Accurate A/D conversion with inaccurate devices
Sinan Güntürk (CIMS)

This talk aims to present a mathematical study of the robustness issue in analog-to-digital (A/D) conversion. Any A/D converter has to operate with analog devices, and is therefore highly susceptible to component variations. A simplistic point of view assumes that the accuracy of a converter is dictated by the accuracy of the arithmetical operations implemented in its analog circuitry. However this is far from the truth, as the encoding mechanisms of these converters can be designed to be robust against specific types of imperfections by introducing redundant codewords. These encoders operate very differently compared to classical error-correcting codes as their 'corrupted' codewords differ greatly in the Hamming metric, but very little in their decoding neighborhood. We will present some explicit examples of encoding strategies based on dynamical systems ideas.