In signal processing applications it is often required to compute the integral of the bivariate Gaussian probability density function (pdf) over the four quadrants. When the mean of the random variables are non-zero, computing the closed form solution to these integrals with the usual techniques of integration is infeasible. Many numerical solutions have been proposed, however, the accuracy of these solutions depends on various constraints. In this paper, we derive the closed form solution to this problem using the characteristic function method. The solution is derived in terms of the well-known confluent hypergeometric function. When the mean of the random variables is zero, the solution is shown to reduce to a known result for the value of the integral over the first quadrant. The solution is implementable in software packages such as MAPLE.

In this paper, we investigate a sequential test for binary hypothesis testing for stationary, first-order Markov dependent observations in steady state. Wald's first and second lemmas are generalized. For a Markov chain with symmetric transition probability matrix the average sample number required by the test to decide a hypothesis is derived. Numerical analysis shows that accounting for a positive correlation in the observations results in a significant decrease in the average sample number for fixed error probabilities.

Sequential feedback communications has wide ranging applications such as low power communications, error-resilience protocols etc. Two kinds of feedback communication systems can be indentified: information feedback and decision feedback.

Covert channels are of two types: (a) timing channel and (b) storage channel. Most previous works have studied these channels from the encoder’s perspective, namely, information theoretic capacity, algorithms and protocols for hiding information etc. This paper investigates the covert channel problem from an passive adversary’s perspective. A sequential distinguisher for storage channel identification by an adversary is proposed and its properties are derived analytically. The impact of correlation in the observations received by the adversary is studied analytically as well as numerically.

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