design of Raptor codes.

In this paper, we consider the problem of estimating the number of unrecovered active users in a coded random access systems over a collision channel with both packet erasures and slot erasures. Each user transmits multiple packet replicas in random slots of the frame and successive interference cancellation (SIC) is exploited at the receiver. Each packet replica is transmitted over an erasure channel. Moreover, the whole signal received in a slot may be erased, making the slot content useless. The developed algorithm can track over SIC iterations the probability distribution of the sought number of users, given all information that it is possible to gather through SIC iterations. The algorithm is validated by numerical simulation, showing that it can considerably reduce the mean square error of the estimation process.

A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble-specific interval of erasure probabilities, when the ensemble weight spectral shape function tends to a negative value as the fractional codeword weight tends to zero. For these ensembles we can therefore lower bound the block-wise ML decoding threshold. Two examples are presented, namely, linear random parity-check codes and fixed-rate Raptor codes with linear random precoders. While for the former a full analytical solution is possible, for the latter we can lower bound the ML decoding threshold on the erasure channel by simply solving a 2 × 2 system of nonlinear equations.

In this paper, we present a system that performs joint channel coding and constellation shaping for physical-layer network coding (PNC) with quadrature amplitude modulation (QAM). Traditional bit-level PNC (based on the exclusive-OR) has been shown to be effective in increasing the system throughput, but requires a specific design of PNC mapping and shaping code when used with non-binary modulation in order to avoid ambiguity in bit-level detection. We show that PNC applied at symbol level does not present any ambiguity for QAM modulation, so that a wider range of PNC mapping and shaping code designs are possible. Furthermore, we show that the symbol-level PNC approach ensures a shaped signal transmission in both communication phases even with a simple denoising operation at the relay. The simplicity of this denoising operation also facilitates an achievable rate analysis, which is used in the design of shaping codes. Simulation results demonstrate that for end-to-end communication in a PNC system with 16-QAM, the proposed approach achieves a shaping gain of 0.75 dB at a bit error rate of 10-4with a low-complexity (4, 2) shaping block code.

We develop a maximum a posteriori detector for the number of unrecovered users in coded random access systems based on the irregular repeat slotted Aloha (IRSA) protocol, where each user transmits in random slots multiple packet replicas whose number (known as the user degree) is drawn according to a given probability mass function and where successive interference cancellation (SIC) is exploited at the receiver. The detector is capable to track over SIC iterations the a posteriori probability distribution of a vector whose elements are the numbers of not yet recovered active users of the various degrees. Numerical results are provided to illustrate the capability of the detection algorithm to considerably reduce the mean square error on the number of active users, taking advantage of the iterative SIC process.

This paper addresses the problem of detecting the number of unrecovered active users in a coded random access system with successive interference cancellation (SIC) at the receiver. The considered transmission protocol is contention resolution diversity slotted Aloha, where each user generates and transmits in random slots multiple packet replicas. A maximum a posteriori detector, capable to track the a posteriori probability mass function of the number of not yet recovered active users over SIC iterations, is developed for the case of availability of a priori information on the active users' distribution. Numerical results are provided, illustrating the detection algorithm capability to achieve low mean square error values taking advantage of new observations gathered throughout the SIC process.

Precise localization and tracking of moving objects is of great interest for a variety of emerging applications including the Internet-of-Things (IoT). The localization and tracking tasks are challenging in harsh wireless environments, such as indoor ones, especially when objects are not equipped with dedicated tags (noncollaborative). The problem of detecting, localizing, and tracking noncollaborative objects within a limited area has often been undertaken by exploiting a network of radio sensors, scanning the zone of interest through wideband radio signals to create a radio image of the objects. This paper presents a sensor network for radio imaging (sensor radar) along with all of the signal processing steps necessary to achieve highaccuracy objects tracking in harsh propagation environments. The described sensor radar is based on the impulse radio (IR) ultrawideband (UWB) technology, entailing the transmission of very short duration pulses. Experimental results with actual UWB signals in indoor environments confirm the sensor radar's potential in IoT applications.

Random access protocols relying on the transmission of packet replicas in multiple slots and exploiting interference cancellation at the receiver have been shown to achieve performance competitive with that of orthogonal schemes. So far the optimization of the repetition degree profile, defining the probability for a user to transmit a given number of replicas, has mainly been performed targeting the collision channel model. In this paper the analysis is extended to a block fading channel model, also assuming capture effect at the receiver. Density evolution equations are developed for the new setting and, based on them, some repetition degree profiles are optimized and analyzed via Monte Carlo simulation in a finite frame length setting. The derived distributions are shown to achieve throughputs largely exceeding 1 [packet/slot].

In this paper, we present a low-density parity-check coded modulation approach addressing orthogonal modulations with moderate order (between 8 and 32) over the additive white Gaussian noise channel. The proposed design is based on a constrained optimization of a non-binary low-density parity-check ensemble degree distribution, where the iterative decoding threshold is optimized via extrinsic information transfer analysis while restricting the search to degree distributions that target low error floors. For various orthogonal modulation orders, we provide useful approximations to the extrinsic information transfer functions, which enable a fast optimization with respect to the iterative decoding threshold. The approach is validated via codeword error rate Monte Carlo simulations and complemented by an error floor analysis, showing gains up to 0.8 dB at a codeword error rate of 10-4with respect to existing designs, down to information block lengths as short as 192 bits.

We propose graph-defined IRSA (G-IRSA), a new approach to design irregular repetition slotted ALOHA (IRSA) uncoordinated multiple access schemes for a controlled-size population of users that become active sporadically. The proposed scheme considers a joint design of the distribution according to which users select their repetition factors and the distribution determining how many packet replicas are transmitted per slot, as well as the connectivity of the underlying graph, i.e., to which slots users transmit. This is in sharp contrast to standard IRSA, where only the users degree distribution is optimized, while active users place their packet replicas uniformly at random and thus there is no control on how many replicas are transmitted per slot and in which slots users transmit. The key idea is to establish a link between the IRSA for the considered scenario and low-density parity-check (LDPC) codes for transmission over the binary erasure channel (BEC). Using this parallelism, the design of a G-IRSA scheme can be cast as the design of a high-rate LDPC code over the BEC. We show that the proposed scheme achieves significantly lower error floors than the original IRSA and very good decoding thresholds.

This paper investigates the design of non-binary protograph low-density parity-check codes for the Poisson channel with m-ary pulse position modulation. The field order over which the code is constructed is matched to the pulse position modulation order yielding a coded modulation scheme. The optimization of the low-density parity-check code structure is performed via protograph density evolution on a surrogate m-ary erasure channel. The surrogate design is illustrated to be not only accurate, but also robust for a range of practical values of channel background noise and various modulation orders. As a result the proposed codes show excellent performance over the Poisson channel with pulse position modulation outperforming competing schemes. As a side-product of this paper, finite-length benchmarks on the block error probability are provided, together with a union bound to characterize the code performance in the error floor region.

In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn randomly from some ensemble of codes. The bound is shown to be tight by means of simulations. This bound provides a new insight into Raptor codes since it shows how Raptor codes can be analyzed similarly to a classical fixed rate serial concatenation.

Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance. The condition involves the rate of the outer code, the rate of the inner fixed-rate Luby Transform (LT) code and the LT code degree distribution. Additionally, it is shown that for ensembles fulfilling this condition, the minimum distance of a code randomly drawn from the ensemble has a linear growth with the block length. The analytical results can be used to make accurate predictions of the performance of finite length Raptor codes. These results are particularly useful for fixed-rate Raptor codes under maximum likelihood erasure decoding, whose performance is driven by their weight distribution.

In this paper Raptor code ensembles with linear random precodes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight distribution. The asymptotic growth rate analysis is then exploited to develop a necessary and sufficient condition under which the fixed-rate Raptor code ensemble exhibits a strictly positive typical minimum distance.

The code design of non-binary low-density paritycheck codes for the erasure channel, under maximum a posteriori decoding, is addressed. In particular, a partially structured ensemble of codes, characterized by a careful control of the amount and of the connectivity of the variable nodes of small degrees, is proposed. The identified ensemble of codes is analyzed in terms of asymptotic thresholds and weight distribution and it is shown that codes from the ensemble provide a remarkable trade-off between waterfall performance, error floor, and decoding complexity. As an example, the performance curve of a short (256,128) code on the memoryless 16-ary erasure channel tightly approaches the Singleton bound at least down to a codeword error rate of 10-9, at low decoding complexity.

In this paper, a random access scheme is introduced, which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes through a density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed, and component code distributions tightly approaching the bound are derived.

A coded modulation scheme for the Poisson channel is investigated. The scheme relies on the serial concatenation of an outer low-density parity-check (LDPC) code over an order-q finite field and q-ary pulse position modulation (PPM). Due to the matching between code and modulation symbols, no iterative message exchange between the decoder and the modulator is required. The PPM capacity limit serves as a reference to evaluate the efficiency of the proposed scheme in the asymptotic setting via density evolution. A simplified form of the Gallager random coding bound (RCB) is also developed and used as a reference for the finite-length performance of the coded modulation scheme. The optimization via density evolution is performed on a surrogate (erasure) channel, yielding excellent iterative decoding thresholds for a wide range of channel parameters. The proposed coded modulation technique performs close to the theoretical bounds not only asymptotically, but also for moderate block lengths. It turns to represent a viable solution for deep-space direct detection optical links, for which the Poisson channel is adopted as a model.

This paper establishes sufficient conditions under which a memoryless channel with real, scalar and peak power limited input exhibits a capacity achieving input probability measure that is discrete with a finite number of probability mass points. A proof for the sufficiency of the proposed conditions is presented. Some examples are also illustrated as further evidence for the presented theory.

The finite-length design of non-binary low-density parity-check (LDPC) codes for the q-ary erasure channel under maximum a posteriori (MAP) decoding is addressed. A low-complexity MAP decoding algorithm is reviewed for which a code design strategy is proposed. In particular, it is illustrated how a judicious code design permits to find a trade-off between performance in terms of codeword error rate (CER) and decoding complexity. As an example, the performance curve of a short (400, 200) code on the memoryless 4-ary erasure channel tightly approaches the Singleton bound at least down to a CER of 10-8.

A new communication paradigm, namely piggyback communication, is introduced. The founding principle of piggyback communication is to recycle source of opportunity (SoO) signals, already available in the surrounding environment for other services, to establish short-range passive radio links between a certain number of wireless nodes and a receiver without the injection of additional power in the environment, thus achieving close zero-power wireless communications.

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.

In this paper, tight bounds on the block error probability of linear block codes over order-q finite fields for the q-ary erasure channel, under maximum-likelihood (ML) decoding, are developed. Upper bounds are obtained for uniform parity-check ensembles, sparse parity-check ensembles, general parity-check ensembles (e.g., Gallager regular nonbinary low-density parity-check ensembles), and for any given linear code with known distance spectrum. The tightness of the upper bounds is confirmed both by the comparison with simple lower bounds and, for Gallager low-density parity-check ensembles, by extensive Monte Carlo simulations. Exploiting the derived bounds, it is shown how already for short blocks and small q>2 sparse ensembles attain block error probabilities close to those of idealized maximum distance separable (MDS) codes, down to low error probabilities, whereas in the same regime binary codes show visible losses with respect to the Singleton bound. Thanks to the accurate performance estimates, the developed bounds can support the design of near-optimum erasure correcting codes with short and moderate lengths.

Two classes of turbo codes constructed on high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (2,3) regular low-density parity-check (LDPC) code ensemble. The first construction results in a parallel concatenation of two non-binary, time-variant accumulators. The second construction consists of the serial concatenation of a non-binary time-variant differentiator with a non-binary time-variant accumulator, and provides a highly structured flexible encoding scheme for (2,4) LDPC codes. A cycle graph representation is also provided. The proposed codes can be decoded efficiently either as LDPC codes (via belief propagation decoding on their bipartite graphs) or as turbo codes (via the forward-backward algorithm applied to the component code trellises) by means of the fast Fourier transform. The proposed codes provide remarkable coding gains (more than 1 dB at a codeword error rate 10-4) over binary LDPC and turbo codes in the moderate-short block length regime.

Low-rate non-binary low-density parity-check (LDPC) codes for coherent and blockwise non-coherent additive white Gaussian noise (AWGN) channels are developed. The proposed construction is based on the concatenation of non-binary outer LDPC codes with inner binary codes. In case the binary codes are chosen to be Hadamard or Reed-Muller (RM) codes, the complexity of the decoding scheme is considerably reduced. An asymptotic analysis of the concatenation with help of composite capacity considerations anddensity evolution (DE) is provided, from which guidelines on the choice of both inner and outer codes are devised. Finite length designs presented in this work confirm the excellent performance of the proposed codes.

This paper analyzes the asymptotic exponent of the weight spectrum for irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient numerical technique for its evaluation is presented, involving the solution of a 4 × 4 system of polynomial equations. The expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. The spectral shape is shown to admit a particularly simple form in the special case where all variable nodes are repetition codes of the same degree, a case which includes Tanner codes; for this case it is also shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function. Finally, using these new results, weight and stopping set size spectral shapes are evaluated for some example generalized and doubly-generalized LDPC code ensembles.

Short non-binary irregular repeat-accumulate (IRA) codes based on well-known Hamiltonian and Hypohamiltonian graphs with large girth are presented. The mapping of the code coordinates on the graph edges is discussed for Hamiltonian graphs, and two encoding methods on Hypohamiltonian graphs are introduced. The performance of the presented codes on order-256 finite fields (F256) is provided for both the additive white Gaussian (AWGN) channel and the binary erasure channel (BEC) under iterative (IT) decoding. For the latter case, the performance under maximum likelihood (ML) decoding is also presented, to illustrate that the proposed codes not only attain performances close to the random coding bound, but also show limited losses when decoded iteratively.

In this paper we investigate the effect of spatial coupling applied to the recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to the bridge between the graphical model describing the iterative interference cancellation process of CSA over the random access frame and the erasure recovery process of low-density parity-check (LDPC) codes over the binary erasure channel (BEC), we propose an access protocol which is inspired by the convolutional LDPC code construction. The proposed protocol exploits the terminations of its graphical model to achieve the spatial coupling effect, attaining performance close to the theoretical limits of CSA. As for the convolutional LDPC code case, large iterative decoding thresholds are obtained by simply increasing the density of the graph. We show that the threshold saturation effect takes place by defining a suitable counterpart of the maximum-a-posteriori decoding threshold of spatially-coupled LDPC code ensembles. In the asymptotic setting, the proposed scheme allows sustaining a traffic close to 1 [packets/slot].

This paper investigates efficient maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over erasure channels. A set of algorithms, referred to as pivoting algorithms, is developed. The aim is to limit the average number of pivots (or reference variables) from which all the other erased symbols are recovered iteratively. The suggested algorithms exhibit different trade-offs between complexity of the pivoting phase and average number of pivots. Moreover, a systematic procedure to design LDPC code ensembles for efficient ML decoding is proposed. Numerical results illustrate that the designed LDPC codes achieve a near-optimum performance (very close to the Singleton bound, at least down to a codeword error rate level 10-8) with an affordable decoding complexity. For one of the presented codes and algorithms, a software implementation has been developed which is capable to provide data rates above 1.5 Gbps on a commercial computing platform.

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.

A random access scheme for the collision channel without feedback is proposed. The scheme is based on erasure correcting codes for the recovery of packet segments that are lost in collisions, and on successive interference cancellation for resolving collisions. The proposed protocol achieves reliable communication in the asymptotic setting and attains capacities close to 1 [packets/slot]. A capacity bound as a function of the overall rate of the scheme is derived, and code distributions tightly approaching the bound developed.

Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a parallel concatenation of two non-binary, time-variant accumulators. The second construction is based on the serial concatenation of a non-binary, time-variant differentiator and of a non-binary, time-variant accumulator, and provides a highly-structured flexible encoding scheme for (dv=2,dc=4) ensemble codes. A cycle graph representation is provided. The proposed codes can be decoded efficiently either as low-density parity-check codes (via belief propagation decoding over the codes bipartite graph) or as turbo codes (via the forward-backward algorithm applied to the component codes trellis). The forward-backward algorithm for symbol maximum a posteriori decoding of the component codes is developed and simplified by means of the fast Fourier transform. The proposed codes provide remarkable gains (~1 dB) over binary low-density parity-check and turbo codes in the moderate-short block regimes.

In this paper, coded slotted ALOHA (CSA) is introduced as a powerful random access scheme to the MAC frame. In CSA, the burst a generic user wishes to transmit in the MAC frame is first split into segments, and these segments are then encoded through a local a packet-oriented code prior to transmission. On the receiver side, iterative interference cancellation combined with decoding of the local code is performed to recover from collisions. The new scheme generalizes the previously proposed irregular repetition slotted ALOHA (IRSA) technique, based on a simple repetition of the users' bursts. An interpretation of the CSA interference cancellation process as an iterative erasure decoding process over a sparse bipartite graph is identified, and the corresponding density evolution equations derived. Based on these equations, asymptotically optimal CSA schemes are designed for several rates and their performance for a finite number of users investigated through simulation and compared to IRSA competitors. Throughputs as high as 0.8 are demonstrated. The new scheme turns out to be a good candidate in contexts where power efficiency is required.

In this paper, packet-level coding is considered in the framework of H.264/AVC video transmission. Two distinct solutions are proposed and compared in different realistic communication scenarios. The first is based on classical Reed-Solomon (RS) codes applied at the RTP layer, while the second on modern LDPC codes implemented at the UDP-Lite layer. An end-to-end Quality of Experience (QoE) evaluation is presented, in terms of achieved peak signal-to-noise power ratio (PSNR). Our numerical results show that, in low-latency video applications across communication channels introducing errors and erasures, the adoption of a packet-level coding scheme becomes essential to guarantee a satisfactory quality. The solution based on LDPC codes exhibits better performances in presence of severe packet loss rates.

Availability of higher capacity for both uplinks and downlinks is expected in the future deep-space missions on Mars, thus enabling a large range of services that could eventually support human remote operations. The provisioning for deep-space links offering data rate up to several megabits per second will be a crucial element to allow new services for the space domain along with the common telecommand and telemetry services with enhanced communication capabilities. On the other hand, also the geometry proper of this scenario with orbiting and landed elements sharing only partial visibility among them and towards Earth provides another challenge. This paper surveys the reliability options that are available in the Consultative Committee for Space Data Systems (CCSDS) Protocol Stack for application in the deep-space missions. In particular, the solutions implemented from the physical up to the application layer are illustrated in terms of channel coding and Automatic Retransmission reQuest (ARQ) schemes. Finally, advanced reliability strategies possibly applicable in next-generation deep-space missions are explored as well.

A deterministic method to design degree distributions for low-density parity-check codes over the binary erasure channel is proposed. This method consists of matching the first and high-order derivatives of the extrinsic information transfer (EXIT) function of the variable node set to the corresponding derivatives of the inverse EXIT function of the check node set, in order to reduce the gap between the two curves in the EXIT chart. A sufficient condition for a check-concentrated distribution to achieve derivative matching up to some order is first obtained, and then a deterministic design algorithm, enabled by the Fourier-Budan theorem, is developed exploiting this sufficient condition. A comparison with other deterministic design techniques is also provided, revealing the potential of the proposed algorithm.

In this paper, the asymptotic growth rate of the weight distribution of irregular doubly generalized LDPC (D-GLDPC) codes is derived. The analysis yields a compact expression which accurately approximates the growth rate function for the case of small linear-weight codewords. This paper generalizes existing results for LDPC and generalized LDPC (GLDPC) codes. Ensembles with smallest check or variable node minimum distance greater than 2 are shown to have good growth-rate behavior, while for other ensembles a fundamental parameter is identified which discriminates between an asymptotically small and an asymptotically large expected number of small linear-weight codewords. Also, in the latter case it is shown that the growth rate depends only on the check and variable nodes with minimum distance 2. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes. Finally, it is shown that the analysis may be extended to include the growth rate of the stopping set size distribution of irregular D-GLDPC codes.

Ensemble design of low-density parity-check (LDPC) codes and their generalizations is usually performed via numerical optimization techniques, such as differential evolution, in which a threshold analysis tool is always necessary. Threshold analysis of unstructured doubly-generalized LDPC (D-GLDPC) code ensembles over the binary erasure channel (BEC) can be performed via extrinsic information transfer (EXIT) chart, exploiting the information functions and split information functions of the check and variable component codes, respectively. In this paper, multi-type information functions of linear block codes are introduced as an extension of the concept of information functions, when the bit positions are assumed to be associated with different types. It is shown how multi-type information functions (together with their split counterparts) can be exploited within an EXIT analysis approach to perform threshold analysis over the BEC of multi-edge type D-GLDPC code ensembles. The proposed technique for threshold analysis captures D-GLDPC codes based on protographs as a special case.

This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.

In this paper, a method for the asymptotic analysis of generalized low-density parity-check (GLDPC) codes and doubly generalized low-density parity-check (D-GLDPC) codes over the binary erasure channel (BEC), based on extrinsic information transfer (EXIT) chart, is described. This method overcomes the problem consisting of the impossibility to evaluate the EXIT function for the check or variable component codes, in situations where the information functions or split information functions for component codes are unknown. According to the proposed technique, GLDPC codes and D-GLDPC codes where the generalized check and variable component codes arerandomcodes with minimum distance at least 2, are considered. A technique is then developed which finds the EXIT chart for the overall GLDPC or D-GLDPC code, by evaluating the expected EXIT function for each check and variable component code. This technique is finally combined with the differential evolution algorithm in order to generate some good GLDPC and D-GLDPC edge distributions. Numerical results of long, random codes, are presented which confirm the effectiveness of the proposed approach. They also reveal that D-GLDPC codes can outperform standard LDPC codes and GLDPC codes in terms of both waterfall performance and error floor.

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 × 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.

This paper investigates efficient maximum-likelihood (ML) decoding algorithms for low-density parity-check (LDPC) codes over erasure channels. In particular, enhancements to a previously proposed structured Gaussian elimination approach are presented. The improvements are achieved by developing a set of algorithms, here referred to as pivoting algorithms, aiming to limit the average number of reference variables (or pivots) from which the erased symbols can be recovered. Four pivoting algorithms are compared, which exhibit different trade-offs between the complexity of the pivoting phase and the average number of pivots. Numerical results on the performance of LDPC codes under ML erasure decoding complete the analysis, confirming that a near-optimum performance can be obtained with an affordable decoding complexity, up to very high data rates. For example, for one of the presented algorithms, a software implementation has been developed, which is capable to provide data rates above 1.5 Gbps on a commercial computing platform.

The design of moderate-length erasure correcting low-density parity-check (LDPC) codes over correlated erasure channels is considered. Although the asymptotic LDPC code design remains the same as for a memoryless erasure channel, robustness to the channel correlation shall be guaranteed for the finite length LDPC code. This further requirement is of great importance in several wireless communication scenarios where packet erasure correcting codes represent a simple countermeasure for correlated fade events (e.g., in mobile wireless broadcasting services) and where the channel coherence time is often comparable with the code length. In this paper, the maximum tolerable erasure burst length (MTBL) is adopted as a simple metric for measuring the code robustness to the channel correlation. Correspondingly, a further step in the code construction is suggested, consisting of improving the LDPC code MTBL. Numerical results conducted over a Gilbert erasure channel, under both iterative and maximum likelihood decoding, highlight both the importance of the MTBL improvement in the finite-length code construction and the possibility to tightly approach the performance of maximum distance separable codes.

A class of doubly-generalized low-density parity-check (D-GLDPC) codes, where single parity-check (SPC) codes are used as variable nodes (VNs), is investigated. An expression for the growth rate of the weight distribution of any D-GLDPC ensemble with a uniform check node (CN) set is presented at first, together with an analytical technique for its efficient evaluation. These tools are then used for detailed analysis of a case study, namely, a rate-1/2 D-GLDPC ensemble where all the CNs are (7, 4) Hamming codes and all the VNs are length-7 SPC codes. It is illustrated how the VN representations can heavily affect the code properties and how different VN representations can be combined within the same graph to enhance some of the code parameters. The analysis is conducted over the binary erasure channel. Interesting features of the new codes include the capability of achieving a good compromise between waterfall and error floor performance while preserving graphical regularity, and values of threshold outperforming LDPC counterparts.

In this paper, a simple and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists of starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance over the memoryless erasure channel, and suitable also for the iterative correction of single erasure bursts. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm. It executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed to achieve a good performance over the memoryless erasure channel, then the code obtained after the application of the algorithm provides a good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the algorithm effectiveness when applied to different categories of LDPC codes.

The iterative decoding threshold of low-density parity-check (LDPC) codes over the binary erasure channel (BEC) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. This bound is a consequence of the stability condition, and is here referred to as stability bound. In this paper, a stability bound over the BEC is developed for doubly-generalized LDPC codes, where variable and check nodes can be generic linear block codes, assuming maximumaposteriorierasure correction at each node. It is proved that also in this generalized context the bound depends only on the variable and check component codes with minimum distance 2. A condition is also developed, namely, the derivative matching condition, under which the bound is achieved with equality. The stability bound leads to consider single parity-check codes used as variable nodes as an appealing option to overcome common problems created by generalized check nodes.

In this paper, a family of low-density parity-check (LDPC) degree distributions, whose decoding threshold on the binary erasure channel (BEC) admits a simple closed form, is presented. These degree distributions are a subset of the check regular distributions (i.e. all the check nodes have the same degree), and are referred to as p-positive distributions. It is given proof that the threshold for a p-positive distribution is simply expressed by [lambda'(0)rho'(1)]-1. Besides this closed form threshold expression, the p-positive distributions exhibit three additional properties. First, for given code rate, check degree and maximum variable degree, they are in some cases characterized by a threshold which is extremely close to that of the best known check regular distributions, under the same set of constraints. Second, the threshold optimization problem within the p-positive class can be solved in some cases with analytic methods, without using any numerical optimization tool. Third, these distributions can achieve the BEC capacity. The last property is shown by proving that the well-known binomial degree distributions belong to the p-positive family.

In this paper, the stability condition for low-density parity-check (LDPC) codes on the binary erasure channel (BEC) is extended to generalized LDPC (GLDPC) codes and doubly-generalized LDPC (D-GLDPC) codes. It is proved that, in both cases, the stability condition only involves the component codes with minimum distance 2. The stability condition for GLDPC codes is always expressed as an upper bound to the decoding threshold. This is not possible for D-GLDPC codes, unless all the generalized variable nodes have minimum distance at least 3. Furthermore, a condition called derivative matching is defined in the paper. This condition is sufficient for a GLDPC or D- GLDPC code to achieve the stability condition with equality. If this condition is satisfied, the threshold of D-GLDPC codes (whose generalized variable nodes have all minimum distance at least 3) and GLDPC codes can be expressed in closed form.

Future space missions will put severe constraints on communication links in terms of data rates, bandwidth occupancy, complexity, and performance. The requirements imposed by the new missions and their consequences on channel code design are presented in the first part of the paper. All relevant issues, including code rates, frame lengths, modulation formats, performance metrics, complexity, and others, are discussed. In the second part of the paper, long erasure correcting codes are presented and their properties explained. These codes operate at the upper layers of the space link protocol and constitute an attractive new frontier for zero packet loss in future space communications.

In this work we deal with Low-Density Parity-Check (LDPC) codes under iterative message passing decoding algorithm, over channels introducing bursts of erasures. The burst erasure channel model we consider in this paper can be seen as an erasure channel based on a hidden Markov chain (HMC-EC). In order to characterize the channel, in the first part of the paper the expression of mutual information is recalled for any erasure channel with memory and with i.i.d. and equiprobable input symbols. In the second part of the paper an optimization algorithm is proposed which is able to heavily improve LDPC iterative decoder performance. This algorithm can be in principle applied to any given LDPC code. Simulation results relative to both random and IRA / eIRA codes are shown comparing the performance before and after the application of our optimization algorithm.