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Partial Ordering and Stochastic Resonance in Discrete Memoryless Channels

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Technical Report

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The University of the District of Columbia Washington United States

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In this thesis, we study the performance of Discrete Memoryless Channels DMCs arising in the context of cooperative underwater wireless sensor networks. We introduce a partial ordering for the binary-input ternary-output 2,3 DMC. In the particular case of the Binary Symmetric Channel with Symmetric Erasure BSCSE, we use majorization theory, channel convexity and directional derivative in order to obtain a partial solution to the open problem of partial ordering of the DMCs. In addition, we analyze the stochastic resonance SR phenomenon impact upon the performance limits of a distributed underwater wireless sensor networks operating with limited transmitted power and computational capabilities. We focus on the threshold communication systems where, due to the underwater environment, non-coherent communication techniques are affected both by noise and threshold level. The binary-input ternary-output channel is used as a theoretical model for the DMC. We derived the capacity of the threshold 2,3 DMC in the presence of additive noise. In order to evaluate stochastic resonance, we model the theoretical 2,3 DMC as a physical communication channel corrupted by additive noise with different probability distributions. The 2,3 DMC becomes the BSCSE when the probability density function of the additive noise is an even function such as Gaussian, Laplace, and Cauchy distribution. Due to the complexity and the non-linearity of the channel capacity analytical expression, the Pinsker and Helgert capacity bounds are also used to evaluate the stochastic resonance in the case of the 2,3 DMC. Our contribution consists in improving the state of the art on the issue of partial ordering for the 2,3 DMC and deriving the optimal noise level required to obtain the maximum capacity for a given threshold decision level in the case of the binary-input ternary-output DMC.

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  • Operations Research
  • Cybernetics

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