On nuclearity of Köthe spaces

In this study we observe that the Köthe spaces Klp(A) is nuclear when it is complementedly embedded in Klq (B) for 1 p 2

Varentropy Decreases Under the Polar Transform

We consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair $(X,Y)$ consisting of a binary random variable $X$ and an arbitrary side information random variable $Y$. The varentropy of $(X,Y)$ is defined as the variance of the random variable $-\log p_{X|Y}(X|Y)$. A polar transform of order two is a certain mapping that takes two independent BDEs and produces two new BDEs that are correlated with each other. It is shown that the sum of the varentropies at the output of the polar transform is less than or equal to the sum of the varentropies at the input, with equality if and only if at least one of the inputs has zero varentropy. This result is extended to polar transforms of higher orders and it is shown that the varentropy decreases to zero asymptotically when the BDEs at the input are independent and identially distributed.Comment: Presented in part at ISIT 2014. Accepted for publication in the IEEE Trans. Inform. Theory, March 201

A Packing Lemma for Polar Codes

A packing lemma is proved using a setting where the channel is a binary-input discrete memoryless channel $(\mathcal{X},w(y|x),\mathcal{Y})$, the code is selected at random subject to parity-check constraints, and the decoder is a joint typicality decoder. The ensemble is characterized by (i) a pair of fixed parameters $(H,q)$ where $H$ is a parity-check matrix and $q$ is a channel input distribution and (ii) a random parameter $S$ representing the desired parity values. For a code of length $n$, the constraint is sampled from $p_S(s) = \sum_{x^n\in {\mathcal{X}}^n} \phi(s,x^n)q^n(x^n)$ where $\phi(s,x^n)$ is the indicator function of event $\{s = x^n H^T\}$ and $q^n(x^n) = \prod_{i=1}^nq(x_i)$. Given $S=s$, the codewords are chosen conditionally independently from $p_{X^n|S}(x^n|s) \propto \phi(s,x^n) q^n(x^n)$. It is shown that the probability of error for this ensemble decreases exponentially in $n$ provided the rate $R$ is kept bounded away from $I(X;Y)-\frac{1}{n}I(S;Y^n)$ with $(X,Y)\sim q(x)w(y|x)$ and $(S,Y^n)\sim p_S(s)\sum_{x^n} p_{X^n|S}(x^n|s) \prod_{i=1}^{n} w(y_i|x_i)$. In the special case where $H$ is the parity-check matrix of a standard polar code, it is shown that the rate penalty $\frac{1}{n}I(S;Y^n)$ vanishes as $n$ increases. The paper also discusses the relation between ordinary polar codes and random codes based on polar parity-check matrices.Comment: 5 pages. To be presented at 2015 IEEE International Symposium on Information Theory, June 14-19, 2015, Hong Kong. Minor corrections to v

Source Polarization

The notion of source polarization is introduced and investigated. This complements the earlier work on channel polarization. An application to Slepian-Wolf coding is also considered. The paper is restricted to the case of binary alphabets. Extension of results to non-binary alphabets is discussed briefly.Comment: To be presented at the IEEE 2010 International Symposium on Information Theory

The Causality Analysis of External Debt Service and GNP : The Case of Turkey

It is argued that debt service burden has a negative impact on investment and capital accumulation. The main reason is that the greater percentage of reserves (foreign currency) goes to meet debt service and there will be a reduction in external capital because of a decrease in creditworthiness. This paper extends the model of Cunningham (1992) and uses multivariate cointegration techniques to develop a vector error correction model useful for investigating the long-run effects of external debt service on GNP level. Moreover, the information on cointegration (Johansen ,1988 and Johansen &Juselius ,1990) in variables are taken into consideration in specifying the correct model. We apply our methodology to Turkey and show how external debt service is having a negative short -run impact on economic growth. The results also show that there is a uni-directional causal relationship between debt service and GNP level.Turkey, External Debt, Cointegration, Causality

The relationship between the F-test and the Schwarz criterion: Implications for Granger-causality tests

In applied research, the Schwarz Bayesian Information Criterion (BIC) and the F-test might yield different inferences about the causal relationships being investigated. This paper examines the relationship between the BIC and the F-tests in the context of Granger-causality tests. We calculate the F-test significance levels as a function of the model dimensionality and the sample size that would lead to the same conclusion as the BIC. We illustrate that the BIC would reject the null hypothesis of no-causality less often compared to an F-test conducted at five percent significance level for sample sizes above 50 especially when the chosen model dimensionality is small. Putting the philosophical issues aside, we suggest that the decision to choose between the F-test and the BIC should be made in view of the sample size.F-test, Schwarz Bayesian Information Criterion, Model selection, Granger-causality

Quarantine region scheme to mitigate spam attacks in wireless sensor networks

The Quarantine Region Scheme (QRS) is introduced to defend against spam attacks in wireless sensor networks where malicious antinodes frequently generate dummy spam messages to be relayed toward the sink. The aim of the attacker is the exhaustion of the sensor node batteries and the extra delay caused by processing the spam messages. Network-wide message authentication may solve this problem with a cost of cryptographic operations to be performed over all messages. QRS is designed to reduce this cost by applying authentication only whenever and wherever necessary. In QRS, the nodes that detect a nearby spam attack assume themselves to be in a quarantine region. This detection is performed by intermittent authentication checks. Once quarantined, a node continuously applies authentication measures until the spam attack ceases. In the QRS scheme, there is a tradeoff between the resilience against spam attacks and the number of authentications. Our experiments show that, in the worst-case scenario that we considered, a not quarantined node catches 80 percent of the spam messages by authenticating only 50 percent of all messages that it processe

Single Mothers Working at Night: Standard Work, Child Care Subsidies, and Implications for Welfare Reform

Using a data set from the post welfare reform environment (the 1999 National Survey of America's Families), this paper investigates the impact of child care subsidies on the standard work (i.e., work performed during the traditional work hours of 8 a.m. and 6 p.m. through Monday and Friday) decision of single mothers and tests whether this impact differs between welfare recipients and nonrecipients. The econometric strategy accounts for sample selection into the labor force and the potential endogeneity of child care subsidy receipt and welfare participation. Results suggest that child care subsidies are associated with a 6 percentage point increase in the probability of single mothers working at standard jobs. When the impact of subsidies is allowed to differ between welfare recipients and non-recipients, results indicate that welfare recipients are 14 percentage points more likely to work at standard jobs than others when they are offered a child care subsidy. Among non-recipients, child care subsidies increase standard work probability by only 1 percentage point. These results underscore the importance of child care subsidies helping low-income parents, especially welfare recipients, find jobs with conventional or standard schedules and lend support to the current practice of states' giving priority to welfare recipients for child care subsidies. Results are found to be robust to numerous specification checks.