The ability to collect via satellite status updates from vessels is a key enabler for a number of maritime applications. In these settings, maintaining an up to date perception of the state of a ship is paramount, yet challenging due to the large number of vessels in the satellite coverage. To tackle the problem, we study the impact of different transmission policies, capturing system performance in terms of age of incorrect information (AoII). Modelling channel contention as slotted ALOHA, we consider a benchmark inspired by the de-facto AIS/VDES transmission standard in which ships periodically report their state, and compare it to solutions that adapt the transmission probability to current ship-to-satellite channel conditions and to relevant changes in the ship state. By means of a Markovian analysis, we derive closed-form expressions for the average AoII, and discuss the performance in settings of representative of practical conditions. The potential of solutions that tie channel access to the evolution of the process to be tracked clearly emerges. The work aims at stimulating further research in this domain, having in mind future enhancements of ship communication standards.

We investigate the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. We let the devices adjust the transmission probabilities based on their current battery level. Using a Markovian approach, we derive analytically the average AoI. We further provide an approximate analysis for accurate and easy-to-compute approximations of both the average AoI and the age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. We also analyze the average throughput. Via numerical results, we investigate two baseline strategies: transmit a new update whenever possible to exploit every opportunity to reduce the AoI, and transmit only when sufficient energy is available to increase the chance of successful decoding. The two strategies are beneficial for low and high update-generation rates, respectively. We show that an optimized policy that balances the two strategies outperforms them significantly in terms of both AoI metrics and throughput. Finally, we show the benefit of decoding multiple packets in a slot using successive interference cancellation and adapting the transmission probability based on both the current battery level and the time elapsed since the last transmission.

We examine the age of information (AoI) of a status update system that incorporates energy harvesting and uses the slotted ALOHA protocol. We derive analytically the average AoI and the probability that the AoI exceeds a given threshold. Via numerical results, we investigate two strategies to minimize the age of information (AoI): transmitting a new update whenever possible to exploit every chance to reduce the AoI, and transmitting only when sufficient energy is available to increase the chance of successful delivery. The two strategies are beneficial for low and high update generation rates, respectively. However, an optimized approach that balances the two strategies outperforms them significantly in terms of both AoI and throughput.

We consider a set reconciliation setting in which two parties hold similar sets that they would like to reconcile. In particular, we focus on set reconciliation based on invertible Bloom lookup tables (IBLTs), a probabilistic data structure inspired by Bloom filters. IBLT-based set reconciliation schemes have the advantage of exhibiting low computational complexity, however, the schemes available in the literature are known to be far from optimal in terms of communication complexity (overhead). The inefficiency of IBLT-based set reconciliation can be attributed to two facts. First, it requires an estimate of the cardinality of the difference between the sets, which implies an increase in overhead. Second, to cope with uncertainties in the estimation of the cardinality of the set difference, IBLT schemes in the literature oversize the data structures, thus further increasing the overhead. In this work, we present a novel IBLT-based set reconciliation protocol that does not require estimating the cardinality of the set difference. The proposed scheme relies on what we termed multi-edge-type (MET) IBLTs. The simulation results illustrate that the novel scheme outperforms state-of-the-art IBLT-based approaches to set reconciliation in terms of communication cost, i.e., in terms of the number of bits to be exchanged.

We study the dynamic behavior of frameless ALOHA, both in terms of throughput and age of information (AoI). In particular, differently from previous studies, our analysis accounts for the fact that the number of terminals contending the channel may vary over time, as a function of the duration of the previous contention period. The stability of the protocol is analyzed via a drift analysis, which allows us to determine the presence of stable and unstable equilibrium points. We also provide an exact characterization of the AoI performance, through which we determine the impact of some key protocol parameters, such as the maximum length of the contention period, on the average AoI. Specifically, we show that configurations of parameters that maximize the throughput may result in a degradation of the AoI performance.

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.

This paper presents a finite length analysis of multi-slot type frameless ALOHA based on a dynamic programming approach. The analysis is exact, but its evaluation is only feasible for moderate number of users due to the computational complexity. The analysis is then extended to derive continuous approximations of its key parameters, which, apart from providing an insight into the decoding process, make it possible to estimate the packet error rate with very low computational complexity. Finally, a feedback scheme is presented in which the slot access scheme is dynamically adapted according to the approximate analysis in order to minimize the packet error rate. The results indicate that the introduction of feedback can substantially improve the performance of frameless ALOHA.

We present a novel decoding algorithm for q-ary low-density parity- check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature.

One of the novelties brought by 5G is that wireless system design has increasingly turned its focus on guaranteeing reliability and latency. This shifts the design objective of random access protocols from throughput optimization towards constraints based on reliability and latency. For this purpose, we use frameless ALOHA, which relies on successive interference cancellation (SIC), and derive its exact finite-length analysis of the statistics of the unresolved users (reliability) as a function of the contention period length (latency). The presented analysis can be used to derive the reliability-latency guarantees. We also optimize the scheme parameters in order to maximize the reliability within a given latency. Our approach represents an important step towards the general area of design and analysis of access protocols with reliability-latency guarantees.

In this paper, we analyze Luby transform (LT) and Raptor codes under inactivation decoding. A first-order analysis is introduced, which provides the expected number of inactivations for an LT code, as a function of the output distribution, the number of input symbols, and the decoding overhead. The analysis is then extended to the calculation of the distribution of the number of inactivations. In both cases, random inactivation is assumed. The developed analytical tools are then exploited to design LT and Raptor codes, enabling a tight control on the decoding complexity versus failure probability tradeoff. The accuracy of the approach is confirmed by numerical simulations.

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.

We present a simple model of inactivation decoding for LT codes which can be used to estimate the decoding complexity as a function of the LT code degree distribution. The model is shown to be accurate in variety of settings of practical importance. The proposed method allows to perform a numerical optimization on the degree distribution of a LT code aiming at minimizing the number of inactivations required for decoding.

The potential of Time Interference Alignment is investigated in this work, with particular reference to the attainable degrees of freedom. The K-user interference channel is considered, in which transmitters and receivers are placed randomly in a Euclidean space. A model for long delay networks is introduced and the degrees of freedom for different cases (with and without transmitter delay coordination) are evaluated. It is shown how time interference alignment can provide more degrees of freedom than TDMA when the transmitters jointly coordinate their transmission delay and the number of pairs is K ≥ 5. Closed form expressions are derived for several cases of interest which provide insight and useful predictions. This work is concluded with an investigation of the achievable degrees of freedom for multi-satellite networks, where it is shown that the results obtained under several assumptions do predict accurately the degrees of freedom in a real setting.

The performance and the decoding complexity of a novel coding scheme based on the concatenation of maximum distance separable (MDS) codes and linear random fountain codes are investigated. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of a MDS code and a linear random fountain code, both operating on the same finite field. Upper and lower bounds on the decoding failure probability under maximum-likelihood (ML) decoding are developed. It is shown how, for example, the concatenation of a (15,10) Reed-Solomon (RS) code and a linear random fountain code over a finite field of order 16, {F}_{16}, brings to a decoding failure probability 4 orders of magnitude lower than the one of a linear random fountain code for the same receiver overhead in a channel with a erasure probability of ε=5\cdot10^{-2}. It is illustrated how the performance of the novel scheme approaches that of an idealized fountain code for higher-order fields and moderate erasure probabilities. An efficient decoding algorithm is developed for the case of a (generalized) RS code.

The necessity of accurate channel estimation for Successive and Parallel Interference Cancellation is well known. Iterative channel estimation and channel decoding (for instance by means of the Expectation-Maximization algorithm) is particularly important for these multiuser detection schemes in the presence of time varying channels, where a high density of pilots is necessary to track the channel. This paper designs a method to analytically derive a weighting factor a, necessary to improve the efficiency of interference cancellation in the presence of poor channel estimates. Moreover, this weighting factor effectively mitigates the presence of incorrect decisions at the output of the channel decoder. The analysis provides insight into the properties of such interference cancellation scheme and the proposed approach significantly increases the effectiveness of Successive Interference Cancellation under the presence of channel estimation errors, which leads to gains of up to 3 dB.

Time Interference Alignment is a flavor of Interference Alignment that increases the network capacity by suitably staggering the transmission delays of the senders. In this work the analysis of the existing literature is generalized and the focus is on the computation of the dof for networks with randomly placed users in a n-dimensional Euclidean space. In the basic case without coordination among the transmitters analytical expressions of the sum dof can be derived. If the transmit delays are coordinated, in 20% of the cases time Interference Alignment yields additional dof with respect to orthogonal access schemes. The potential capacity improvements for satellite networks are also investigated.

Accurate channel models are of high importance for the design of upcoming mobile satellite systems. Nowadays most of the models for the land mobile satellite channel (LMSC) are based on Markov chains and rely on measurement data, rather than on pure theoretical considerations. A key problem lies in the determination of the model parameters out of the observed data. In this work we face the issue of state identification of the underlying Markov model whose model parameters are a priori unknown. This can be seen as a hiddem Markov model (HMM) problem. For finding the maximum likelihood (ML) estimates of such model parameters the Baum-Welch (BW) algorithm is adapted} to the context of channel modeling. Numerical results on test data sequences reveal the capabilities of the proposed algorithm. Results on real measurement data are finally presented.

The performance of a novel fountain coding scheme based on maximum distance separable (MDS) codes constructed over Galois fields of order q ≥ 2 is investigated. Upper and lower bounds on the decoding failure probability under maximum likelihood decoding are developed. Differently from Raptor codes (which are based on a serial concatenation of a high-rate outer block code, and an inner Luby-transform code), the proposed coding scheme can be seen as a parallel concatenation of an outer MDS code and an inner random linear fountain code, both operating on the same Galois field. A performance assessment is performed on the gain provided by MDS based fountain coding over linear random fountain coding in terms of decoding failure probability vs. overhead. It is shown how, for example, the concatenation of a (15,10) Reed-Solomon code and a linear random fountain code over F16brings to a decoding failure probability 4 orders of magnitude lower than the linear random fountain code for the same overhead in a channel with a packet loss probability of ϵ = 5 · 10-2. Moreover, it is illustrated how the performance of the concatenated fountain code approaches that of an idealized fountain code for higher-order Galois fields and moderate packet loss probabilities. The scheme introduced is of special interest for the distribution of data using small block sizes.