Design of Finite-Length Irregular Protograph Codes with Low Error Floors over the Binary-Input AWGN Channel Using Cyclic Liftings

We propose a technique to design finite-length irregular low-density parity-check (LDPC) codes over the binary-input additive white Gaussian noise (AWGN) channel with good performance in both the waterfall and the error floor region. The design process starts from a protograph which embodies a desirable degree distribution. This protograph is then lifted cyclically to a certain block length of interest. The lift is designed carefully to satisfy a certain approximate cycle extrinsic message degree (ACE) spectrum. The target ACE spectrum is one with extremal properties, implying a good error floor performance for the designed code. The proposed construction results in quasi-cyclic codes which are attractive in practice due to simple encoder and decoder implementation. Simulation results are provided to demonstrate the effectiveness of the proposed construction in comparison with similar existing constructions.Comment: Submitted to IEEE Trans. Communication

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle $c$ of length $\ell(c)$ in the base graph such that the inverse image of $c$ in the lifted graph consists of only cycles of length strictly larger than $\ell(c)$. The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, encoder and decoder structure, and in some cases, the code rate. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel

Improved Energy Detector for Wideband Spectrum Sensing in Cognitive Radio Networks

In this paper, an improved energy detector for a wideband spectrum sensing is proposed. For a better detection of the spectrum holes the overall band is divided into equal non-overlapping sub-bands. The main objective is to determine the detection thresholds for each of these subbands jointly. By defining the problem as an optimization problem, we aim to find the maximum aggregated opportunistic throughput of cognitive radio networks. Introducing practical constraints to this optimization problem will change the problem into a convex and solvable one. The results of this paper show that the proposed improved energy detector will increase the aggregated throughput considerably

Optimal Rate for Irregular LDPC Codes in Binary Erasure Channel

In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). Compared to some new researches, which are based on application of asymptotic analysis tools out of optimization process, the proposed method is much simpler, faster, accurate and practical. Because of not using any relaxation or any approximate solution like previous works, the found answer with this method is optimal. We can construct optimal variable node degree distribution for any given binary erasure rate, {\epsilon}, and any check node degree distribution. The presented method is implemented and works well in practice. The time complexity of this method is of polynomial order. As a result, we obtain some degree distribution which their rates are close to the capacity.Comment: 5 pages, to be presented at the 2011 IEEE Information Theory Workshop (ITW 2011), Paraty, Brazil, October, 201

U-Pb geochronology of the El Jadida rhyolite and relation to possible Lower Cambrian recycling (Coastal block, Moroccan Meseta).

The El Jadida (Mazagan) dome, whose existence was reported as early as 1934 by Yovanovitch and Freys, constitutes one of the first outcrops of the Moroccan Meseta where the Precambrian (PIII?)-Paleozoic (Lower Cambrian?) boundary was established (Gigout, 1951; Cornée et al., 1984). Since then, it is listed as one of the few locations where the basement of the Moroccan Variscan belt can be observed (Hoepffner et al.. 2005; Michard et al., 2010).Despite, the absence of geochronological and biostratigraphic precise data to constrain the time interval recorded here, there are stratigraphic similarities that allow a correlation with the Ediacaran-Cambrian geological record of Anti-Atlas belt (Cornée et al., 1984). In this study, we developed a petrographic, geochemical and U-Pb geochronological study using zircon extracted from: (i) the El Jadida rhyolite with the aim of characterizing the magma source and estimate the age of crystallization; (ii) a microbreccia sampled at the base of the El Jadida Dolomitic Formation for determining provenance

Sedimentary provenance of siliciclastic rocks from the Lalla Mouchaa Calcschists Formation (Coastal Block, Western Rehamna): Evidence of denudation of ca. 2 Ga basement in the Moroccan Meseta.

Paleoproterozoic basement rocks (ca. 2Ga) are scarce along the European and North African Paleozoic mountain chains (Fig.1a). In Morocco, ca. 2.2-2Ga granitic rocks (Gasquet et al., 2008; Kouyaté et al., 2013) have been exclusively reported in the Western Anti-Atlas at southwest of the Anti-Atlas Major Fault, (Choubert, 1963). In Eastern and Central Anti-Atlas and in the Moroccan Meseta, the existence of a Paleoproterozoic basement has only been recognized through indirect evidence (Gasquet et al., 2008; Michard et al., 2010). In the Anti- Atlas belt, ca. 2Ga detrital zircon grains are found in the Ediacaran siliciclastic rocks of the Bou Salda, Saghro and Taghdout groups (Abati et al., 2010). In the Moroccan Meseta, Paleoproterozoic (ca. 2Ga) zircon grains were extracted from gneiss and granitic xenoliths found in Triassic lamprophyre dykes, and from Carboniferous granophyric microgranite intrusions of central Jebilet (Dostal et al., 2005, Essaifi et al., 2003). Recently, a porphyritic rhyolite from the Rehamna Massif was dated at ca. 2.05Ga (Pereira et al., 2015), demonstrating for the first time, the exposure of the Eburnian basement in the Western Meseta. These Eburnian arc-related magmatic rocks, which are exposed to the south of the Permian Sebt Brikiyine granite in the core of anticlines from the Lalla Mouchaa Anticlinorium, are allegedly unconformably overlained by transgressive siliciclastic and carbonate beds (Corsini, 1988; Pereira et al., 2015). At north of the Sebt Brikiyine granite the probable Lower Cambrian sequence (Lalla Mouchaa Calcschists Formation; Guezou & Michard, 1976; Corsini, 1988) comprises a basal unit of microbreccias, arkosic sandstones and siltstones (lower member) that pass towards the top to centimeter-thick beds of calcschists interbedded with limestones and dolomites (upper member) that are conformably overlain by the “Paradoxides Shale Formation” composed of siltstone, greywacke and sandstone with Middle Cambrian fauna. In order to study the potential sources of the Lalla Mouchaa Calcschists Formation (probable Lower Cambrian), we have sampled a microbreccia at the Koudiat El Hamra region, for U-Pb geochronology on detrital zircon. This foliated microbreccia is composed of elongated Kfeldspar and quartz phenocrysts surrounded by a fine-grained matrix. Detrital zircon grains gave 206Pb/238Ub ages that in the Probability density plot curve are distributed by two main age peaks at ca. 2.05Ga and ca. 2.03Ga (Fig.1b), yielding a 206Pb/238U age-weighted mean of ca. 2.04Ga (El Houicha et al., 2018). The obtained U-Pb results point to a provenance from a Paleoproterozoic source, suggesting a possible contribution from rocks of the same age of the 2Ga porphyritic rhyolite exposed at south of the Sebt Brikiyine granite. Thus, there is a possibility that the Paleoproterozoic basement extends bellow the Paleozoic and Neoproterozoic sequences of the Rehamna massif

Reasons for cooperation and defection in real-world social dilemmas

Interventions to increase cooperation in social dilemmas depend on understanding decision makers’ motivations for cooperation or defection. We examined these in five real-world social dilemmas: situations where private interests are at odds with collective ones. An online survey (N = 929) asked respondents whether or not they cooperated in each social dilemma and then elicited both open-ended reports of reasons for their choices and endorsements of a provided list of reasons. The dilemmas chosen were ones that permit individual action rather than voting or advocacy: (1) conserving energy, (2) donating blood, (3) getting a flu vaccination, (4) donating to National Public Radio (NPR), and (5) buying green electricity. Self-reported cooperation is weakly but positively correlated across these dilemmas. Cooperation in each dilemma correlates fairly strongly with self-reported altruism and with punitive attitudes toward defectors. Some strong domain-specific behaviors and beliefs also correlate with cooperation. The strongest example is frequency of listening to NPR, which predicts donation. Socio-demographic variables relate only weakly to cooperation. Respondents who self-report cooperation usually cite social reasons (including reciprocity) for their choice. Defectors often give self-interest reasons but there are also some domain-specific reasons—some report that they are not eligible to donate blood; some cannot buy green electricity because they do not pay their own electric bills. Cooperators generally report that several of the provided reasons match their actual reasons fairly well, but most defectors endorse none or at most one of the provided reasons for defection. In particular, defectors often view cooperation as costly but do not endorse free riding as a reason for defection. We tentatively conclude that cooperation in these settings is based mostly on pro-social norms and defection on a mixture of self-interest and the possibly motivated perception that situational circumstances prevent cooperation in the given situation