We analyze the trade-off between the undetected error probability (i.e., the probability that the channel decoder outputs an erroneous message without detecting the error) and the total error probability in the short blocklength regime. We address the problem by developing two new finite blocklength achievability bounds, which we use to benchmark the performance of two coding schemes based on polar codes with outer cyclic redundancy check (CRC) codes—also referred to as CRC-aided (CA) polar codes. The first bound is obtained by considering an outer detection code, whereas the second bound relies on a threshold test applied to the generalized information density. Similarly, in the first CA polar code scheme, we reserve a fraction of the outer CRC parity bits for error detection, whereas in the second scheme, we apply a threshold test (specifically, Forney’s optimal rule) to the output of the successive cancellation list decoder. Numerical simulations performed on the binary-input AWGN channel reveal that, in the short-blocklength regime, the threshold-based approach is superior to the CRC-based approach, both in terms of bounds and performance of CA polar code schemes. We also consider the case of decoding with noisy channel-state information, which leads to a mismatched decoding setting. Our results illustrate that, differently from the previous case, in this scenario, the CRC-based approach outperforms the threshold-based approach, which is more sensitive to the mismatch.

Rate-adaptive MacKay-Neal (MN) codes based on protographs are analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code. The performance achievable by the resulting code structure, that is nonlinear, is studied by means of an equivalent communication model that reduces the problem to the analysis of the inner (linear) LDPC code with transmission that takes place in parallel over the communication channel, and over a suitably defined binary symmetric channel. A density evolution analysis of protograph MN code ensembles is outlined, and it is complemented by an error floor analysis that relies on the derivation of the average input-output weight distribution of the inner LDPC code ensemble. Conditions on the shape of the normalized logarithmic asymptotic input-output weight distribution are defined, which allow discarding code ensembles with bad error floor properties during the code design phase. Examples of code designs are provided, showing how the use of a single LDPC code ensemble allows operating within 1 dB from the Shannon limit over a wide range of code rates, where the code rate is selected by tuning the DM parameters. By enabling rate flexibility with a constant blocklength, and with a fixed LDPC code as inner code, the construction provides an appealing solution for very high-throughput wireless (optical) links that employ binary-input modulations.

The rapid growth of loT applications in which a large number of devices need to deliver information to a central monitor in a timely fashion has focused attention on the age of information performance of random access protocols. This paper provides the first study of one such strategy, Frame Asynchronous Coded Slotted ALOHA (FA-CSA) Through de-tailed network simulations, we compare its performance to a benchmark in the field, namely Irregular Repetition Slotted ALOHA (IRSA). The results show that FA-CSA achieves fresher information on average compared to IRSA, especially at low to moderate channel loads. Additionally, the study sheds light on the implications of asynchrony in access protocols, particularly in the context of loT applications with strict information freshness requirements.

This article is a tutorial introduction to the field of unsourced multiple access (UMAC) protocols. We first provide a historical survey of the evolution of random access protocols, focusing specifically on the case in which uncoordinated users share a wireless broadcasting medium. Next, we highlight the change of perspective originated by the UMAC model, in which the physical and medium access layer’s protocols cooperate, thus reframing random access as a novel coding-theoretic problem. By now, a large variety of UMAC protocols (codes) emerged, necessitating a certain classification that we indeed propose here. Although some random access schemes require a radical change of the physical layer, others can be implemented with minimal changes to existing industry standards. As an example, we discuss a simple modification to the 5G New Radio (5GNR) Release 16 random access channel that builds on the UMAC theory and that dramatically improves energy efficiency for systems with even moderate number of simultaneous users (e.g., 5–10-dB gain for 10–50 users) and also enables handling of high number of users, something completely out of reach of the state of the art.

Error correction coding (i.e., channel coding) is a key ingredient of any digital communications system. In mobile wireless communications, channel codes have evolved from simple convolutional codes in Global System for Mobile Communications (GSM) (2G), parallel concatenated (turbo) codes in Universal Mobile Telecommunications Service (UMTS) (3G), and long-term evolution (LTE) (4G), to carefully designed multirate/multilength low-density parity-check (LDPC) codes in 5G, combined with polar codes for short messages on the synchronization channel. Based on this rich history, and by accounting for the technological advances in very large-scale integration, this article will outline some recent trends in channel coding as they may be applied in 6G systems, ranging from novel approaches for short blocklengths such as automorphism ensemble decoding, via ideas of coding for multiple access, to concepts for unified coding schemes that may simplify encoding/decoding hardware at competitive error-correcting performance.

Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their error-correction performance is studied over two channel models, in the Lee metric. The first channel model is a discrete memoryless channel, whereas in the second channel model an error vector is drawn uniformly at random from all vectors of a fixed Lee weight. It is known that the two channel laws coincide in the asymptotic regime, meaning that their marginal distributions match. For both channel models, we derive upper bounds on the block error probability in terms of a random coding union bound as well as sphere packing bounds that make use of the marginal distribution of the considered channels. We estimate the decoding error probability of regular LDPC code ensembles over the channels using the marginal distribution and determining the expected Lee weight distribution of a random LDPC code over a finite integer ring. By means of density evolution and finite-length simulations, we estimate the error-correction performance of selected LDPC code ensembles under belief propagation decoding and a low-complexity symbol message passing decoding algorithm and compare the performances. The analysis developed in this paper may serve to design regular low-density parity-check (LDPC) codes over integer residue rings for storage and cryptographic application.

We study a system in which terminals monitoring two-state Markov sources communicate towards a common receiver over a slotted ALOHA random access channel. We analyze the system performance in terms of state estimation entropy (SEE), which measures the uncertainty at the receiver about the sources’ state. Two channel access strategies are studied, one that is influenced by the source behaviour and one that is independent of it. By means of density evolution analysis, we show that the former can yield a remarkable reduction of the SEE.

A class of rate-adaptive protograph MacKay-Neal (MN) codes is introduced and analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code, whose base matrix is optimized via density evolution analysis to approach the Shannon limit of the binary-input additive white Gaussian noise (biAWGN) channel over a given range of code rates. The density evolution analysis is complemented by finite-length simulations, and by a study of the error floor performance.

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.

The finite-length trapping and (elementary) absorbing set enumerators for nonbinary protograph-based LDPC code ensembles are derived. Both constrained and unconstrained edge labeling approaches are considered. The normalized logarithmic asymptotic distributions of trapping and (elementary) absorbing sets are obtained through an efficient method that requires solving a system of equations. Using these results, the asymptotic distributions of trapping and (elementary) absorbing sets are evaluated for some example nonbinary protograph-based LDPC code ensembles.

The performance of generalized low-density parity-check (GLDPC) codes under binary and ternary message passing decoding (BMP/TMP) is analyzed from a density evolution (DE) perspective. At the check nodes, two types of local decoders are considered, namely optimum a-posteriori probability (APP) soft-input soft-output decoding, and bounded distance decoding (BDD). The purpose is to shed light on the performance loss incurred by BMP and TMP decoding of GLDPC codes with respect to unquantized belief propagation (BP) decoding. A DE analysis for irregular code ensembles is developed for all the algorithms, which allows obtaining the scaling coefficients needed for the variable node operation of BMP and TMP decoders. The stability analysis for the case of bounded distance decoding at the check nodes is derived. The asymptotic DE analysis is confirmed by the finite-length simulation results. For the codes analyzed in this paper, which rely on extended Hamming component codes, the study shows that under BMP decoding, BDD at the check nodes yields almost the same performance as optimum APP check node processing, while under TMP decoding the loss incurred by the sub-optimum BDD at check nodes is within 0.7 dB, when compared with APP decoding at the check nodes.

A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within 0.7 dB from the random coding union bound are provided.

This paper presents the implementation and experimental evaluation of a short-packet physical-layer network coding (PNC) system. Implementation of short-packet PNC systems is challenging. First, short packets may have only a few pilot symbols for synchronization and channel estimation purposes. Increasing the number of pilots increases the overhead; decreasing the number of pilots, on the other hand, degrades the packet error rate performance. Second, many short-packet systems are meant for applications with very stringent delay requirements. Employing advanced but complex PNC channel decoding may result in unacceptable delay due to the processing delay. This work presents a low-complexity and low-overhead physical-layer design of OFDM-based short-packet PNC systems, implemented over the software-defined radio platform. Our design makes use of only a small number of pilots (without separate OFDM preamble symbols) to address issues such as slot synchronization, packet detection, carrier frequency offsets, and mismatched channel state information. Our design employs reduced-complexity XOR channel decoding based code-aided parameter estimation (that includes synchronization and channel estimation) to compensate for the limitations imposed by having a small number of pilots. This is the first demonstration that provides a practical framework for applying PNC to short-packet communications.

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distributions of the two channels coincide, in the limit of large block length. Random coding union bounds on the block error probability are derived for both channels. Moreover, the performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm and it is compared to the derived bounds.

Wireless random access protocols are attracting a revived research interest as a simple yet effective solution for machine-type communications. In the quest to improve reliability and spectral efficiency of such schemes, the use of multiple receivers has recently emerged as a promising option. We study the potential of this approach considering a population of users that transmit data packets following a simple slotted ALOHA policy to a set of uncoordinated relays (phase-1). These, in turn, independently forward - part of - what decoded towards a collecting sink (phase-2). For an on-off fading channel model, we provide exact expressions for phase-1 throughput and packet loss rate for an arbitrary number of relays, characterising the benefits of multi-receiver schemes. Moreover, a lower bound on the minimum amount of phase-2 resources needed to deliver all information collected at the relays is provided. The bound is proven to be achievable via random linear coding when no constraints in terms of latency are set, with an overhead that approaches zero with the inverse of the packet length. We complement our study discussing a family of simple forwarding policies that require no packet-level coding, and optimising their performance based on the amount of available phase-2 resources. The behaviour of both random linear coding and simplified policies is also characterised when receivers are equipped with finite buffers, revealing non-trivial tradeoffs.

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.

The finite-length absorbing set enumerators for non-binary protograph based low-density parity-check (LDPC) ensembles are derived. An efficient method for the evaluation of the asymptotic absorbing set distributions is presented and evaluated.

This paper explores the application of physical-layer network coding (PNC) for short-packet transmissions. PNC can potentially reduce the communication delay in relay-assisted wireless networks and can thus be instrumental in realizing short-packet communication systems with stringent delay requirements. In this work, first, we first derive an achievability bound for channel-coded short-packet PNC systems. Based on the random-coding error-exponent, the bound serves as a benchmark for short-packet PNC operating with traditional preamble-aided channel estimation and XOR channel decoding. Second, we design a blind channel estimation algorithm and a code-aided channel estimation algorithm for short-packet PNC systems. Both outperform the traditional preamble-aided channel estimation for PNC systems operating with mismatched channel-state-information. As a case study, we compare the three algorithms for packets of 128 symbols over a two-way relay channel. The results show that the blind algorithm outperforms the code-aided algorithm and preamble-aided algorithm by almost 0.2 and 1.5 dB respectively. Furthermore, the blind algorithm achieves the target packet error rate of 10-4within 0.5 dB of the random coding bound of an imaginary system in which perfect channel-state-information is available at the relay at no cost (i.e., channel estimation is not required in the imaginary system). The bound and the algorithms give us a fundamental framework for applying PNC to short-packet transmissions.

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.

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.

This paper considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK)-modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with the Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and the decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1.2 dB from finite-length bounds is obtained, down to a CER of 10-3.

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no a priori channel state information available at the transmitter or at the receiver. An upper bound built upon the min-max converse is compared with two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver and the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, in Rayleigh fading, for the case when a coded packet of 168 symbols is transmitted using a channel code of rate 0.48-bits/channel use, over a block-fading channel with block size equal to eight symbols, PAT requires an additional 1.2 dB of energy per information bit to achieve a packet error probability of 10-3compared with a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered-statistics decoding, whose performance is close (1-dB gap at 10-3packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.

In this paper, we provide an analysis of the performance of concatenation of polar codes with outer cyclic redundancy check (CRC) codes, separated by an interleaver, in the short and moderate block length regimes. The analysis addresses maximum likelihood decoding as a proxy to the code performance under successive cancellation list decoding. The analysis is carried out by introducing the concatenated polar code (CPC) ensembles, whose distance properties can be analyzed (for sufficiently short block lengths) by means of the uniform interleaver approach. At moderate block lengths, we resort to the Monte Carlo simulations. Results show that if the inner polar code possesses a low minimum distance and the outer CRC code has a sufficiently large amount of redundancy, then the choice of the outer code generator polynomial and the interleaver may yield to a large variability in the performance of the resulting CPC.

We propose a novel binary message passing decoding algorithm for product-like codes based on bounded distance decoding (BDD) of the component codes. The algorithm, dubbed iterative BDD with scaled reliability (iBDD-SR), exploits the channel reliabilities and is therefore soft in nature. However, the messages exchanged by the component decoders are binary (hard) messages, which significantly reduces the decoder data flow. The exchanged binary messages are obtained by combining the channel reliability with the BDD decoder output reliabilities, properly conveyed by a scaling factor applied to the BDD decisions. We perform a density evolution analysis for generalized low-density parity-check (GLDPC) code ensembles and spatially coupled GLDPC code ensembles, from which the scaling factors of the iBDD-SR for product and staircase codes, respectively, can be obtained. For the white additive Gaussian noise channel, we show performance gains up to 0.29 dB and 0.31 dB for product and staircase codes compared to conventional iterative BDD (iBDD) with the same decoder data flow. Furthermore, we show that iBDD-SR approaches the performance of ideal iBDD that prevents miscorrections.

Future multi-terminal communication networks such as machine-to-machine, telecommand and remote control communication systems will be based on short-packet transmissions. Physical-layer network coding (PNC) in such multi-terminal communication systems can potentially enhance network throughput and reduce communication latency. For practical PNC systems, preambles are contained in transmissions for accurate estimation of the channel-state-information (CSI). Identifying good preamble-length regimes, however, is critical for good performance of short-packet PNC systems. Long preambles for short packets reduce spectral efficiency. On the other hand, short preambles compromise accuracy of estimated CSI, leading to sub-par packet error rate (PER) performance. This paper studies the impact of preamble length on the performance of short-packet PNC systems. Specifically, we use random coding bound to quantify PER of channel-coded mismatched-CSI PNC systems and identify the preamble-length regime that achieves the target PER with minimum Eb/No. As an example, we consider a simple yet practically relevant setup of a BPSK modulated PNC system in a two-way relay channel operating with short packets of 128 symbols. Our results show that a preamble of 20 to 30 symbols provides the minimum PER for a wide range of Eb/N0and achieves a target PER of 10-3with minimum Eb/No.

This work shows how non-binary low-density parity-check codes over GF(2^p) can be combined with probabilistic amplitude shaping (PAS) (Böcherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.

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.

In this paper, we study digital transmission over an additive white Gaussian noise (AWGN) channel with mary differential phase-shift keying (DPSK) modulation in the presence of phase noise. At the receiver side, non-coherent iterative detection and decoding is assumed. We present a non-binary low-density generator matrix (LDGM) code design which is suitable for both coherent and non-coherent channels. The code construction is strongly related to the one of non-binary irregular repeat-accumulate (IRA) low-density parity-check (LDPC) codes.

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.

We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding.

In this paper, we study of the performance of the concatenation of a short polar code with an outer binary linear block code from a distance spectrum viewpoint. Our analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is defined placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, to attain low error floors. We also investigate the performance of a number of randomly chosen interleavers, with the aim to discuss the dispersion around the ensemble.

In this work, we derive the random coding error exponent for the uplink phase of a two-way relay system where physical layer network coding (PNC) is employed. The error exponent is derived for the practical (yet sub-optimum) XOR channel decoding setting. We show that the random coding error exponent under optimum (i.e., maximum likelihood) PNC channel decoding can be achieved even under the sub-optimal XOR channel decoding. The derived achievability bounds provide us with valuable insight and can be used as a benchmark for the performance of practical channel-coded PNC systems employing low complexity decoders when finite-length codewords are used.

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.

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.

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation with probabilistic shaping is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform inputs and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63 and 0.69 dB of 1/2 log2(1 + SNR) for a target frame error rate of 10-3at spectral 1 efficiencies of 1.38 and 4.25 bits/channel use, respectively.

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.

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels are constructed and used for code design. The constructed codes perform as good as multi-edge type codes of Zhang and Kschischang (2013). For 64-ASK with probabilistic shaping, a blocklength 64800 code is constructed that operates within 0.69 dB of 1 over 2 log2(1 + SNR) at a spectral efficiency of 4.25 bits/channel use and a frame error rate of 10-3.

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.

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 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.

This work aims at introducing two novel packet retransmission techniques for reliable multicast in the framework of Instantly Decodable Network Coding (IDNC). These methods are suitable for order- and delay-sensitive applications, where some information is of high importance for an earlier gain at the receiver's side. We introduce hence an Unequal Error Protection (UEP) scheme, showing by simulations that the Quality of Experience (QoE) for the end-users is improved even without complex encoding and decoding.

We introduce a class of structured (protograph-based) doubly generalized low-density parity-check (DGLDPC) codes. The proposed class leads to quasi-cyclic codes for which efficient encoder and decoder implementations are possible. In particular, we illustrate that on the additive white Gaussian noise (AWGN) channel, the introduced structured DGLDPC codes do not lose in performance with respect to unstructured DGLDPC codes. Furthermore, a sufficient condition on the code graph is derived, which allows unveiling the quasi-cyclic nature of the designed codes.

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.

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.

In many applications erasure correcting codes are used to recover packet losses at high protocol stack layers. The objects (e.g. files) to be transmitted often have variable sizes, resulting in a variable number of packets to be encoded by the packet-level encoder. In this paper, algorithms for the (on-line) flexible design of parity-check matrices for irregular-repeat-accumulate codes are investigated. The proposed algorithms allow designing in fast manner parity-check matrices that are suitable for low-complexity maximum-likelihood decoding. The code ensembles generated by the algorithms are analyzed via extrinsic information transfer charts. Numerical results show how the designed codes can attain codeword error rates as low as 10-5without appreciable losses w.r.t. the performance of idealized maximum-distance separable codes. Finally, we apply the proposed codes to the upcoming aeronautical communication standard, showing large performance improvements and proving the efficiency and the flexibility of the developed method.

A novel protograph-based construction of low-density parity-check (LDPC) codes for the relay channel is proposed, which provides an enhanced unequal error protection property named unequal diversity. The focus is on quasi-static fading channels and on the high-code-rate (R>1/2) regimes, for which (according to the Singleton bound) no full diversity can be achieved. In the proposed construction, some nodes (and the corresponding codeword fragment) associated with the code graph enjoy the diversity provided by the relay, whereas the remaining nodes do not experience any diversity. The proposed approach can be thus tailored to transmit information blocks with different priority levels. An extrinsic information transfer (EXIT) analysis is developed, which allows an accurate performance prediction over the considered channel model, and more in general over block-fading channels.

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.

An accurate extrinsic information transfer (EXIT) analysis is developed for protograph low-density parity-check (LDPC) codes over the block fading channel (BFC). The analysis is thus exploited for analyzing the behavior of distributed protograph LDPC ensembles over block fading relay channels. A novel protograph-based construction of low-density parity-check (LDPC) codes for the relay channel is proposed, which provides an enhanced unequal error protection (named unequal diversity, UD) property. The focus is on quasi-static fading channels and on the high-code-rate (R >; 1/2) regimes, for which (according to the Singleton bound) no full diversity can be achieved. In the proposed construction, some nodes (and the corresponding codeword fragments) associated with the code graph enjoy the diversity provided by the relay, whereas the remaining nodes do not experience any diversity. The proposed approach can be thus tailored to transmit information blocks with different priority levels.

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.

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.

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.

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.

In many applications erasure correcting codes are used to recover packet losses at high protocol stack layers. The objects (e.g. files) to be transmitted often have variable sizes, resulting in a variable number of packet to be encoded by the packet-level encoder. In this paper, algorithms for the (on-line) flexible design of parity-check matrices for irregular-repeat-accumulate codes are investigated. The proposed algorithms allow designing in fast manner parity-check matrices that are suitable for low-complexity maximum-likelihood decoding. The code ensembles generated by the proposed algorithms are analyzed via extrinsic information transfer charts. Numerical results show how the designed codes can attain codeword error rates as low as 10-5without appreciable losses w.r.t. the performance of idealized maximum-distance separable codes. The application of the proposed techniques to the upcoming aeronautical communication standard is investigated, proving the efficiency and the flexibility of the approach.

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.

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.

Contention resolution diversity slotted ALOHA (CRDSA) is a simple but effective improvement of slotted ALOHA. CRDSA relies on MAC bursts repetition and on interference cancellation (IC), achieving a peak throughput T ≅ 0.55, whereas for slotted ALOHA T ≅ 0.37. In this paper we show that the IC process of CRDSA can be conveniently described by a bipartite graph, establishing a bridge between the IC process and the iterative erasure decoding of graph-based codes. Exploiting this analogy, we show how a high throughput can be achieved by selecting variable burst repetition rates according to given probability distributions, leading to irregular graphs. A framework for the probability distribution optimization is provided. Based on that, we propose a novel scheme, named irregular repetition slotted ALOHA, that can achieve a throughput T ≅ 0.97 for large frames and near to T ≅ 0.8 in practical implementations, resulting in a gain of ~ 45% w.r.t. CRDSA. An analysis of the normalized efficiency is introduced, allowing performance comparisons under the constraint of equal average transmission power. Simulation results, including an IC mechanism described in the paper, substantiate the validity of the analysis and confirm the high efficiency of the proposed approach down to a signal-to-noise ratio as a low as Eb/N0=2 dB.

Contention resolution diversity slotted ALOHA is a simple but effective improvement of slotted ALOHA. It relies on MAC bursts repetition and on interference cancellation to increase the throughput of a classic slotted ALOHA access scheme. This improvement permits to achieve a throughput up to T ≃ 0.55, whereas slotted ALOHA is capable of providing T ≃ 0.37. In this paper we show that the iterative interference cancellation process used in contention resolution diversity slotted ALOHA can be described by a bipartite graph. Such representation permits to establish a bridge between the iterative interference cancellation process and the iterative erasure recovery process of graph-based codes. Exploiting this analogy, we show how a higher throughput (close to T ≃ 0.9) can be achieved by selecting variable burst repetition rates, leading to irregular graphs, according to given probability distributions. A framework for the probability distribution optimization is provided as well. Simulation results including the actual interference cancellation mechanism confirm the high efficiency of the proposed approach.

We consider terminated LDPC convolutional codes (LDPC-CC) constructed from photographs and explore the performance of these codes on correlated erasure channels including a single-burst channel (SBC) and Gilbert-Elliott channel (GEC). We consider code performance with a latency-constrained message passing decoder and the belief propagation decoder. We give theoretical bounds on the code efficiency over the SBC and describe a construction that achieves this bound.We show that the designed codes with belief propagation (BP) decoding perform as well as the regular LDPC-CCs presented in the literature on the binary erasure channel (BEC) and the GEC, while achieving significant gains on the SBC. In the case of windowed decoding, our codes perform much better than the best known regular LDPC-CCs over the BEC and the GEC, with very low decoding latencies.

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.

In this paper an analytical framework is introduced for the optimization of TCP performance through joint channel coding and transmission power management in satellite communications, where both energy and bandwidth are scarce and costly resources. More specifically, the analysis takes into account the use of Low-Density Parity-Check (LDPC) codes as coding scheme for high data rate satellite communications. The analytical framework allows for the evaluation of the transmission power and coding rate that maximize the TCP throughput per unitary cost, which is a metric defined in terms of energy cost and bandwidth cost when related to throughput. Numerical examples demonstrate the usability of the proposed framework.

In this paper, we study the provision of broadband interactive services to passengers of Korean high-speed train in the ISM 2.4 GHz band. We address in particular the design of tunnel gap-fillers (GFs) able to provide bi-directional connectivity to train-based terminals. The work has been developed in the broader context of interactive services provision for high-speed trains through satellite networks. First, a channel model for the in-tunnel propagation is derived. Taking into account the results of the propagation analysis, a comparison between commercial technologies (belonging to both the IEEE and the DVB standard families) is provided, showing the possible strengths and weaknesses of the proposed solutions with respect to architectural and performance point of views.

The railroad satellite channel is characterized by frequent signal outages due to tunnels, bridges and electrical trellises. While for medium/long tunnels the main option to offer reliable and uninterrupted connectivity deals with the adoption of gap-filling techniques, signal outages due to small bridges/tunnels or electrical trellises can be faced with ad-hoc recovery techniques. In this paper, we face the problem from a link layer perspective, showing how a proper design of an erasure correcting code operating at link layer represents a valuable countermeasure against short outage events. The performance evaluation is developed in comparison with a more traditional technique based on physical layer coding in combination with a long channel interleaver. Advantages of the link layer coding scheme will be shown.

In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

In this paper, a novel extrinsic information transfer (EXIT) analysis is presented for protograph-based and multi- edge type low-density parity-check (LDPC) codes. A protograph defines a subset of an LDPCC ensemble (identified by the degree distributions of the bipartite graph), introducing further constraints about the edge connections. For many codes belonging to this class, the conventional approach based on EXIT charts cannot be applied. The proposed EXIT analysis takes into account edge connections, permitting the decoding convergence evaluation for protograph-based LDPC codes, allowing the design of highly-structured capacity approaching LDPC codes.

In this paper, a novel methodology for designing structured generalized low-density parity-check (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call low-density parity-check (LDPC) code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.