Perfect Equality Research Articles

Our Discrete and Insular Founders: American 'Degeneracy' and the Birth of Constitutional Equality

Equality burst onto the American scene in the 1780s and 1790s, and it appeared in reaction to a theory held by Englishmen and continental Europeans that Americans were degenerate Europeans who should be treated as inferiors. This Article contends that the sudden appearance of the American ideal of equality cannot be understood without understanding the constitutional ideal of inequality that preceded it. The Article makes three points of fundamental importance: First, British imperial policy was premised on the longstanding belief that colonial Americans were degenerate Englishmen who were not entitled to the rights of true Englishmen -- a discrete and insular people who should constitute a permanent underclass in the Empire. The American Revolution was the constitutional counter-statement to this Second, the degeneracy theory was more than a constitutional cause of the Revolution; it had important and enduring constitutional consequences as well. The American response to the imperial ideal of inequality was to affirm an ideal of equality that has occupied center stage in constitutional discourse ever since. Almost overnight an ideal of inequality was completely supplanted by an ideal of equality. Third, the influence of this new ideal reached far beyond constitutional confines, as American reaction to the imperial ideal of inequality led to the beginnings of a reevaluation of domestic inequality based on gender, race, and social status. At the same time, equality did not apply to all people, and from the start American equality had an equivocal character which is still reflected in constitutional discourse.The importance of the English belief in the degenerate character of American colonists can hardly be overstated, yet it has gone almost unnoticed. English imperial policy-makers described American colonists in a variety of unflattering ways -- as convicts, servants, farmers, laborers, and even as Indians -- intended to remind them that they were not true Englishmen, but imperial servants without either a political voice or constitutional rights. From an imperial vantage point the colonists appeared quite similar to Britain’s other colonial people -- the Indians -- and colonists were being told that like the Indians, their tributary status required them to make imperial contributions even though they had no voice in imperial governance.Colonists resented the Sugar and Stamp Acts so bitterly because they represented a legal revolution based on the degeneracy theory. The Article traces the origins of this longstanding theory back to colonial Ireland and then follows its career as it passed into colonial America. Then the Article shows how from the middle of the eighteenth century through the 1770s, British policy sought to cement alliances with Indian tribes and to reign in English-American colonists by treating them as a perpetual imperial underclass. Finally, the Article shows how the degeneracy theory led Americans to endorse a new constitutional ideal -- the ideal of equality -- to an extent which would have been unthinkable before the Revolution. The Founders quickly began to think on a grand scale, and whereas imperial thinkers had insisted that inequality was essential to the well-being of the Empire, the Founders declared that equality was the essential component of their new constitutional polity. Repudiating the degeneracy critique forced the Founders to explore the depth of their new found attachment to equality. Revulsion inspired by the charge of inferiority led Americans to inquire more deeply than ever before into the desirability of equality based on race, gender, and social status. Understanding the operation of the 200 year-old degeneracy theory and the ideal of inequality on which it was based permits us to see how far-reaching and stunning was its rejection in favor of an ideal of equality. The rejection of the degeneracy critique did not make America into a land of perfect equality; indeed, from its origins the ideal has had an equivocal quality which it maintains to the present day. Nonetheless, the appearance of the ideal of equality did introduce a revolution which has dominated American constitutional discourse ever since. The Founders closed one long chapter in constitutional history, and their ardent desire to repudiate the degeneracy theory forced them to open another.

A Novel Unconstrained Criterion for Blind Equalization Based on the Property of Vector Norm

This paper proposes a novel unconstrained criterion of blind equalization, which is based on minimizing the difference between two norms of the joint channel-equalizer impulse response. There is no need to impose any constraint on the equalizer coefficients when adjusting. The algorithm is convergent in the sense that a perfect equalization solution is achieved at every local optimum of the function. And we propose a batch algorithm and online-recursive method for implementation. Finally, the reliability, validity and good performance of the proposed algorithm are verified by evaluation of residual ISI through computer simulations.

Defending the One Percent

Imagine a society with perfect economic equality. Then, one day, this egalitarian utopia is disturbed by an entrepreneur with an idea for a new product. Think of the entrepreneur as Steve Jobs as he develops the iPod, J. K. Rowling as she writes her Harry Potter books, or Steven Spielberg as he directs his blockbuster movies. The new product makes the entrepreneur much richer than everyone else. How should the entrepreneurial disturbance in this formerly egalitarian outcome alter public policy? Should public policy remain the same, because the situation was initially acceptable and the entrepreneur improved it for everyone? Or should government policymakers deplore the resulting inequality and use their powers to tax and transfer to spread the gains more equally? In my view, this thought experiment captures, in an extreme and stylized way, what has happened to US society over the past several decades. Since the 1970s, average incomes have grown, but the growth has not been uniform across the income distribution. The incomes at the top, especially in the top 1 percent, have grown much faster than average. These high earners have made significant economic contributions, but they have also reaped large gains. The question for public policy is what, if anything, to do about it.

The Behavior of Other as a Reference Point

We use prospect theory to model reference dependent consumers, where the reference point is the average behavior of the society in the current period. We show that after a finite number of steps under any equilibrium, the distribution of wealth will become and remain equal, or admit a missing class (a particular form of polarization). Under equilibria that admit the highest growth rates, the initial wealth distribution that maximizes this growth rate is one of perfect equality. Conversely, under equilibria that admit the lowest growth rates, perfect equality minimizes this growth rate and societies with a small level of initial inequality grow the fastest. In addition growth rates in corresponding economics without reference dependent consumers admit lower growth rates.

The Behavior of Others as a Reference Point

We study a model in which consumers are reference-dependent, modeled using prospect-theory, and their reference point is the average behavior of the society in that period. We show that in any of the equilibria of the economy after a finite number of periods the wealth distribution will become, and remain, either of perfect equality, or admit a missing class, a particular form of polarization between the rich and the poor. We then study growth rates and show that, if we look at the equilibria with the highest growth, then the society with the highest growth rate is the one that starts with perfect equality. If we look at the equilibria with the lowest growth, however, then the society with a small amount of initial inequality is the one that attains the highest growth rate, while a society with perfect equality is the one with the lowest performance. All of these growth rates are weakly higher than the growth rate of a corresponding economy without reference-dependence.

Income Inequality and Inflation in the EU

1. Introduction There is extended research analyzing relationship between income inequality and selected macroeconomic variables such as growth rate, inflation rate, openness etc. Azzoni (2001) has analyzed regional inequality in Brazil using data from period 1939-1995. Barro (2000) has used a panel data approach to investigate 100 countries for period 1960-1990. Bandelj and Mahutga (2010) have presented one of cross-national analyses of Central and Eastern European States after fall of communistic regimes. While Azzoni (2001) and Barro (2000) have focused on linkage of inequality and growth, Bandelj and Mahutga (2010) have assessed inequality and socio-economic changes. Beckfield (2009) has developed an argument that regional integration in Europe has affected economic inequality. Also Forbes (2000) has investigated relationship between inequality and growth. In this research data from 13 EU4 countries have been used from period 2000-2009 in an attempt to investigate relationship between income inequality and inflation. The paper is organized as follows: Section 2 gives a brief introduction to income inequality and inflation and outlines some related theoretical and empirical literature. Section 3 presents methodology and results while section 4 concludes research. 2. Inequality and Inflation The GINI coefficient is a widely used statistic for measuring inequality. It is derived from Lorenz curve and defined as ratio of area between Lorenz curve and perfect equality line. The Lorenz curve plots relation between cumulative percentage of population and proportion of total income earned by each cumulative percentage. The dependent variable is GINI coefficient; a common measure of inequality that varies from 0 to 1, where 0 presents perfect equality and 1 perfect inequality. As it is stated in Duro (2004) the GINI coefficient is more sensitive to income changes occurred at middle of income distribution, treating symmetrically lower and upper tails of incomes ranking. Due to fact that income distribution may have long run effects policy makers should be concerned with distributional implications of government policies. Also extent of inequality-inflation link is important in designing of stabilization programs as it is stated in Al-Mahrubi (2000). When unemployment rates increase it usually affect more people in lower tail of personal income distribution, thus lowering average per capita income (Levernier, et al., 1995). Checchi and Garcia-Penalosa (2008) argue that when unemployment rate is not too high unemployment and inequality linkage is positive. Beetsma and Van Der Ploeg (1996), Al-Mahrubi (1997), Romer and Romer (1998) and Albanesi (2001, 2007) have found a strong positive relation between inflation and inequality. Cardoso (1992) has concluded that inflation shifts wage profile. Bulif (1998) has used a cross-sectional approach regressing GINI coefficients and has found that higher inflation is associated with more inequality (Crowe, 2004). Milanovic (1994) argues about factors which determine income distribution. Factors are in short run, from point of view of policy makers or society as a whole given and by social (or public policy) choice. Milanovic (1994) tests hypothesis according to which government policies can significantly change income distribution and Kuznet holds. Al-Marhubi (1997) investigates inflation-inequality link by using positive political-economy approach and finds that countries which have a greater inequality have a higher average rate of inflation. The dependent variable which is used in Al-Mahrubi model is average annual inflation rate in log form and independents are GINI coefficient, openness, political instability, turnover of Central Bank Governors and legal Central Bank independence. …

Time‐reversal techniques for MISO and MIMO wireless communication systems

We consider the application of different time‐reversal (TR) signal processing and beamforming techniques to multiple‐input single‐output (MISO) and multiple‐input multiple‐output (MIMO) wireless communication systems. Conventional TR beamforming provides spatial focusing at the intended receiver; however, it does not yield perfect channel equalization. Time‐reversed pilot can be normalized to provide perfect equalization at the expense of power level. This equalization is particularly important for high data rates where the bit error rate performance is dominated by internal noise due to intersymbol interference. To increase physical layer covertness, TR beamforming is combined with the multiple‐signal‐classification (MUSIC) technique to produce null fields at eavesdroppers. This technique is also applied to MIMO setups to eliminate interuser interference and hence increase system capacity. Differential TR is used to obtain and update pilot signals for passive moving receivers, i.e., those that cannot (or do not) transmit pilot signals. Time‐reversed differential backscattered signal is able to provide satisfactory spatial and temporal focusing at the moving receiver.

Equity implications of coverage and use of insecticide treated nets distributed for free or with co-payment in two districts in Tanzania: A cross-sectional comparative household survey

BackgroundIn Tanzania, the distribution and coverage of insecticide-treated nets (ITNs) is inequitable. Arguments about the most effective and equitable approach to distributing ITNs centre around whether to provide ITNs free of charge or continue with existing social marketing strategies. The Government has decided to provide free ITNs to all children under five in the country. It is still uncertain whether this strategy will achieve equitable coverage and use. This study examined the equity implications of ownership and use of ITNs in households from different socioeconomic quintiles in a district with free ITNs and a district without free ITN distribution.MethodsA cross-sectional comparative household survey was conducted in two districts: Mpanda in Rukwa Region (with free ITN roll out) and Kisarawe in Coast region (without free ITNs). Heads of 314 households were interviewed in Mpanda and Kisarawe. The concentration index was estimated and regression analysis was performed to compare socioeconomic inequalities in ownership and use of ITNs.ResultsOwnership of ITNs increased from 29% in the 2007/08 national survey to 90% after the roll out of free ITNs in Mpanda, and use increased from 13% to 77%. Inequality was considerably lower in Mpanda, with nearly perfect equality in use (concentration index 0.009) and ownership (concentration index 0.010). In Kisarawe, ownership of ITNs increased from 48% in the 2007/08 national survey to 53%, with a marked inequality concentration index 0.132. ITN use in Kisarawe district was 42% with a pro rich concentration index of 0.027.ConclusionsThe results shed some light on the possibilities of reducing inequality in ownership and use of ITNs and attaining Roll Back Malaria and Millennium Development Goals through the provision of free ITNs to all. This has the potential to decrease the burden of disease and reduce disparity in disease outcome.

Gut microbiota and obesity

Intestinal epithelium, mucosal immune system, and bacterial flora represent a morpho-functional system on dynamic balance responsible for the intestinal metabolic and trophic functions, and the regulation of mucosal and systemic host's immunity. Obesity is a pathological condition affecting a growing number of people especially in the Western countries resulting from the failure of the organism's energetic balance based on the perfect equality of income, waste, and storage. Recent evidences explain the mechanisms for the microbial regulation of the host's metabolism both in health and disease. In particular, animal studies have explained how quali-/quantitative changes in microflora composition are able to affect the absorption of the nutrients and the energy distribution. Antibiotics, prebiotics, probiotics, and symbiotics are the instruments utilized in the current clinical practice to modulate the intestinal bacterial flora in man both in health and pathologic conditions with promising preliminary results on prevention and therapy of obesity and related metabolic diseases.

Design and Evaluation of Instrumented Smart Knee Implant

The goal of ligament balancing in total knee arthroplasty (TKA) is to distribute the tibiofemoral compressive forces symmetrically between the medial and lateral compartments of a well-aligned prosthetic knee, as well as to reestablish a rectangular and identical tibiofemoral gap in both flexion and extension. Nowadays, the proper alignment of knee mechanical axis and the perfect equalization of flexion and extension gaps are ensured by computer-assisted TKA (CATKA). Nevertheless, any residual imbalance of collateral ligaments at the time of surgery can lead to an excessive imbalance in the postoperative period during the weight-bearing activities, which subject the knee collateral ligaments to increased loading. This in turn leads to an accelerated polyethylene wear, and consequently, to early failure of TKA. The instrumented tibial implant proposed in this study can postoperatively assess and monitor the progression of residual postoperative ligament imbalance of a prosthetic knee, which is perfectly aligned during the surgery thanks to CATKA, via a center-of-pressure (COP)-based approach. This approach depends on the measurement of relative displacement of COP position during the postoperative period with respect to a reference position recorded at the beginning of this period. This measurement is performed for six predetermined flexion angles representative of an entire gait cycle. The tibial implant can also generate the electrical power in addition to their role in monitoring the COP position thanks to the piezoceramics embedded within the tibial tray to achieve this twofold task. Experimental and finite-element analysis (FEA) studies have been conducted to validate the methodology used for the postoperative assessment of residual knee laxity. The issues concerning electrical energy generation and data transmission will be thoroughly discussed in another paper.

Social Protection during Disasters: Evidence from the Wenchuan Earthquake

Using evidence from the Wenchuan earthquake (12 May 2008) in China, this article examines the impact of disaster on the functioning of China's social protection system. The article examines the social protection system and the recipients of social protection. It presents four main findings: (1) the impact of the disaster on the social protection system itself was considerable; (2) the system was able to cope fairly successfully with the enormous demands created by the earthquake by a surge of resource utilisation; (3) there was an alarming rate of burnout and possible degradation in capabilities after several months, which may affect the effectiveness of the reconstruction stage, and (4) the demands of the public for perfect equality of treatment has hindered targeting of resources, but also simplified the operation at the relief stage. The article concludes with tentative proposals as to the nature of the institutional resilience expressed in the surge.

Geographical Distribution of Ophthalmologists Before and After the New Postgraduate Training Program in Japan

Purpose: To assess the geographical distribution of ophthalmologists in Japan before and after the start of a new postgraduate training program, which was suggested to exacerbate the uneven distribution of physicians.Methods: The number of physician per million population was calculated for ophthalmologists by using adjusted municipal boundaries and the data from physician censuses performed in 1996 and 2006, as well as the population censuses performed in 1995 and 2005, respectively. The Gini coefficients, income inequality measure that ranges from 0 (perfect equality) to 1 (perfect inequality), and 95% confidence intervals (95%CIs) were computed from the Lorenz curves for the 2 periods.Results: The total number of ophthalmologists increased from 10,982 to 12,362 over the last decade. The Gini coefficient (95%CI) for ophthalmologists was 0.405 (0.314–0.496) and 0.353 (0.272–0.434) in 1996 and 2006, respectively.Conclusions: The geographical distribution of ophthalmologists in 2006 was better than that in 1996, although there was no statistically significant change. There is no evidence that the new postgraduate training program encouraged an imbalance in the geographical distribution of ophthalmologists.

Theoretical Determination of the Structural, Bonding, and Magnetoresponsive Properties of Square-Planar Ligand-Protected Noble Metal (Cu, Ag, Au) Clusters

Electronic structure calculations (DFT) suggest that “ligand-protected” four-membered rings of noble metals formulated as [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) are thermodynamically stable molecules with respect to their dissociation either to ML monomers or to M2L2 dimers. The M2L2 dimers are the products of the thermodynamically favored oxidative addition reactions of the L2 to M2 diatomic species. The [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules adopt square-planar structures involving bridging stabilizing ligands L, except [c-Au4(μ2-CH3)4]. All [c-M4(μ2-L)4] clusters are characterized by perfect planarity and equalization of all metal−metal bonds in the metallic rings, with the only exception being the [c-Cu4(μ2-Br)4] and [c-Cu4(μ2-I)4] clusters, which adopt a diamond-like core structure. In all four-membered metallic rings the intermetallic interactions are relatively weak, described as cuprophilic, argentoph...

A closed approximated formed expression for the achievable residual intersymbol interference obtained by blind equalizers

In this paper I propose for the noiseless, real and independent quadrature carrier case a closed approximated formed expression for the achievable residual intersymbol interference (ISI) that depends on the step-size parameter, equalizer's tap length, input signal statistics and channel power. In addition, a new closed formed approximated expression is proposed for the above mentioned case, that indicates if the chosen blind equalization method leads to perfect equalization performance from the residual ISI point of view. This new approximated expression can be a useful tool for equalization performance comparison between blind equalizers. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need anymore to carry out any simulation with various step-size parameters in order to reach the required residual ISI. The new approximated expression for the residual ISI is applicable for type of blind equalizers where the error that is fed into the adaptive mechanism which updates the equalizer's taps can be expressed as a polynomial function of the equalized output. It should be pointed out that Godard's algorithm for example, belongs to the mentioned type of blind equalizers.

Poverty and Disequalization

We study the intergenerational transmission of inequality using a model in which parents can make both financial and occupational bequests to their children. An equal steady state with high per capita skill can co-exist with unequal steady states with low per capita skill. We investigate dynamics starting from arbitrary initial conditions. The main result is that even if a country starts with a perfectly equal wealth distribution, it converges to an unequal steady state if its initial per capita wealth falls below a threshold, and to the equal steady state otherwise. Hence initial poverty (even with perfect equality) can generate long-term inequality, and undermine economic development.

Economic and Equity Evaluation of Delhi Metro

This paper examines the economic and equity implications of the introduction of a metro system in Delhi. Generalized cost of each mode is used as an indicator of mobility, where as, accessibility is measured in terms of consumer surplus. A combined mode destination choice model is employed to assess the change in the generalized costs of existing modes after the metro introduction. The accessibility benefits of a metro are estimated using the logsum approach to estimate the consumer surplus of transit riders. The well established quantitative measure of equity, the GINI coefficient, is used to link mobility and accessibility to equity. Results indicate a reduction in the generalized costs of three existing modes, i.e. bus, car and the two wheelers. The magnitude of change is the lowest for bus and the highest for two wheelers. The estimated average change in welfare according the calibrated model is 45.32 Rs/trip (0.923 $US) which equals 90.64 Rs/day (1.85 $US), assuming two work trips per person per day. The results of the equity measure indicate a shift towards the line of perfect equality, concluding that the introduction of metro shows a positive impact on equity (of mobility and accessibility).

But what is government itself but the greatest of all reflections on human nature?

I n the last chapter of his book, On the Origin of Species, Charles Darwin wrote famously: ‘‘Light will be thrown on the origin of man and his history.’’ Not many of us have taken him literally. People interested in Darwinian theory have tried to understand the roughly 200,000-year-old origins of Homo sapiens; but they’ve had very little to say about the roughly 5,000-year-old written record that is human history. Nearly 40 years after his boat docked at Falmouth, Darwin did his best to explain the ‘‘low condition’’ of people he’d met aboard the Beagle. The trouble seemed to have something to do with their ‘‘nomadic habits, unfavorable to human progress,’’ he thought. ‘‘Whilst observing the barbarous inhabitants of Tierra del Fuego, it struck me that the possession of some property, a fixed abode, and the union of many families under a chief were the indispensable requisitions for civilization. Such habits almost necessitate the cultivation of the ground.’’ Like most nineteenth-century British aristocrats, Darwin did not consider egalitarianism an asset. ‘‘The perfect equality among the individuals composing the Fuegian tribes, must for a long time retard their civilization,’’ he wrote. But he knew, as well as anybody, that inequality wasn’t always good for the weak—if beneficial to chiefs. He’d visited the natives in Australia, where ‘‘the women are the constant cause of war both between members of the same tribe and between distinct tribes.’’ And he had read about North American Indians, where ‘‘the contest is reduced to a system,’’ no weak man being permitted to keep a wife that a stronger man thought worth his notice. Besides, having been brought up on the classics, Darwin remembered his Horace: ‘‘Nam fuit ante Helenam mulier teterrima belli causa;’’ they’d gone to war for a girl in Troy. For Homo sapiens, as for any other species, the point of politics had always been sex—in an evolutionary sense. Winners became breeders; but losers did not. ‘‘This fact is so notorious it would be superfluous to give instances.’’ Only in the last half century have we started to use Darwin’s theory to solve Darwin’s problem: to understand why some animals are more ‘‘civilized’’ than others. As it turns out, most animals live alone, most of the time. More than 98% of all insect, bird and mammal species are solitary. But a few live in groups. And when they do, some animals—usually bigger, stronger animals—lay or fertilize most of the eggs; and other animals—usually smaller, weaker animals—do most of the work or help. Some animals have been referred to as ‘‘cooperative breeders,’’ or alloparental. They live in societies ranging in size from a handful to hundreds of individuals; and most of those individuals are temporary, or ‘‘facultative,’’ nonbreeders. Roughly 220 species of birds, roughly 120 species of mammals, and a variety of other species are considered cooperative breeders. 6 So what turns hundreds of otherwise fertile individuals into helpers-at-the-nest? One answer seems to be: a hard-to-escape habitat. Cooperative breeders live on clumps of stunted oak along Florida’s old sand dunes; or on patches of lush Maldonado meadow grasses; or under the protective eaves of houses; or in the dense cover of shrubs and thickets. Where prey is abundant and predators are scarce, animals tend to get together in groups, where a handful doi: 10.2990/28_2_102

A Quadratic Programming Approach to Blind Equalization and Signal Separation

Blind equalization and signal separation are two well-established signal processing problems. In this paper, we present a quadratic programming algorithm for fast blind equalization and signal separation. By introducing a special non-mean-square error (MSE) objective function, we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem. Based on a clear geometric interpretation and a formal proof, we show that a perfect equalization solution is obtained at every local optimum of the quadratic program. Because blind source separation is, by nature and mathematically, a closely related problem, we also generalize the algorithm for blind signal separation. We show that by enforcing source orthogonalization through successive processing, the quadratic programming approach can be applied effectively. Moreover, the quadratic program is easily extendible to incorporate additional practical conditions, such as jamming suppression constraints. We also provide evidence of good performance through computer simulations.

Analysis of the land use structure changes based on Lorenz curves

Land use change has become a new field in global change research, and it is closely related to land resource security and sustainable development. The environmental simulation model was mostly used to study the land-use change before. In this paper, we use the Economic Lorenz curve and Gini coefficient of economic model to study the land use structure changes in the western plain of Jilin Province, China. The results showed that the Lorenz curve has the phenomenon of "two near and two far" and Gini coefficient "two increased and two decreased". That is to say, during the 15 years from 1989 to 2004, the areas of cultivated land and unused land had increased, Lorenz curves were near to the perfect equality line, and the distribution tended to be uniform; the areas of grassland and water body were reduced, the Lorenz curves were away from the perfect equality line, and the distribution tended to be increasingly uneven, which reflects the main process of the land use structure changes. Studying on the land use changes based on Economic model is simpler and more intuitionistic, and had the generalization values.

Semi-Blind Layered Space-Frequency Equalization for Single-Carrier MIMO Systems with Block Transmission

This letter proposes a novel semi-blind layered space-frequency equalization (LSFE) receiver for single- carrier cyclic-prefix (SC-CP) multiple-input multiple-output (MIMO) systems with block transmission, based on independent component analysis (ICA). Simulation results show that semi- blind LSFE with various Doppler shifts can provide performance close to the case with perfect channel state information (CSI), using a training overhead of only 0.05%. It also significantly outperforms its orthogonal frequency division multiplexing (OFDM) counterpart with perfect CSI and semi-blind linear SC frequency domain equalization (SC-FDE) over a wide range of signal to noise ratios (SNRs).