Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Mutual information of IID complex Gaussian signals on block Rayleigh-faded channels

We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, this mutual information represents the highest spectral efficiency that can be attained using Gaussiancodebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified when multiple transmit antennas are used. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.

Mutual Information of IID complex Gaussian signals on block Rayleigh-faded channels

We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, this mutual information represents the highest spectral efficiency that can be attained using Gaussiancodebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified when multiple transmit antennas are used. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.

Full diversity product codes for block erasure and block fading channels

We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a familyreferred to as root product codes.

What is the value of joint processing of pilots and data in block-fading channels?

The spectral efficiency achievable with joint processing of pilot and data symbol observations is compared with that achievable through the conventional (separate) approach of first estimating the channel on the basis of the pilot symbols alone, and subsequently detecting the datasymbols. Studied on the basis of a mutual information lower bound, joint processing is found to provide a non-negligible advantage relative to separate processing, particularly for fast fading. It is shown that, regardless of the fading rate, only a very small number of pilot symbols (at most one per transmit antenna and per channel coherence interval) shouldbe transmitted if joint processing is allowed.

Optimum pilot overhead in wireless communication: a unified treatment of continuous and block-fading channels

The optimization of the pilot overhead in wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. It is also shown that the widely-usedblock fading model is a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency. Furthermore, it is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with thenormalized Doppler frequency multiplied by the number of transmit antennas.

On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper presents our investigation on iterativedecoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes.Also, we show analytically that, in the case of 2 fading blocks,the iterative threshold root of Root-LDPC codes is proportional to (α1 α2)1, where α1 and α2 are corresponding fading gains.From this result, the full diversity property of Root-LDPC codes immediately follows.

Juridical double taxation by cross border transactions: the Block Case (C-67/08)

Treaty Establishing the European Community, operative until December 1st 2009, had already established in its article 2 the mission of the up until then European Community and actual European Union is to promote an harmonious, equilibrated and sustainable development of the economic activities of the whole Community. This Mission must be achieved by establishing a Common Market, an Economic and Monetary Union and the realization of Common Policies. One of the instruments to obtain these objectives is the use of free circulation of people, services and capitals inside the Common and Interior Market of the European Union. The European Union is characterized by the confirmation of the total movement of capitals, services and individuals and legal peoples’ freedom; freedom that was already predicated by the Maastricht Treaty, through the suppression of whatever obstacles which are in the way of the objectives before exposed. The old TEC in its Title III, now Title IV of the Treaty on the Functioning of the European Union, covered the free circulation of people, services and capitals. Consequently, the inclusion of this mechanism inside one of the regulating texts of the European Union indicates the importance this freedom supposes for the European Union objectives’ development. Once stood up the relevance of the free movement of people, services and capitals, we must mention that in this paper we are going to centre our study in one of these freedoms of movement: the free movement of capital. In order to analyze in detail the free movement of capital within the European framework, we are going to depart from the analysis of the existent case law of the Court of Justice of the European Union. The use of jurisprudence is basic to know how Community legislation is interpreted. For this reason, we are going to develop this work through judgements dictated by the European Union Court. This way we can observe how Member States’ regulating laws and the European Common Law affect the free movement of capital. The starting point of this paper will be the Judgement C-67/08 European Court of Justice of February 12th 2009, known as Block case. So, following the argumentation the Luxemburg Court did about the mentioned case, we are going to develop how free movement of capital could be affected by the current disparity of Member States’ legislation. This disparity can produce double taxation cases due to the lack of tax harmonized legislation within the interior market and the lack of treaties to avoid double taxation within the European Union. Developing this idea we are going to see how double taxation, at least indirectly, can infringe free movement of capital.

Trade, firm selection, and innovation: the competition channel

The availability of rich firm-level data sets has recently led researchers to uncover new evidence on the effects of trade liberalization. First, trade openness forces the least productive firms to exit the market. Secondly, it induces surviving firms to increase their innovation efforts and thirdly, it increases the degree of product market competition. In this paper we propose a model aimed at providing a coherent interpretation of these findings. We introducing firm heterogeneity into an innovation-driven growth model, where incumbent firms operating in oligopolistic industries perform cost-reducing innovations. In this framework, trade liberalization leads to higher product market competition, lower markups and higher quantity produced. These changes in markups and quantities, in turn, promote innovation and productivity growth through a direct competition effect, based on the increase in the size of the market, and a selection effect, produced by the reallocation of resources towards more productive firms. Calibrated to match US aggregate and firm-level statistics, the model predicts that a 10 percent reduction in variable trade costs reduces markups by 1:15 percent, firm surviving probabilities by 1 percent, and induces an increase in productivity growth of about 13 percent. More than 90 percent of the trade-induced growth increase can be attributed to the selection effect.

A block solver for the exponentally fitted IIPG-0 method

We consider an exponentially fitted discontinuous Galerkin method for advection dominated problems and propose a block solver for the resulting linear systems. In the case of strong advection the solver is robust with respect to the advection direction and the number of unknowns.

Impaired fast-spiking, suppressed cortical inhibition and increased susceptibility to seizures in mice lacking Kv3.2 K+ channel proteins

Voltage-gated K+ channels of the Kv3 subfamily have unusual electrophysiological properties, including activation at very depolarized voltages (positive to −10 mV) and very fast deactivation rates, suggesting special roles in neuronal excitability. In the brain, Kv3 channels are prominently expressed in select neuronal populations, which include fast-spiking (FS) GABAergic interneurons of the neocortex, hippocampus, and caudate, as well as other high-frequency firing neurons. Although evidence points to a key role in high-frequency firing, a definitive understanding of the function of these channels has been hampered by a lack of selective pharmacological tools. We therefore generated mouse lines in which one of the Kv3 genes, Kv3.2, was disrupted by gene-targeting methods. Whole-cell electrophysiological recording showed that the ability to fire spikes at high frequencies was impaired in immunocytochemically identified FS interneurons of deep cortical layers (5-6) in which Kv3.2 proteins are normally prominent. No such impairment was found for FS neurons of superficial layers (2-4) in which Kv3.2 proteins are normally only weakly expressed. These data directly support the hypothesis that Kv3 channels are necessary for high-frequency firing. Moreover, we found that Kv3.2 −/− mice showed specific alterations in their cortical EEG patterns and an increased susceptibility to epileptic seizures consistent with an impairment of cortical inhibitory mechanisms. This implies that, rather than producing hyperexcitability of the inhibitory interneurons, Kv3.2 channel elimination suppresses their activity. These data suggest that normal cortical operations depend on the ability of inhibitory interneurons to generate high-frequency firing.

K(+) channel expression distinguishes subpopulations of parvalbumin- and somatostatin-containing neocortical interneurons

Kv3.1 and Kv3.2 K+ channel proteins form similar voltage-gated K+ channels with unusual properties, including fast activation at voltages positive to −10 mV and very fast deactivation rates. These properties are thought to facilitate sustained high-frequency firing. Kv3.1 subunits are specifically found in fast-spiking, parvalbumin (PV)-containing cortical interneurons, and recent studies have provided support for a crucial role in the generation of the fast-spiking phenotype. Kv3.2 mRNAs are also found in a small subset of neocortical neurons, although the distribution of these neurons is different. We raised antibodies directed against Kv3.2 proteins and used dual-labeling methods to identify the neocortical neurons expressing Kv3.2 proteins and to determine their subcellular localization. Kv3.2 proteins are prominently expressed in patches in somatic and proximal dendritic membrane as well as in axons and presynaptic terminals of GABAergic interneurons. Kv3.2 subunits are found in all PV-containing neurons in deep cortical layers where they probably form heteromultimeric channels with Kv3.1 subunits. In contrast, in superficial layer PV-positive neurons Kv3.2 immunoreactivity is low, but Kv3.1 is still prominently expressed. Because Kv3.1 and Kv3.2 channels are differentially modulated by protein kinases, these results raise the possibility that the fast-spiking properties of superficial- and deep-layer PV neurons are differentially regulated by neuromodulators. Interestingly, Kv3.2 but not Kv3.1 proteins are also prominent in a subset of seemingly non-fast-spiking, somatostatin- and calbindin-containing interneurons, suggesting that the Kv3.1–Kv3.2 current type can have functions other than facilitating high-frequency firing.

A unified treatment of optimum pilot overhead in multipath fading channels

The optimization of the pilot overhead in single-user wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. It is also shown that the widely-used block fading model is a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency. Furthermore, it is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with the normalized Doppler frequency multiplied by the number of transmit antennas.

Interplay of spectral efficiency, power and doppler spectrum for reference-signal-assisted wireless communication

Expressions relating spectral efficiency, power, and Doppler spectrum, are derived for Rayleigh-faded wireless channels with Gaussian signal transmission. No side information on the state of the channel is assumed at the receiver. Rather, periodic reference signals are postulated in accordance with the functioning of most wireless systems. The analysis relies on a well-established lower bound, generally tight and asymptotically exact at low SNR. In contrast with most previous studies, which relied on block-fading channel models, a continuous-fading model is adopted. This embeds the Doppler spectrum directly in the derived expressions, imbuing them with practical significance. Closed-form relationships are obtained for the popular Clarke-Jakes spectrum and informative expansions, valid for arbitrary spectra, are found for the low- and high-power regimes. While the paper focuses on scalar channels, the extension to multiantenna settings is also discussed.

On fast-decodable space-time block codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2 x 2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.