In the above article[1], the author characterizes the capacity of power-constrained channels with additive stationary Gaussian noise. Specifically, inSection III, the feedback capacity is shown to correspond with the solution to a variational optimization problem. Section IV gives structural properties of the solution for this optimization problem. Among these properties, it stands out the capacity-achieving optimality of using a short-length input$V$with arbitrarily small variance, and thus a power spectral density$S_{V}$equal to zero. These structural properties are further developed in its sections V and VI for first- and$m$-th-order autoregressive moving average channel noise, respectively, also showing the capacity-achieving optimality of the Schalkwijk-Kailath scheme for this scenario. In this note, we show that the proof ofCorollary 4.4in[1](which claims that the choice$S_{V} = 0$is capacity achieving) is erroneous. As a consequence, the proofs of theorems 4.1, 4.6, 5.3, and 6.1, propositions 4.7 and 5.1, as well asremarks 4.5and 5.2, and Lemma 6.1 in[1]are invalid, because they rely upon the optimality of choosing$S_{V} =0$.

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal “test-channel” of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.

In this work we obtain capacity gaps for a class of N-pair bidirectional Gaussian relay networks, where one relay can help communications between the corresponding user pairs. For the uplink, we apply the generalization of successive compute-and-forward strategy (SCAF) for decoding the linear combinations of the messages of each user pair at the relay. The downlink channel is considered as a broadcast network with N receiver groups. It is shown that for all channel gains, the achievable rate boundary lies within gaps of (N - 1 + log2N)=2N and (N + log2N)/2N bits/sec/Hz below the cut-set upper bound for restricted and non-restricted models, respectively. These gaps tend to 1/2 bits/sec/Hz per user as N goes to infinity. We first derive a comprehensive formulation for the N-step asymmetric SCAF and use it to derive the capacity result for our problem.

Based on measurements for a street-canyon-type femto-cell, we compare the downlink spectral efficiencies of various intra-cell interference mitigation systems. This includes zero-forcing (ZF), regularized ZF (RZF), and dirty-paper coding (DPC). As a reference for comparison, we consider subsectorization and time-division multiple access (TDMA). Outof-cell interference, treated as additive Gaussian noise, is included in two modes: 1) all cells transmit simultaneously and 2) neighboring cells transmit in alternated time slots. We find that ZF, RZF, and DPC can offer increases in spectral efficiency over subsectorization and TDMA by factors of ~4 under interference-limited conditions. This contrasts with the estimated gains of only ~2 when using a standard 3GPP mode instead of our measured data. This difference is due to the greater inter-cell isolation that characterizes our street-canyon-type test environment. We find that RZF achieves over 80% of the DPC's spectral efficiency under virtually all operating conditions.

The authors present an improved achievable rate region for two‐pair bidirectional Gaussian relay networks based on successive compute‐and‐forward method. In these networks, one relay helps in the communication between two pairs of users. In their proposed scheme, the authors use nested lattice codes for encoding the messages at the users, and Gaussian random codes for the encoding at the relay. They use the successive compute‐and‐forward strategy to decode two integer linear combinations of the lattice codewords in the uplink, and successive interference cancellation for decoding the Gaussian codewords in the downlink. The downlink channel can be considered as a broadcast channel with two receiver groups, but within each group, a pair of users is considered as an additive white Gaussian noise channel (instead of a broadcast channel) because each node knows its own transmitted message. It is shown that for all channel gains of downlink channels and all channel gains of symmetric uplink channel pairs, the strategy achieves rates to within constant gaps of 1/2 and 3/4 bit/s/Hz per user of the cut‐set upper bound for restricted and non‐restricted models, respectively. These gaps are tighter than those previously obtained for this network, which have not exploited the successive compute‐and‐forward method.

We present an empirically based model for the gain of an indoor antenna array. This corresponds to the re-parametrization of the Greenstein-Erceg model, as applied to 5 m-50 m narrowband outdoor-indoor links. Our model is applicable to a few adjacent tones in an OFDM femtocell system such as LTE. We find that as much as 14 out of 16 dB of antenna-gain are attainable even in rich indoor scattering conditions. At the same time, no larger fade margin is required when using the array vs. the omnidirectional antenna. To provide a reference for the observed results we consider a simple propagation model, which is analyzed theoretically and via simulation. This model is found to match our empirical results very well.

In this paper, we study a 3-node asymmetric full-duplex AWGN two-way relay channel with relay private messages where two nodes can communicate with each other only through a third node called the relay, while the relay can itself exchange private messages with two other nodes. Cut-set upper bound and single sided genie upper bound are presented for this channel. To obtain an achievable rate, we use a superposition of nested lattice codes and random Gaussian codes for encoding at the senders, and successive interference cancelation for decoding at the receivers. It is shown that capacities are achieved within constant gaps 2/3 and 2.5/3 bits/sec/Hz per user of single sided genie for restricted and non-restricted models, respectively.

The characterization of ℓp-compressible random sequences is revisited and extended to the case of stationary and ergodic processes. The main result of this work offers a simple-to-check necessary and sufficient condition for a stationary and ergodic sequence to be ℓp-compressible in the sense proposed by Amini, Unser and Marvasti [1, Def. 6]. Furthermore, for non ℓp-compressible random sequences, we provide a closed-form expression for the best k-term relative approximation error given a rate of coefficients as the block-length tends to infinity.

This paper presents closed-form expressions for the space-frequency (SF) second-order statistics for the power gain of indoor wideband channels. These expressions hold for channel models in which multi-path components are clustered, both in their arrival angles and their arrival times. Assuming that the arrival times are independent of the angles of arrival, we derive a closed-form expression for the covariance between the channel power gains at two receiving antenna positions d meters apart, at any pair of frequencies ω1and ω2. This expression reveals that increasing d yields the same SF covariance asymptotic reduction attainable by increasing |ω1- ω2|, only if |ω1- ω2|≠0, and that the covariance is symmetric in its dependence with ω1- ω2and with ω1+ ω2. Thus, the channel power gain at higher frequency bands has less variation than at lower frequencies. Finally, we show that the variable part of the SF covariance decays approximately as 1/d.

We obtain the maximum average data rates achievable over block-fading channels when the receiver has perfect channel state information (CSI), and only an entropy-constrained quantized approximation of this CSI is available at the transmitter. We assume channel gains in consecutive blocks are independent and identically distributed and consider a short term power constraint. Our analysis is valid for a wide variety of channel fading statistics, including Rician and Nakagami-m fading. For this situation, the problem translates into designing an optimal entropy-constrained quantizer to convey approximated CSI to the transmitter and to define a rate-adaptation policy for the latter so as to maximize average downlink data rate. A numerical procedure is presented which yields the thresholds and reconstruction points of the optimal quantizer, together with the associated maximum average downlink rates, by finding the roots of a small set of scalar functions of two scalar arguments. Utilizing this procedure, it is found that achieving the maximum downlink average capacity C requires, in some cases, time sharing between two regimes. In addition, it is found that, for an uplink entropy constraint H̅2(L), a quantizer with more than L cells provides only a small capacity increase, especially at high SNRs.

We present empirical results on the achievable cellular system throughput gains stemming from the use of remote radio heads (RRH) in an urban environment. Our work is based on simultaneous path-loss measurements of the base station (BS) and RRH links to outdoor street-level users. We calculated the increase in received power, when a RRH is added to improve the coverage achieved by a BS. We consider diverse settings for the RRH and diverse expected coverage areas for the mobile station (MS), evaluating the effect of RRH height and position with respect to the intended users. We also compare the power gains that would be obtained in practice from combining schemes such as selection combining (SC) and maximum ratio combining (MRC). We conclude that under practical conditions, the benefits of using RRHs will depend very strongly on the existence of line-of-sight links between the RRH and the intended users. For RRHs placed at low heights, below the clutter, only users in a "street-canyon" position with respect to the RRH will obtain a significant benefit. Our data also shows that the gains in signal-to-noise ratio achieved when using MRC are only marginally better than those of the much simpler SC.

We present empirical results on the achievable gains stemming from the use of wireless remote radio heads (RRH) in a typical urban environment. Our work is based on simultaneous path-loss measurements of the base station and RRH links to outdoor street level users. We statistically characterize the increase in received power, when a RRH is added to improve the coverage achieved by a base station. We consider diverse expected coverage areas for the mobile terminal, evaluating the effect of RRH position with respect to the intended users. We also compare the power gains that would be obtained in practice from combining the signals from the base with those of the RRH, using schemes such as selection combining and maximum ratio combining. We conclude that under practical conditions, the benefits of using RRHs will depend very strongly on the existence of line-of-sight links between the RRH and the intended users. For RRHs placed at low heights, below the clutter, only users in a street-canyon position with respect to the RRH will obtain a significant benefit. Our data also shows that the gains in signal-to-noise ratio achieved when using maximum ratio combining are only marginally better than those of the much simpler selection combining.

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by Rcit(D), for first-order Gauss-Markov processes. Rcit(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rcop(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rcop(D) ≤ Rcit(D) + 0.5 log2(2πe) bits/sample. In order to analyze Rcit(D) for arbitrary zero-mean Gaussian stationary sources, we introduce Rcit̅(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon Rcit̅(D), we derive three closed-form upper bounds to the additive rate loss defined as Rcit̅(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D ≤ σx2, RU(D) can be realized by an additive white Gaussian noise channel surrounded by a unique set of causal pre-, post-, and feed- back niters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal niters and is guaranteed to converge to Rcit̅(D). Finally, by establishing a connection to feedback quantization, we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves an operational rate lower than Rcit̅(D) +0.254 and Rcit̅(D) + 0.754 bits/sample, respectively. This implies that the OPTA among all zero-delay source codes, denoted by Rzdop(D), is upper bounded as Rzdop(D)cit̅(D) + 1-254 <; R(D) + 1.754 bits/sample.

Americanae nace como un proyecto conjunto que surge dentro de la Red Europea de Información y Documentación sobre América Latina (REDIAL), y que ha afrontado la Biblioteca de la Agencia Española de Cooperación Internacional para el Desarrollo (AECID). Esta nueva biblioteca virtual hace más accesibles los libros digitales de tema americanista a los investigadores y usuarios interesados de cualquier parte del mundo.

This work addresses the problem of universal density estimation under an operational data-rate constraint. We present a coding theorem that stipulates necessary and sufficient conditions to learn and transmit a memoryless source distribution with arbitrary precision (in total variations), under an asymptotic zero-rate regime, in bits per sample. In the process, we propose a concrete coding scheme to achieve this learning objective, adopting the Skeleton estimate developed by Y. Yatracos [1], [2].

This paper presents an empirical study of the achievable data rates of network multiple-input multiple-output (MIMO) techniques including zero-forcing (ZF), zero-forcing dirty paper coding (ZF-DPC) and dirty paper coding (DPC) using actual 4-by-4 indoor wireless channel measurements at 3.5 GHz. Their performances are contrasted with those of conventional techniques, in which either the base stations are not coordinated (NC), or their interference is avoided using frequency division (FD) multiplexing. The measurements were taken in aisle-to-office and large unobstructed hall scenarios. The study of these results reveals that, at high signal-to-noise ratios (SNRs), DPC and ZF-DPC can yield more than a three-fold increase in attainable data rates when compared to NC and FD. The gains obtained using ZF are smaller, but still significant. At low SNRs the system is noise-(rather than interference-) limited, and only DPC exhibits gains. The evaluations in this paper also show that collaborative systems such as DPC can benefit from interference-prone environments to yield increased transmission capacity. With regard to the propagation channel, the classical log-normal plus Rayleigh/Ricean fading model, with parameters fitted to the scenario type, was found to be good at predicting the statistics of the achievable data rates of all the strategies considered.

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources for mean squared error (MSE) distortion. First, we define the information-theoretic causal rate-distortion function (RDF), Rcit(D). In order to analyze Rcit(D), we introduce Rcit̅(D), the information theoretic causal RDF when reconstruction error is jointly stationary with the source. Based upon Rcit̅(D), we derive four closed form upper bounds to the gap between Rcit̅(D) and Shannon's RDF, two of them strictly smaller than 0.5 bits/sample at all rates. We then show that Rcit̅(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem and propose an iterative procedure to solve it. Finally, we build upon Rcit̅(D) to improve existing bounds on the optimal performance attainable by causal and zero-delay codes.

We derive closed form expressions for the second-order statistics of the spectral power gain of wide-band microwave indoor channels. We obtain our results within a framework general enough to be compatible with several popular channel models, such as those proposed by the IEEE 802.15.3a task group, as well as the Saleh-Valenzuela channel model. As all these models, our channel description is based upon clusters and rays with Poisson arrivals and random amplitudes. Our results consist of closed form expressions for the second-order statistics of the channel power frequency response, where statistical averages involve expectations over ray amplitudes and arrival times. We first express the auto-covariance of this frequency response in closed-form. We then use this result to obtain an analytical expression for the variance and second-order moment of the channel power within any given interval of frequencies. This allows us to express the channel spectral diversity as a function of model parameters and bandwidth. From this function, we determine the range within which diversity scales approximately linearly with bandwidth and its upper limit.

We analyze the behavior of the mean squared error (MSE) achievable by oversampled, uniform scalar quantization using feedback, pre- and post-filters of unrestricted order, when encoding wide-sense stationary discrete-time random sources having (possibly) unbounded support. Our results are based upon the use of subtractively dithered uniform scalar quantizers. We consider the number of quantization levels,N, to be given and fixed, which lends itself to fixed-rate encoding, and focus on the cases in whichNis insufficient to avoid overload. In order to guarantee the stability of the closed-loop, we consider the use of a clipper before the scalar quantizer. Our results are valid for zero-mean sources having independent innovations whose moments satisfy some mild requirements, which are met by infinite-support distributions such as Gaussian and Laplacian. We show that, for fixedN, the MSE can be made to decay with the oversampling ratio lambda asO(e-c0lambda1/3) when lambda tends to infinity, wherec0[0.5(N-1)]2/3. We note that the latter bound is asymptotic in lambda but not inN, and that it includes clipping errors.

We characterize the rate-distortion function for zero-mean stationary Gaussian sources under the MSE fidelity criterion and subject to the additional constraint that the distortion is uncorrelated to the input. The solution is given by two equations coupled through a single scalar parameter. This has a structure similar to the well known water-filling solution obtained without the uncorrelated distortion restriction. Our results fully characterize the unique statistics of the optimal distortion. We also show that, for all positive distortions, the minimum achievable rate subject to the uncorrelation constraint is strictly larger than that given by the un-constrained rate-distortion function. This gap increases with the distortion and tends to infinity and zero, respectively, as the distortion tends to zero and infinity.

This paper presents novel results on scalar feedback quantization (SFQ) with uniform quantizers. We focus on general SFQ configurations where reconstruction is via a linear combination of frame vectors. Using a deterministic approach, we derive two necessary and sufficient conditions for SFQ to be optimal, i.e., to produce, for every input, a quantized sequence that is a global minimizer of the 2-norm of the reconstruction error. The first optimality condition is related to the design of the feedback quantizer, and can always be achieved. The second condition depends only on the reconstruction vectors, and is given explicitly in terms of the Gram matrix of the reconstruction frame. As a by-product, we also show that the the first condition alone characterizes scalar feedback quantizers that yield the smallest MSE, when one models quantization noise as uncorrelated, identically distributed random variables.

This paper presents novel results on the joint problem of sampling and quantization of non bandlimited signals. Existing literature typically focuses either on sampling in the absence of quantization, or, conversely, studies quantization for already sampled signals. Our emphasis here is on the issues that arise al the intersection of these two design problems. We argue that the joint problem can be formulated and solved to any desired level of accuracy, using moving horizon optimization methods. We present several examples which show that consideration of the combined sampling and quantization problem gives important performance gains, relative to strategies which don't specifically address the interaction between these two problems