This paper deals mainly with the study of the asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity of orthogonal space-time block code (OSTBC) multiple-input multiple-output (MIMO) systems over Rayleigh channels. Drawing upon known statistical properties for the asymptotic behavior of chi-squared processes at low levels, we provide approximate solutions for the PDF, the cumulative distribution function (CDF), and the kth-order moments of the outage intervals of the underlying capacity processes. Then, as an application of the derived PDF, the performance assessment of capacity simulators is reported. Following this, we introduce the newly defined average-to-trough capacity ratio (ATCR) metric, and investigate its PDF and CDF. The validity of the derived results is confirmed by specializing them to already known ones, although they have been obtained by using a rather different approach. The accuracy and applicability of the asymptotic analysis to practical values of capacity thresholds have been examined by means of computer simulations. The theoretical results presented contribute to the statistical characterization of outage events, the study of which has mainly been limited to the analysis of the probability, the occurrence rate, and the average duration of outages.

In this paper, the outage statistics are studied for non-isotropic Beckmann fading channel model. Non-isotropic scattering generally results in an asymmetrical Doppler power spectral density (PSD). In this context, an expression for the outage probability (OP) (or equivalently the cumulative distribution function (CDF)) of the fading envelope is first derived. Then, the probability density function (PDF) of the rate of change of the fading envelope is investigated. Thereafter, an expression for the average rate of outages (ARO) (or equivalently the level-crossing rate (LCR)) is provided. Finally, by making use of the analytical results of the ARO and OP, an expression for the average duration of outages (ADO) (or equivalently the average duration of fades (ADF)) is attained. The obtained results, which are given in the form of finite-range integrals that can efficiently be computed numerically, are verified to include a variety of already known expressions for models that are special cases of the Beckmann model. Numerical and simulation results are provided to verify the validity of the derivations and to analyze the effect of the fading parameters on the obtained metrics.

In this paper, we investigate the second-order statistics of Hoyt fading channels under non isotropic scattering scenarios. Assuming an asymmetrical Doppler power spectral density (PSD), we derive, in the form of single finite-range integrals, expressions for the level-crossing rate (LCR) and average duration of fades (ADF). These new results are then applied to obtain the LCR and ADF of selection combining (SC) diversity over non-isotropic Hoyt channels. In addition to their importance for studying the system performance and characterizing the dynamic behavior of multipath fading channels, the formulas derived are general in that they can be applied to many non-isotropic scattering situations. Furthermore, they are shown to unify some existing results for Rayleigh and Hoyt channels. The validity of the analytical expressions is verified by means of computer simulations where a mobile-to-mobile (M2M) propagation scenario is considered in which the angle of departure (AOD) and angle of arrival (AOA) of multipath components are both described by the von Mises distribution.

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the outage intervals only over its initial part. By applying the asymptotic behavior of level crossings of Gaussian processes, an alternative expression, valid only for low capacity thresholds, is obtained, which, in turn, is applied to determine an approximate solution for the kth-order moments of the outage intervals. Also presented is the PDF of the so- called instantaneous capacity loss with respect to the average capacity. Simulation results have been shown to be in good agreement with the theoretical approximations, thereby confirming their validity. Although, the focus of the study is on massive MIMO systems, it has been observed that the approximations are accurate even for a moderate number of antennas such as the case of 4×4 MIMO-OSTBC systems.

Kudekar et al. proved that the belief-propagation (BP) performance for low-density parity check codes can be boosted up to the maximum a posteriori (MAP) performance by spatial coupling. In this paper, spatial coupling is applied to sparsely spread code-division multiple-access systems to improve the performance of iterative multiuser detection based on BP. Two iterative receivers based on BP are considered: 1) one receiver is based on exact BP and 2) the other on an approximate BP with Gaussian approximation. The performance of the two BP receivers is evaluated via density evolution (DE) in the dense limit after taking the large-system limit, in which the number of users and the spreading factor tend to infinity while their ratio is kept constant. The two BP receivers are shown to achieve the same performance as each other in these limits. Furthermore, taking a continuum limit for the obtained DE equations implies that the performance of the two BP receivers can be improved up to the performance achieved by the symbol-wise MAP detection, called individually optimal detection, via spatial coupling. Numerical simulations show that spatial coupling can provide a significant improvement in bit-error rate for finite-sized systems especially in the region of high system loads.

This paper deals with the study of asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity (also referred to as the mutual information) in orthogonal space-time block code (OSTBC) transceiver systems over multiple-input multiple-output (MIMO) Rayleigh fading channels. The Rayleigh fading subchannels are assumed to be frequency-nonselective and mutually uncorrelated, whereas the associated Doppler power spectral density is supposed to be symmetric about the origin. In addition, the channel state information (CSI) is considered to be available only at the receiver side. Taking these assumptions into account, and drawing upon known statistical properties for the asymptotic behavior of chi-square processes at low levels, we provide a closed-form approximate solution for the PDF of the outage intervals of the underlying capacity processes. Furthermore, an analytical expression is also provided for the kth-order moments of the outage intervals. These statistical quantities will as well be shown to be useful for studying the statistics of the capacity outage durations of single-input multiple-output (SIMO) and multiple-input single-output (MISO) systems. The validity of the obtained approximate asymptotic solutions has been confirmed by means of computer simulations.

We discuss the properties of Jeffreys mixture for a Markov model. First, we show that a modified Jeffreys mixture asymptotically achieves the minimax coding regret for universal data compression, where we do not put any restriction on data sequences. Moreover, we give an approximation formula for the prediction probability of Jeffreys mixture for a Markov model. By this formula, it is revealed that the prediction probability by Jeffreys mixture for the Markov model with alphabet$\{0,1\}$is not of the form$(n_{x \vert s}+\alpha)/(n_{s}+\beta)$, where$n_{x \vert s}$is the number of occurrences of the symbol$x$following the context$s \in \{0,1\}$and$n_{s}=n_{0 \vert s}+n_{1 \vert s}$. Moreover, we propose a method to compute our minimax strategy, which is a combination of a Monte Carlo method and the approximation formula, where the former is used for earlier stages in the data, while the latter is used for later stages.

Kudekar et al. proved that the belief-propagation (BP) threshold for low-density parity-check codes can be boosted up to the maximum-a-posteriori (MAP) threshold by spatial coupling. In this paper, spatial coupling is applied to randomly-spread code-division multiple-access (CDMA) systems in order to improve the performance of BP-based multiuser detection (MUD). Spatially-coupled CDMA systems can be regarded as multi-code CDMA systems with two transmission phases. The large-system analysis shows that spatial coupling can improve the BP performance, while there is a gap between the BP performance and the individually-optimal (IO) performance.

We study quantizers with lpnorm, with p ≥ 1, for the root lattices. Our algorithms extend the ones proposed by Conway and Sloane [1] with l2norm. They proposed an interesting algorithm for Anlattice, but without proof of the optimality. We give the proof of the optimality with our extended case of lpnorm. We also give an algorithm for E6and its dual, which are not described in [1].

The Muroga method is an algebraic method of computing the capacity of discrete memoryless channels. Shannon interpreted the method geometrically. However, in the process, he ignored the meaning of the intermediate vector x, although which played a key computational role in Muroga's work. Although Shannon's view was inherited thereafter, by Gallager, and Csiszsár and Körner, the algebra of Muroga was not. We revisit the original Muroga method, and while following Shannon's view, will give a geometry of Muroga's algebraic computation. This view enables new applications. One class of application is directly related to the capacity computation; We first give a sensitivity analysis of the capacity. Next, we give a capacity computation algorithm for the channels which have more input symbols than the output symbols. The other class of application is the universal noiseless source coding, in particular, the universal expected redundancy. For the latter, we propose a new (Muroga) upper bound and a stochastic complexity bound.

The performance analysis of mobile-to-mobile (M2M) radio communications over double Hoyt fading channels perturbed by additive white Gaussian noise (AWGN) is considered. First, the probability density function (PDF) of the instantaneous signal-to-noise ratio (SNR) per bit is derived under the assumption that the fading channel is a concatenation (product) of two independent but not necessarily identically distributed Hoyt processes. Then, an expression for the bit error probability (BEP) is investigated for several modulation schemes commonly used in wireless communication systems. In the derivation, the underlying propagation channel is assumed to be slowly varying and having the frequency-flat fading characteristics. Numerical results, considering the impact of the fading severity on the BEP, are presented. Furthermore, the validity of the theoretical results is checked by means of computer simulations for some of the modulation schemes used in the analysis. The obtained BEP expression is general and includes, as special cases, results corresponding to the channel combinations given by Rayleigh×Hoyt, Rayleigh×one-sided Gaussian, Hoyt×one-sided Gaussian, double one-sided Gaussian, and double Rayleigh fading channels.

Approximations for the probability density functions (PDFs) of the capacity outage and inter-outage durations over Rayleigh fading channels are studied. Exact closed form expressions for the Rice probability functions of the level-crossing intervals of the capacity process are derived, assuming a symmetrical Doppler power spectral density (PSD). These probability functions, which are obtained by applying the classical level-crossing theory, are known to describe the PDFs of outage and inter-outage durations only over their initial behavior. Additionally, the derived quantities are used to calculate approximate solutions for the considered PDFs based on the assumption of statistical independence between the level-crossing intervals. Numerical examples, considering Rayleigh mobile-tomobile fading channels, are presented together with simulation results to illustrate the analysis and examine the validity of the derived expressions. Particularly, it is shown that the theoretical results obtained provide accurate approximations for the PDFs of outage and inter-outage durations at low and high outage levels, respectively.

For each l = 1, 2, 3, … recursively, we define wlto be the unique prefix of xl∞, which is in the external leaf set of the trie {λ, w1, w2, …, wl−1}, for a given data xl∞. This definition gives the Lempel-Ziv 77 parsing and associated data compression algorithm. We give a simple implementation which utilizes an enumerative code. Furthermore, we introduce and apply a simple post-processing mechanism which matches to this code.

We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.

A binary broadcast channel with a single input X isin {0, 1} and two outputs Y1isin {0, 1}, Y2isin {0, 1} is examined. We assume that each state or noise Si= Yioplus X, is independent to each other, and is known to the sender but unknown to both receivers. The capacity of the channel, which is defined as the maximal rate of the common information reliability transferable to both receivers, is shown to be C= 1 - (1/2)(S1oplus S2)

The symbol decomposition algorithm is proposed by Willems et. al. as an efficient and practical symbol predictor applicable for compressing multi-alphabet data. However, no theoretical analysis of the algorithm has been presented. In this paper, we first elucidate a natural parameterization that the algorithm assumes and derive a prior distribution on which the algorithm is based. Based on this framework, we first analyze the redundancy of the algorithm for memoryless source with a structured alphabet. Then we interpret the algorithm compared with the Krichevsky-Trofimov estimator for multi-alphabet, through the prior distribution over our parameterization. We demonstrate an effectiveness of the algorithm through a computer simulation of the redundancy, and also reveal a non-optimal character. Finally, we propose a practical modification of the symbol decomposition algorithm, and show that the it achieves the asymptotic optimal redundancy

A zero-redundancy estimator is defined by a weighted sum of Krichevsky-Trofimov (KT) sequential probability estimators i.e., the minimax Bayes of the memoryless process, over all possible alphabets. This estimator is effective for non-binary sources whose alphabet is embedded in a larger alphabet. We propose a new weighting recursive computation. Next we use the estimator to construct a finite window predictor for lossless data compressor, and we show that its average redundancy for memoryless source has optimal 1st order asymptotics.

Data compression of independent samples drawn from a fractal set is considered. The asymptotic ratio of rate to magnitude log distortion characterizes the effective dimension occupied by the underlying distribution. This quantity is shown to be identical to Renyi's (1959) information dimension. For self-similar fractal sets this dimension is distribution dependent-in sharp contrast with the behavior of absolutely continuous measures. The rate-distortion dimension of a set is defined as the maximal rate-distortion dimension for distributions supported on this set. Kolmogorov's metric dimension is an upper bound on the rate-distortion dimension, while the Hausdorff dimension is a lower bound. Examples of sets for which the rate-distortion dimension differs from these bounds are provided.>

A new mathematical method in coding theory that is applicable to various practical problems in communication systems is introduced. The uniform switching system based on k-sets is defined, and its cardinalities, an index system, and error correctabilities are studied. The cardinalities of a uniform switching system based on general families of switching sets are discussed. The asymptotic cardinality is obtained for the Reed-Muller codes of general order.>

The authors apply the Lempel-Ziv incremental parsing (LZIP) algorithm to an i.i.d. source and obtain the expected length of the ith parsed segment. From this formula, the data compression ratio of LZIP is calculated in the framework of a variable-to-fixed length coding scheme.>

A global message communication network for low-density traffic, using satellites at low altitudes, is described. This network affords around-the-clock service to any part of the globe, including the polar regions. Such a network can accommodate static and mobile user terminals simultaneously. The oblate globe is modeled as a regular polyhedron with 12 facets for setting up the orbits. Satellites are positioned uniformly in low-altitude symmetrical orbits. The symmetrical orbits are those whose axes are symmetrical in the three-dimensional space. The authors study the coverage aspects of the 6-orbit scheme and the 10-orbit scheme, each with satellites deployed at an altitude of 5000 km. At this altitude, the terrestrial user terminals can access satellites at a grazing angle of 45 degrees . The method of access over the crosslinks is the slotted ALOHA scheme. For low-density traffic, the downlink and uplink throughput rates are estimated. Simulation results agree with these analytical estimates for low values of network offered load.>

The underlying mathematical structure of Shannon's information measures was studied in a paper by R.W. Yeung (1991), and the I-Measure mu *, which is a signed measure defined on a proper sigma -field F, was introduced. The I-Measure is a natural extension of Shannon's information measures and is uniquely defined by them. They also introduced as a consequence the I-Diagram as a geometric tool for visualizing the relationship among the information measures. In general, an I-Diagram for n random variables must be constructed in n-1 dimensions. It is shown that for any finite collection of random variables forming a Markov chain, mu * assumes a very simple structure which can be illustrated by an I-Diagram in two dimensions, and mu * is a nonnegative measure.>

Combining a note by J. Rissanen (1983) and an idea of enumerative coding, the authors obtain a new implementation of the Ziv-Lempel incremental parsing algorithm for coding and decoding discrete data sequences. The space and the time complexities are linear for both the encoder and the decoder. The authors describe the algorithm.>