The concepts of a digital twin and extended reality have recently emerged, which require a massive amount of sensor data to be transmitted with low latency and high reliability. For low-latency communications, joint source-channel coding (JSCC) is an attractive method for error correction coding and compared to highly complex digital systems that are currently in use. I propose the use of complex-valued and quaternionic neural networks (QNN) to decode JSCC codes, where the complex-valued neural networks show a significant improvement over real-valued networks and the QNNs have an exceptionally high performance. Furthermore, I propose mapping encoded JSCC code words to the baseband of the frequency domain in order to enable time/frequency synchronization as well as to mitigate fading using robust estimation theory. Additionally, I perform robust statistical signal processing on the high-dimensional JSCC code showing significant noise immunity with drastic performance improvements at low signal-to-noise ratio (SNR) levels. The performance of the proposed JSCC codes is within 5 dB of the optimal performance theoretically achievable and outperforms the maximum likelihood decoder at low SNR while exhibiting the smallest possible latency. I designed a Bayesian minimum mean square error estimator for decoding high-dimensional JSCC codes achieving 99.96% accuracy. With the recent introduction of electromagnetic reconfigurable intelligent surfaces (RIS), a paradigm shift is currently taking place in the world of wireless communications. These new technologies have enabled the inclusion of the wireless channel as part of the optimization process. In order to decode polarization-space modulated RIS reflections, robust polarization state decoders are proposed using the Weiszfeld algorithm and an generalized Huber M-estimator. Additionally, QNNs are trained and evaluated for the recovery of the polarization state. Furthermore, I propose a novel 64-ary signal constellation based on scaled and shifted Eisenstein integers and generated using media-based modulation with a RIS. The waveform is received using an antenna array and decoded with complex-valued convolutional neural networks. I employ the circular cross-correlation function and a-priori knowledge of the phase angle distribution of the constellation to blindly resolve phase offsets between the transmitter and the receiver without the need for pilots or reference signals. Furthermore, the channel attenuation is determined using statistical methods exploiting that the constellation has a particular distribution of magnitudes. After resolving the phase and magnitude ambiguities, the noise power of the channel can also be estimated. Finally, I tune an Sq-estimator to robustly decode the Eisenstein waveform. / Doctor of Philosophy / This dissertation covers three novel wireless communications methods; analog coding, communications using the electromagnetic polarization and communications with a novel signal constellation. The concepts of a digital twin and extended reality have recently emerged, which require a massive amount of sensor data to be transmitted with low latency and high reliability. Contemporary digital communication systems are highly complex with high reliability at the expense of high latency. In order to reduce the complexity and hence latency, I propose to use an analog coding scheme that directly maps the sensor data to the wireless channel. Furthermore, I propose the use of neural networks for decoding at the receiver, hence using the name neural receiver. I employ various data types in the neural receivers hence leveraging the mathematical structure of the data in order to achieve exceptionally high performance. Another key contribution here is the mapping of the analog codes to the frequency domain enabling time and frequency synchronization. I also utilize robust estimation theory to significantly improve the performance and reliability of the coding scheme. With the recent introduction of electromagnetic reconfigurable intelligent surfaces (RIS), a paradigm shift is currently taking place in the world of wireless communications. These new technologies have enabled the inclusion of the wireless channel as part of the optimization process. Therefore, I propose to use the polarization state of the electromagnetic wave to convey information over the channel, where the polarization is determined using a RIS. As with the analog codes, I also extensively employ various methods of robust estimation to improve the performance of the recovery of the polarization at the receiver. Finally, I propose a novel communications signal constellation generated by a RIS that allows for equal probability of error at the receiver. Traditional communication systems utilize reference symbols for synchronization. In this work, I utilize statistical methods and the known distributions of the properties of the transmitted signal to synchronize without reference symbols. This is referred to as blind channel estimation. The reliability of the third communications method is enhanced using a state-of-the-art robust estimation method.