On The Asymptotics of Some Low-Delay Transmission Scenarios

The first part of the thesis focuses on asymptotic energy-distortion performance of zero- and low-delay transmission of Gaussian sources over energy-limited Gaussian channels. A lower bound for the leading term in the negative logarithm of the distortion, termed the energy-distortion exponent, is derived through an achievable scheme based on high-resolution quantization coupled with orthogonal signaling. The higher-order term in the negative logarithm of the distortion, termed the energy-distortion dispersion, is optimized while keeping the leading term, the energy-distortion exponent, at its optimal (respectively, the best known) value for the zero-delay (respectively, low-delay) regime. In contrast with the decaying dispersion previously reported in the literature, the proposed coding scheme achieves a constant dispersion. When the scheme is optimized, this constant can be improved with respect to its naive value, i.e., that achieved by optimizing purely the source coding performance instead of the end-to-end distortion. Lastly, a tradeoff of achievable energy-distortion exponents is derived for broadcast scenarios by extending the point-to-point scheme to include a successive refinement source coder coupled with two rounds of orthogonal signaling. The second part examines the idea of randomized response together with the method of types and large deviations techniques to analyze the accuracy of potential electronic privacy-preserving voting and survey schemes. Previous work by Tuncel [1] proposed a voting scheme in which votes are randomly changed by the system before being transmitted with a chosen flipping probability to preserve the privacy of the voters. The vulnerable interval in [1], where the voting results are very close to 50%-50%, is tackled by introducing a third possible outcome referred to as "too close to call". This third outcome is used as a feedback to adjust the flipping probability so that small upper bounds on the probability of wrongly calling the election could be given. A natural tradeoff arises between the probability of wrongly calling the election and the probability of a too-close-to-call outcome