In vehicular communications, accurate modeling of real-world radio propagation channels is essential. To this end, we propose a novel stochastic model, namedVehicular-Tapped Delay-Line(V-TDL) that accurately captures the statistical behavior of multipath channels characterized by path-dependent gains, delays, and Doppler shifts. V-TDL supports diverse traffic conditions and road geometries by generating channel instances through well-established probability distributions. Also, it effectively models the parameters of the distributions through realistic geometry-based simulations, achieving the accuracy of a ray-tracing-based model while maintaining the low complexity of a purely stochastic approach. In contrast to existing models, V-TDL accounts for the correlation between propagation paths. Our findings show that this correlation is inherent in high-speed vehicular environments and neglecting it leads to a significant overestimation of channel diversity and system performance. We compare our model to existing alternatives to assess the performance of OTFS and OFDM modulations. The results demonstrate that, unlike traditional models such as the 3GPP EVA, V-TDL captures variations in channel diversity influenced by traffic intensity and road geometry, which impact the OTFS and OFDM performance. Although OTFS is penalized by path correlation, it consistently outperforms OFDM in all evaluated vehicular environments, confirming its suitability for high-speed vehicular communication scenarios.

This work addresses the problem of secrecy energy efficiency (SEE) maximization in RIS-aided wireless networks. The use of active and nearly-passive RISs are compared and their trade-off in terms of SEE is analyzed. Considering both perfect and statistical channel state information, two SEE maximization algorithms are developed to optimize the transmit powers of the mobile users, the RIS reflection coefficients, and the base station receive filters. Numerical results quantify the trade-off between active and nearly-passive RISs in terms of SEE, with active RISs yielding worse SEE values as the static power consumed by each reflecting element increases.

Low Earth orbit (LEO) satellite communications play a critical role in achieving global connectivity, yet they face significant challenges due to high satellite mobility and incomplete channel state information (CSI). Moreover, the integration of reconfigurable intelligent surfaces (RIS) in certain scenarios introduces additional complexities. In this paper, we propose a novel MIMO channel prediction framework tailored for LEO satellite communications involving unmanned aerial vehicle-mounted RIS (UAV-RIS), employing a spatiotemporal-attention (ST-attention) mechanism to capture both the spatial correlations among antennas and the temporal dynamics of rapidly varying channels. Furthermore, we leverage masked pretraining to enhance the model’s robustness under scenarios of severe CSI incompleteness, enabling effective reconstruction of missing channel information. Comprehensive simulations demonstrate that our approach outperforms traditional model-based predictors, whether historical CSI is fully available or only partially observed.

Spectrum Sensing will play a pivotal role in 6G Cognitive Radio Networks, in which unlicensed users could dynamically use the spectrum and perform opportunistic transmission. In this paper, we focus on a multiple-antenna data-aided Spectrum Sensing algorithm and we compute the exact Moment Generating Function and probability density function under the null hypothesis of such test statistic, by resorting to tools from finite-dimensional random matrix theory. The test at hand is formulated in terms of a quadratic form with unit-norm random vector and random kernel matrix with determinantal joint probability distribution of its eigenvalues. The algorithm exploits the availability of a set of auxiliary data, collected under the assumption of primary signal presence. Results, presented in terms of Receiver Operating Characteristic curve and detection probability vs. the Signal-to-Noise Ratio, show that the presented test outperforms some well-established sensing schemes, such as the Generalized Likelihood Ratio Test and the Roy's Largest Root Test. Furthermore, we compare the outcomes of our analytical derivation with corresponding Monte Carlo simulated data in scenarios with both spatio-temporally uncorrelated and correlated samples.

The growing interest in Orthogonal Time Frequency Space (OTFS) modulation for vehicular communication systems requires the validation of its advantages using suitable channel models capable of emulating the dynamic and geometric complexities of vehicle-to-infrastructure systems. This paper presents a novel, realistic geometric-based channel model, called V-CORE, specifically designed for evaluating the performance of OTFS in vehicular scenarios. Our model accurately characterizes the scattered paths by exploiting the radar cross-section of the vehicles that populate a road according to a given vehicular traffic intensity. Multiple road scenarios with different geometry and vehicle velocities are considered, resulting in a flexible tool to evaluate system performance in different traffic contexts. The V-CORE model provides the channel variables, particularly relevant to OTFS implementation, such as multipath Doppler shift and delay. We assess the performance of OTFS against that of OFDM under different road structures, traffic intensity, and vehicle velocities. Further, we compare the proposed V-CORE model to the Extended Vehicular A model and demonstrate that ours provides a deeper insight into performance in high-speed vehicular scenarios.

Advancements in communication, manufacturing, and launch technologies have significantly accelerated the development of Low-Earth orbit (LEO) satellite communication constellations. Simultaneously, the rapid expansion of LEO satellite platforms presents new opportunities for navigation enhancements and substantial benefits for internet of things (IoT) applications. This survey highlights the latest advancements in the integrated communication and navigation (ICAN) technologies, emphasizing key research issues. Specifically, we discuss the motivation and feasibility of integrating communication and navigation on LEO satellite platforms, analyzing various LEO-based navigation paradigms while assessing their respective advantages and limitations. We further explore the mutual promotion of navigation and communication under the ICAN paradigm and discuss waveform design, analyzing the characteristics of different waveform design approaches. Finally, we highlight the unique challenges and identify open research topics within the ICAN framework for future exploration.

In this paper we study spreading sequences for Code Division Multiplexing (CDM) generated from the AES algorithm in counter mode. These sequences are robust against jamming because they cannot be reconstructed from one of their segments. Additionally, they are flexible, have a large cardinality, and can be obtained from a small key. We show how their linear complexity profile, error probability, and acquisition performance are aligned with those of random sequences. To further enhance them, we introduce a new family of mixed AES/Gold sequences. First, we demonstrate how we can generate cosets of extended Gold sequences which are perfectly orthogonal for CDM. Then, we combine AES sequences and Gold cosets: the new sequences have better performance in terms of error probability and acquisition, while maintaining protection against jamming. All results are derived analytically and validated through simulation. As a case study, we consider an uplink scenario from a ground station to a constellation of Low Earth Orbit satellites. The proposed mixed sequences allow for a significant increase in the number of satellites that can be served in parallel, while maintaining the same level of performance and protection against jamming.

This paper presents a framework for integrating Low-Earth Orbit (LEO) platforms with Non-Terrestrial Networks (NTNs) in the emerging 6G communication landscape. Our work applies the Mega-Constellation Services in Space (MCSS) paradigm, leveraging LEO mega-constellations’ expansive coverage and capacity, designed initially for terrestrial devices, to serve platforms in lower LEO orbits. Results show that this approach overcomes the limitation of sporadic and time-bound satellite communication links, a challenge not fully resolved by available Ground Station Networks and Data Relay Systems. We contribute three key elements: (i) a detailed MCSS evaluation framework employing Monte Carlo simulations to assess space user links and distributions; (ii) a novel Space User Terminal (SUT) design optimized for MCSS, using different configurations and 5G New Radio Adaptive Coding and Modulation; (iii) extensive results demonstrating MCSS’s substantial improvement over existing Ground Station Networks and Data Relay Systems, motivating its role in the upcoming 6G NTNs. The space terminal, incorporating a multi-system, multi-orbit, and software-defined architecture, can handle Terabit-scale daily data volumes and minute-scale latencies. It offers a compact, power-efficient solution for properly integrating LEO platforms as space internet nodes.

Beyond 5G technologies promise groundbreaking advances on the performance of cellular networks, by taking advantage of Massive MIMO in mmWave scenarios. The aim of this study is to analyze and test the performance of a 5G cell site equipped with large antenna arrays. It is of particular interest the comparison between the typical trisector cell design with a planar array for each sector, and the less investigated cylindrical array, able to maintain a constant pattern through the whole azimuthal range. To validate our analysis, we adopt the latest 3GPP-compliant 3D channel model and we evaluate the performance of multi-user and multi-layer precoding and combining schemes. Several MIMO configurations are taken into account, and we show that cylindrical arrays can improve the overall system performance, both in terms of achievable per-user rate and outage probability.

Bluetooth mesh is a recent technology built on the Bluetooth low energy protocol stack architecture, focusing on the Internet of Things. It represents an excellent solution for commercial and industrial lighting applications, though it is still evolving. One of the biggest challenges of the Bluetooth mesh network is the improvement of confirmation messages reception. In a Bluetooth mesh network, determining the Status of the received messages is a critical aspect that can generate unexpected issues when multiple devices respond simultaneously, as it may occur in some lighting applications. This behavior can reduce the probability of message delivery due to collisions, especially when the number of devices in the network increases. This article aims to improve the reliability in receiving confirmation messages in a Bluetooth mesh network by proposing a new technique of spreading Status overtime. To evaluate the proposed technique’s performance, we compare our technique with a Bluetooth mesh network with standard configuration (SC) using real nodes experimental setup. We evaluated our results in terms of packet-loss rate, obtaining 98.84% of the Status received for the network with our optimized configuration and 96.98% for those with the SC. Finally, an in-depth performance evaluation method for the analysis of the lost Status was also conducted.

A global Internet of Things is possible by embracing constellations of satellites acting as orbiting gateways in a Direct-to-Satellite IoT (DtS-IoT). By removing the dependency on ground gateways, DtS-IoT enables a direct service on the regions illuminated by the passing-by satellite. After an in-depth overview of relevant experiments and candidate technologies, we discover that specific configurations of the Long-Range (LoRa) network protocol specification are particularly appealing to realize the DtS-IoT vision. Specifically, we profit from the maximum clock drift permitted on LoRa devices to propose the sparse satellite constellations concept. This approach significantly reduces the in-orbit DtS-IoT infrastructure at the expense of latency anyway present in resource-constrained IoT networks. We then introduce a novel algorithm comprising specific heuristics to design quasi-optimal topologies for sparse IoT constellations. Obtained results show that LoRa-compatible DtS-IoT services can already be provided world-wide with 10% and 4% of the satellites required for a traditional dense constellation, in different configurations.

In this paper, a novel simplified statistical approach to evaluate the error performance bound of Ordered Statistics Decoding (OSD) of Linear Block Codes (LBC) is investigated. First, we propose a novel statistic which depicts the number of errors contained in the ordered received noisy codeword. Then, simplified expressions for the probability mass function and cumulative distribution function are derived exploiting the implicit statistical independence property of the samples of the received noisy codeword before reordering. Second, we incorporate the properties of this new statistic to derive the simplified error performance bound of the OSD algorithm for all order-I reprocessing. Finally, with the proposed approach, we obtain computationally simpler error performance bounds of the OSD than those proposed in literature for all length LBCs.

In this paper, semi-blind class of spectrum sensing algorithms, Energy Detection (ED) and Roy's Largest Root Test (RLRT), are considered under a typical flat fading channel scenario. The knowledge of the noise variance is imperative for the optimum performance of ED and RLRT. Unfortunately, the variation and unpredictability of noise variance is unavoidable. An idea of auxiliary noise variance estimation is introduced in order to cope with the absence of prior knowledge of the noise variance, thus a hybrid approach of signal detection is set forth for each considered method. The detection performance of the methods are derived and expressed by closed form analytical expressions. The impact of noise estimation accuracy on the the performance of ED and RLRT is compared in terms of Receiver Operating Characteristic (ROC) curves and performance curves (Probability of Detection/Miss-detection as a function of SNR by fixing the false alarm probability). It is concluded that optimum performance of ED and RLRT can be achieved even with the use of estimated noise variance by using a large number of slots for variance estimation. Finally, it is also found out that the impairment due to noise uncertainty is reduced on RLRT w. r. t. ED.

Hosting multiple radio technologies in computing devices is becoming increasingly feasible, common, and widely-adopted by stakeholders to offer better services. Packet-loss analysis is essential for characterizing and evaluating the behavior of wireless systems, and thereby assists the procedures of delivering the required of quality of service level. This paper presents a packet transmission model, based on a finite-state discrete-time Markov chain. The model is used to calculate the packet loss rates of wireless communications; it is applied to multi-radio devices, and considers different transitions probability distributions. Moreover, this paper presents simulation results of the developed model as well as experimental packet loss rate evaluation of multi-radio devices equipped with 6LoWPAN and Wi-Fi radio interfaces.

This paper presents a novel cognitive and cooperative tracking (CCT) approach based on extended Kalman filter (EKF) to localize mobile nodes in wireless networks. The proposed algorithm shows three important features: energy efficient, cognitive and cooperative. More specifically, the tracking algorithm adaptively adjusts the transmission power to optimize the energy consumption while meeting the required localization accuracy Paimposed by a generic application. Moreover, it adopts a self-learning scheme to track the time-variant environment's characteristics (e.g., range measurement noise) and use this knowledge to improve tracking performance. Finally, the algorithm exploits the cooperation among unknown nodes that leads to further improved performance and reduced power consumption. Simulation results show that the proposed CCT approach is able to improve positioning performance and meet the required accuracy Pawhile energy consumption is optimized.

We investigate and compare different options for updating the error correcting code currently used in space mission telecommand links. Taking as a reference the solutions recently emerged as the most promising ones, based on Low-Density Parity-Check codes, we explore the behavior of alternative schemes, based on parallel concatenated turbo codes and soft-decision decoded BCH codes. Our analysis shows that these further options can offer similar or even better performance.

This paper presents a novel ‘Energy Efficient Tracking’ (EET) algorithm that tries to meet the localization accuracy requirement, Pa, imposed by a generic location-based application while the energy consumption for ranging and communication is optimized. More specifically, given the set of range measurements performed by a mobile node with respect to its neighboring anchors (i.e., nodes whose exact positions are known a priori), the proposed EET algorithm selects, on the basis of the Cramér-Rao lower bound (CRLB), the closest set of anchors such that the resulting positioning error is lower than the required Pa. At the same time, the EET approach minimizes the average energy consumption by dynamically adapting the transmitted power, Pt, to be used in the next positioning estimation step. Based on time-of-arrival (TOA) estimation with ultra-wide bandwidth (UWB) nodes, the EET approach uses an Extended Kalman Filter (EKF) to track the mobile node's position. Simulation results show that the EET algorithm effectively reduces the energy consumption while the achieved positioning performance is almost identical to the one achieved by a classical EKF with fixed Pt, named ‘Energy Fixed Tracking’ (EFT) algorithm.

In this paper we propose a decentralized approach for cooperative signal detection, based on peer-to-peer collaboration among sensor nodes. The proposed method combines belief propagation, implemented in a distributed fashion through the exchange of local messages to and from neighboring nodes, with a Neyman-Pearson framework, that allows control over the false-alarm rate of each node. At the same time, nodes gradually learn their degree of correlation with neighbors, and clusters of nodes under homogeneous conditions are formed automatically. The performance of the resulting va Neyman-Pearson belief propagation" (NP-BP) algorithm is shown to be nearly equivalent to that of cooperative energy detection applied separately at each cluster. Thanks to its decentralized structure, NP-BP provides improved robustness, flexibility, and scalability compared to traditional, centralized schemes. In addition, its ability to adaptively form clusters makes the algorithm suitable for heterogeneous or time-varying radio environments.

In this paper we consider signal detection in cognitive radio networks, under a non-parametric, multi-sensor detection scenario, and compare the cases of known and unknown noise level. The analysis is focused on two eigenvalue-based methods, namely Roy's largest root test, which requires knowledge of the noise variance, and the generalized likelihood ratio test, which can be interpreted as a test of the largest eigenvalue vs. a maximum-likelihood estimate of the noise variance. The detection performance of the two considered methods is expressed by closed-form analytical formulas, shown to be accurate even for small number of sensors and samples. We then derive an expression of the gap between the two detectors in terms of the signal-to-noise ratio of the signal to be detected, and we identify critical settings where this gap is significant (e.g., low number of sensors and signal strength). Our results thus provide a measure of the impact of noise level knowledge and highlight the importance of accurate noise estimation.

This study addresses the problem of detecting signals characterised by a discontinuous presence in the detection window. This situation is of particular interest for applications of spectrum sensing in cognitive radio networks where, on the one hand, the sampling frequency may be limited by hardware capabilities and, on the other hand, the signal to be detected may be bursty with a burst duration comparable to or lower than the minimum sampling period. Modified expressions are derived for the detection probability of two popular detectors – energy detector and largest eigenvalue test – in the presence of discontinuous signals. The new expressions, adapted as a function of the signal occupancy rate, provide an accurate estimation of the detection probability under this scenario and allow a more careful selection of the decision threshold.

We propose a novel cooperative positioning algorithm that fuses information from satellites and terrestrial wireless systems, suitable for \acs{GPS}-challenged scenarios. The algorithm is fully distributed over an unstructured network, does not require a fusion center, does not rely on fixed terrestrial infrastructure, and is thus suitable for ad-hoc deployment. The proposed message passing algorithm, named \acf{H-SPAWN}, is described and analyzed. A novel parametric message representation is introduced, to reduce computational and communication overhead. Through simulation, we show that \ac{H-SPAWN} improves positioning availability and accuracy, and outperforms hybrid positioning algorithms based on conventional estimation techniques.

Cooperative positioning algorithms have been recently introduced to overcome the limitations of traditional methods, relying on GNSS or other terrestrial infrastructure. In particular, SPAWN (Sum- Product Algorithm over a Wireless Network) was shown to provide accurate position estimate even in challenged indoor environments, thanks to exchange of local information among peers. In this paper we extend the SPAWN framework by considering a hybrid scenario, where agents combine satellite and peer-to-peer terrestrial measurements. The novel hybrid SPAWN (H-SPAWN) approach allows increased availability and robustness compared to GNSS- only positioning in light and deep indoor scenarios, while keeping the advantages of a distributed implementation of the original SPAWN. A parametric message representation is proposed to reduce the communication overhead, and to improve the estimation accuracy. Simulation results show that the proposed solution outperforms traditional algorithms such as cooperative least squares and the extended Kalman filter.

Periodicities in a DNA sequence contain information about its function and structure. Frequency analysis can be used to reveal such periodicities. A definition of spectrum for DNA sequences is proposed, based on an entropy minimization criterion. It is shown that the properties of the proposed spectrum are those expected from the spectrum of a symbolic sequence. Applications to simulated and experimental DNA sequences are presented and compared against classical techniques to prove the effectiveness of the proposed method.

This paper addresses the problem of spectrum sensing for cognitive radio, in the case of a primary signal characterized by a discontinuous channel occupation within the considered sensing window. Under such conditions, the performance of two different energy detectors is investigated. The first one (energy average detector) decides whether the channel is free or busy on the basis of the energy sample average; the second one (energy threshold detector) performs a soft estimation of the channel occupation probability by comparing the energy samples with a proper threshold. For both the detectors, an analytical model is derived and validated through simulation, and the optimal decision threshold is found as a function of the primary signal parameters.

As a consequence of the diffusion of wireless systems operating in the 2.4 GHz ISM band, harmful interference among heterogeneous networks is becoming a serious issue for their performance. This paper is focused on IEEE 802.15.4 WSNs undergoing the interference of co-located IEEE 802.11b/g WLANs or Bluetooth piconets. On the basis of energy measurements carried out using a standard-compliant testbed, the statistics of the interfering energy are characterized for an extensive set of traffic conditions. Then the impact of each interference pattern onto a practical WSN application is analyzed in terms of packet loss rate at the application layer. The last part of the paper introduces a channel selection algorithm based on the estimation of the information-theoretic capacity of the considered channels.

Eigenvalue-based detection is an efficient signal detection technique, recently introduced in the Cognitive Radio context to guarantee a reliable identification of primary users. In this paper we contribute to the theoretical analysis of this detection scheme by deriving a mathematical expression for the probability of missed detection as a function of the number of cooperating receivers, the number of samples and the signal-to-noise ratio of the primary user. The analysis is referred to a detector using as test statistic the ratio between the largest and the smallest eigenvalue of the covariance matrix. Along with previous results on the probability of false alarm, this contribution completes the performance evaluation of this type of detector.

In this paper, a new variant of the McEliece cryptosystem, based on quasi-cyclic low-density parity-check (QC-LDPC) codes, is studied. In principle, such codes can substitute Goppa codes, originally used by McEliece; their adoption, however, is subject to cryptanalytic evaluation to ensure sufficient system robustness. The authors conclude that some families of QC-LDPC codes, based on circulant permutation matrices, are inapplicable in this context, due to security issues, whilst other codes, based on the "difference families" approach, can be able to ensure a good level of security against intrusions, even if very large lengths are needed.

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 paper, we study a new class of Low Density Parity Check codes, designed for satellite communications, and achieving both high spectral efficiency and large coding gain. Given a constant-envelope 8-PSK constellation, a generic linear binary code does not lead to a geometrically uniform Euclidean-space code. Low Density Parity Check codes over Z_8, the group of integers modulo 8, are considered. When applied to 8-PSK, they generate geometrically uniform Euclidean space codes: distance profile and word error probability are the same for each transmitted codeword. These properties highly simplify both design and analysis. Some insights on code design, encoding, decoding, and simulated performance are provided.

In this paper we study the ML error probability of serially concatenated schemes averaged over different interleaver ensembles. We prove asymptotic results when the interleaver length goes to infinity: differently from the parallel case, the choice of the ensemble can change the decreasing speed of error probability

An efficient algorithm for turbo code minimum distance computation is essential for estimating their performance in the error floor region without resorting to long simulations. Recently, Berrou et al. [1] introduced the innovative error impulse method, based on iterative decoding. In this paper, we present another iterative algorithm for turbo code distance computation. It is based on the decoding of an all-zero received sequence, performed on half of the code: the subset containing all the codewords with a 1 in a given coordinate i. By shifting i along the whole codeword length, the algorithm estimates the code minimum distance and its multiplicity with limited complexity O(k2), k being the interleaver length. Due to the sub-optimality of iterative decoding, the algorithm can produce false results. Investigation by comparison with the exact constrained subcode algorithm [2] shows the all-zero algorithm possesses an excellent reliability.

We study product codes based on extended Hamming codes. We focus on their performance at low error rates, which are important for wireless multimedia applications. We present the basis and a complete set of techniques which allows one to analytically evaluate this performance without resorting to extremely long simulations. We present new theoretical results concerning the popular approximation where the bit error rate is nearly equal to the frame error rate times the ratio of the minimum distance to the codeword length. We prove that: 1) binary codes with a transitive automorphism group satisfy this approximation with equality; and 2) extended Hamming product codes belong to this class. Closed-form expressions for their dominant multiplicity values are derived. Analytical curves are plotted, discussed, and validated by comparison with iterative decoding. This analytical approach is then extended to both shortened and punctured codes, which are important for practical design. The first case is solved by applying the extended MacWilliams identity to the dual codes. For punctured codes, we present a new analytical approach for estimating their average performance using a "random" puncturer.

The well-known uniform error property for signal constellations and codes is extended to encompass information bits. We introduce a class of binary labelings for signal constellations, called bit geometrically uniform (BGU) labelings, for which the uniform bit error property holds, i.e., the bit error probability does not depend on the transmitted signal. Strong connections between the symmetries of constellations and binary Hamming spaces are involved. For block-coded modulation (BCM) and trellis-coded modulation (TCM) Euclidean-space codes, BGU encoders are introduced and studied. The properties of BGU encoders prove quite useful for the analysis and design of codes aimed at minimizing the bit, rather than symbol, error probability. Applications to the analysis and the design of serially concatenated trellis codes are presented, together with a case study which realizes a spectral efficiency of 2 b/s/Hz.

We present a thorough comparison among three alternative solutions for the transmission of medium-high speed data over mobile telecommunication systems with high quality of service. They are based on concatenated codes with interleavers, the first two using the parallel concatenation known as turbo code, and the third the serial concatenation recently proposed. The comparison between the two alternatives has been based on the computation of the free distance of the resulting codes, and on extensive simulations over additive Gaussian noise (AWGN) and correlated multipath fading channels.

Turbo codes have excellent performance at low and medium signal-to-noise ratios (SNR) very close to the Shannon limit, and are at the basis of their success. However, a turbo code performance curve can change its slope at high SNR if the code free distance is small. This "error floor" phenomenon is not acceptable for applications requiring very low values of bit error rates. A knowledge of the free distance and its multiplicity allows one to analytically estimate the error floor. An algorithm for computing the turbo code free distance, based on the notion of constrained subcodes, is described. Some considerations on the free distance distribution of turbo codes with growing interleaver length are also provided.

We present a new algorithm for computing the free distance d/sub free/ of parallel and serially concatenated codes with interleavers, the parameter that dominates the code performance at very high signal-to-noise ratios (SNRs). The knowledge of d/sub free/ allows one to analytically estimate the error floor, which may prevent the use of concatenated codes in applications requiring very low error rates. The algorithm is based on the new notion of constrained subcodes, and permits the computation of large distances for large interleavers without a constraint on the input sequence weight (e.g., up to d/sub free/=40 for a rate-1/3 turbo code with interleaver length N=3568). Applications to practical cases of relevant interest, i.e., (1) the new Consultative Committee for Space Data Systems (CCSDS) standard for deep-space telemetry and (2) the new UMTS/3GPP standard for third-generation personal communications, are presented for the first time. Other related aspects, like a study on the free distance distribution of turbo codes with small/medium interleaver length, and a comparison between parallel and serial concatenation behavior, are also discussed.

In this paper, the basic theory of interleavers is revisited in a semi-tutorial manner, and extended to encompass noncausal interleavers. The parameters that characterize the interleaver behavior (like delay, latency, and period) are clearly defined. The input-output interleaver code is introduced and its complexity studied. Connections among various interleaver parameters are explored. The classes of convolutional and block interleavers are considered, and their practical implementation discussed. The trellis complexity of turbo codes is tied to the complexity of the constituent interleaver. A procedure of complexity reduction by coordinate permutation is also presented, together with some examples of its application.

A turbo code has been included in the new Consultative Committee for Space Data Systems (CCSDS) channel coding standard for space telemetry. Many future missions with critical link budgets will benefit from its large coding gain. In this paper, the properties of this turbo code are analyzed for symbol synchronization recovery, where the transition density is essential. Key parameters like transition/symbol probability and run-length distribution are studied and compared against practical requirements. Critical working conditions are considered separately and discussed. It is shown that, thanks to the interleaver action, turbo-encoded sequences have very good properties in terms of randomness.

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the "best" recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error probability performances of some turbo codes using them.

For pt.I see ibid., vol.42, no.3, p.751-65 (1996). In Part I, general results on rotationally invariant codes and encoders were derived assuming no algebraic structure. In Part II, trellis codes based on group systems are considered as a special case for which code and encoder constructions are particularly simple. Rotational invariance is expressed as an algebraic constraint on a group code, and algebraic constructions are found for both "absorbed precoder" encoders and for encoders with separate differential precoders. Finally, the various encoder forms used to achieve rotational invariance are compared based on their performance on an AWGN channel.

We present a theoretical framework for rotational invariance of trellis codes. The distinction between codes and encoders plays a pivotal role. Necessary and sufficient conditions for rotational invariance are derived under general assumptions, and a construction is presented that obtains a rotationally invariant encoder for almost any rotationally invariant code, independent of the code's algebraic structure. Encoders that use a differential precoder are considered as a separate case, where a system-theoretic characterization of precoding is used to find two alternative and slightly less general encoder constructions.

New geometrically uniform trellis codes over multidimensional unbalanced 4-, 8-, and 16-PSK constellations, obtained with the group code approach, are presented. They improve by up to 1.25 dB the asymptotic performance of the best known trellis codes over multidimensional balanced PSK. To check their "optimality", an upper bound on the free distance of group trellis codes is derived. Some of the new codes achieve the largest obtainable free distance, and several others are close to the bound. Exploiting the symmetry properties of the codes, curves of tight upper bounds to the error probability are also presented.

The theory of group codes simplifies the construction of good rotationally invariant trellis codes for the additive white Gaussian noise channel. New geometrically uniform trellis codes, with spectral efficiency 3 bits/2D, based on multidimensional L/spl times/16-PSK constellations in 4, 6, and 8 dimensions, obtained by group trellis codes over nonbinary groups of the kind Z/sub 16//sup L/, are presented. Most of the codes improve, in terms of asymptotic gain and rotational invariance, the best codes known so far in the literature.>

The theory of group codes has been shown to be a useful starting point for the construction of good geometrically uniform codes. In this paper we study the problem of building multilevel group codes, i.e., codes obtained combining separate coding at different levels in such a way that the resulting code is a group code. A construction leading to multilevel group codes for semi-direct and direct products is illustrated. The codes that can be obtained in this way are identified. New geometrically uniform Euclidean-space codes obtained from multilevel codes over abelian and nonabelian groups are presented.>

The theory of geometrically uniform signal sets and codes over groups is applied to the case of L/spl times/MPSK constellations. Conditions for rotational invariance of group codes are discussed. The tables of geometrically uniform partitions found in Benedetto et al. (1993) are used to construct good geometrically uniform trellis codes over nonbinary Abelian groups. The present authors consider L/spl times/4PSK and L/spl times/8PSK constellations used to transmit information rates of 1 and 2 bit/two dimensions, respectively; and present tables of good codes over generating groups (Z4)/sup L/ and (Z8)/sup L/,for L ranging from 1 to 4. In most cases, they improve the tables of codes known so far. Moreover, the geometrical uniformity of codes allows a very easy performance evaluation, so that the authors also present a complete set of curves of error event probability for the obtained codes.>

The theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK (phase shift keying) constellations. The symmetry group of an L*MPSK (M-ary PSK) constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L*MPSK (M=4,8,16 and L=1,2,3,4) constellations are found, which present good characteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes.>