On the error statistics of turbo decoding for hybrid concatenated codes design

In this paper we propose a model for the generation of error patterns at the output of a turbo decoder using a Context Tree based modelling technique. This model can be used not only to generate the decoder error pattern behaviour with little effort, avoiding simulations, but also to investigate \u2013 with no need of performing neither a turbo code distance spectrum analysis, nor the probabilistic characterization of log-likelihood ratios or of the extrinsic information at a turbo decoder output \u2013 the performance of hybrid concatenated coding (HCC) schemes having a turbo code as component code. These coding schemes combine the features of parallel and serially concatenated codes and thus offer more freedom in code design. It has been demonstrated, in fact, that HCCs can perform closer to capacity than serially concatenated codes while still maintaining a minimum distance that grows linearly with block length

Low-complexity bound on irregular LDPC belief-propagation decoding thresholds using a Gaussian approximation

Since irregular low-density parity-check (LDPC) codes are known to perform better than regular ones, and to exhibit, like them, the so-called \u2018threshold phenomenon\u2019, this Letter investigates a low-complexity upper bound on belief-propagation decoding thresholds for this class of codes on memoryless binary input additive white Gaussian noise channels, with sum-product decoding. A simplified analysis of the belief-propagation decoding algorithm is used, i.e. consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes

3D Millimeter-Wave Peer-to-Peer Networks With Boundary Located Destination

This letter presents a theoretical analysis for estimating the coverage probability and the average link capacity of an interfered peer-to-peer millimeter-wave communication, when the destination lies at the boundary of a three-dimensional cell. The proposed model provides closed-form expressions for the statistics of the desired and undesired signal powers, by accounting for the impact of directional antenna gains, path-loss attenuation, mid-scale fading, interference, and noise

Impact of the neighbor’s order on the capacity of millimeter-wave links with Poisson-distributed nodes in line of sight conditions

This paper presents a theoretical model for investigating the average capacity of a millimeter wave (mmWave) communication link in line of sight conditions, when a fixed binary phase-shift keying (BPSK) or a quadrature PSK (QPSK) modulation is used and the nodes are distributed according to a homogeneous Poisson point process (PPP). In particular, as compared to the existing PPP approaches, which often consider the sole nearest neighbor as a possible destination, the proposed analysis enables to evaluate the link performance for a neighbor of any order, thus providing a more complete view of the achievable capacity. Besides, the adoption of the BPSK/QPSK modulations helps to obtain a more realistic estimation with respect to the ideal one provided by the usually adopted Shannon bound. Moreover, the derived formulas, which are expressed in analytical form and checked by extensive simulations, include the influence of all the main mmWave propagation phenomena: path-loss attenuation, small- and mid-scale fading. The developed model is specifically exploited to explore the impact of the average cell radius and of the selected frequency band on the sustainability of the mmWave link as the destination becomes farther from the source

New Fourier Transform Approach to the Synthesis of Shaped Patterns by Linear Antenna Arrays

A new Fourier Transform (NFT) approach is developed for the synthesis of shaped patterns radiated by linear antenna arrays. The proposed method exploits in an innovative way the FT relation between the source distribution and the radiated pattern. Precisely, the finite dimension of real sources is firstly taken into account by using the sampling theorem to approximate the desired pattern as a band-limited function. It is this step that allows one to obtain an important performance improvement. Then, a continuous source is evaluated from the approximate desired pattern to finally obtain the element excitations. Numerical examples validate the method

Random Directional Access with and without Feedback for 5G/6G Peer-to-Peer Networks

This paper theoretically analyzes the usage of directional slotted Aloha schemes for managing the peer-to-peer random access in fifth and sixth generation (5G/6G) systems. To this aim, the physical layer is modeled by accounting for interference and noise, while a Markov chain approach is developed to investigate the network behavior in the presence and in the absence of a separate feedback channel, which provides information concerning the success or not of each transmission attempt. Closed-form expressions for the coverage probability and for the transition matrices with and without feedback are derived to then evaluate the corresponding throughput. The analytical results, which are validated by independent Monte Carlo simulations, are used to estimate the impact of the antenna gain, of the burst length, and of the node density on the achievable performance, as well as to discuss the directional random access benefit/complexity tradeoff

Coverage and Throughput Analysis for Peer-to-Peer 6G Directional Slotted Aloha Bursty Networks

This paper presents a theoretical framework for investigating the coverage and throughput behavior of sixth generation (6G) peer-to-peer (P2P) directional slotted Aloha (DirSA) networks managing bursty traffic flows. Proper channel models, accounting for interference, noise, path-loss, random node location, power fluctuation, and beam pointing error, are adopted to derive analytical expressions for the statistic of the received power in ground, air, and space propagation contexts. The resulting coverage probability, obtained in simple integral form for different omnidirectional/directional transmission/reception modes, is exploited to derive multidimensional Markov chains for estimating the throughput in the absence and in the presence of a feedback mechanism, considering also the impact of the initial access procedure and of the beam training overhead. The theoretical results, which are validated by exhaustive Monte Carlo simulations, are used to evaluate the influence of the code-modulation scheme, of the operating signal to interference plus noise ratio (SINR), and of the burst length on the performance of 6G terrestrial, aerial, and satellite P2P DirSA subnets

Explicitly Invertible Approximations of the Gaussian Q-Function: A Survey

Communications and information theory use the Gaussian $Q$ -function, a positive and decreasing function, across the literature. Its approximations were created to simplify mathematical study of the Gaussian $Q$ -function expressions. This is important since the $Q$ -function cannot be represented in closed-form terms of elementary functions. In a noise model with the Gaussian distribution function and various digital modulation schemes, closed-form approximations of the Gaussian $Q$ -function are used to predict a digital communications system's symbol error probability (SEP) or bit error probability (BEP). Another significant scenario pertains to fading channels, whereby it is important to accurately determine, through a closed-form expression, the precise evaluations of complex integrals involved in the computations of SEP or BEP. In addition to the aforementioned scenarios, it is imperative for a communications system designer to ascertain the requisite operational signal-to-noise ratio for the specific application, based on the target SEP (or BEP). In this scenario, the crucial role of the explicit invertibility of the Gaussian $Q$ -function approximation is of significant importance in achieving this objective. In this paper we propose a survey of the approximations of the Gaussian $Q$ -function found in the literature, reviewing also the approximations originally given for the 4 classical special functions related to it, restricting the analysis to the explicitly invertible ones, and classifying them on the basis of their accuracy (on the significant range), simplicity, and easiness of inversion, also distinguishing the bounds from approximations. We also list the inverses of some of them, already published or newly found in this research

Performance Study of a Class of Irregular Near Capacity Achieving LDPC Codes

This paper investigates the performance of a class of irregular low-density parity-check (LDPC) codes through a recently published low complexity upper bound on their beliefpropagation decoding thresholds. Moreover, their performance analysis is carried out through a recently published algorithmic method, presented in Babich et al. 2017 paper. In particular, the class considered is characterized by variable node degree distributions λ(x) of minimum degree i1 > 2: being, in this case, λ0(0) = λ2 = 0, this is useful to design LDPC codes presenting a linear minimum distance growth with the block length with probability 1, as shown in Di et al.'s 2006 paper. These codes unfortunately cannot reach capacity under iterative decoding, since the achievement of capacity requires λ2 ≠ 0. However, in this latter case, the block error probability might converge to a constant, as shown in the aforementioned paper

A new accurate approximation of the Gaussian Q-function with relative error less than 1 thousandth in a significant domain

The approximations of the Gaussian Q-function found in the literature have been often developed with the goal of obtaining high estimation accuracies in deriving the error probability for digital modulation schemes. Unfortunately, the obtained mathematical expressions are often too complex, even difficultly tractable. A new approximation for the Gaussian Q-function is presented in the form of the standard normal density multiplied by a rational function. The rational function is simply a linear combination of the first 5 integer negative powers of the same term, linear in x, using only 4 decimal constants. In this paper we make some considerations about the significant interval where to consider the Q-function in telecommunication theory. The relative error in absolute value of the given approximation is less than 0.06% in the considered significant interval