Low complexity extensions of non-linear mappings

Abstract

Linear systems work very well for the transmission of discrete-time continuous amplitude samples in poor signal-to-noise conditions, but their performance does not improve when the quality of the channel increases. Specifically, for high signal-to-noise ratios the gap with respect to the theoretical bounds is extremely large and, therefore, a more suitable method must be found. This is why non-linear encoding schemes have been studied, and several solutions have been proposed that outperform the classic linear approach. In this thesis we present analog non-linear mappings with very simple and flexible design methods, low encoding and decoding complexity, and great robustness against noise. All these characteristics make them very versatile codes ready to be applied in many different scenarios. For example, successful results have been achieved in the transmission of images by creating an analog joint source-channel encoding scheme that combines Compressed Sensing measurements with our non-linear analog codes. We also show an extension of this communication system for underwater acoustic channels and non-linear channels.