Error correcting codes are a fundamental component in modern day communication systems, demanding extremely high throughput, ultra-reliability and low latency. Recent approaches using machine learning (ML) models as decoders offer both improved performance and great adaptability to unknown environments, where traditional decoders struggle. We introduce a general framework to further boost the performance and applicability of ML models. We propose to combine ML decoders with a competing discriminator network that tries to distinguish between codewords and noisy words, and, hence, guides the decoding models to recover transmitted codewords. Our framework is game-theoretic, motivated by generative adversarial networks (GANs), with the decoder and discriminator competing in a zero-sum game. The decoder learns to simultaneously decode and generate codewords while the discriminator learns to tell the difference between decoded outputs and codewords. Thus, the decoder is able to decode noisy received signals into codewords, increasing the probability of successful decoding. We show a strong connection of our framework with the optimal maximum likelihood decoder by proving that this decoder defines a Nash equilibrium point of our game. Hence, training to equilibrium has a good possibility of achieving the optimal maximum likelihood performance. Moreover, our framework does not require training labels, which are typically unavailable during communications, and, thus, seemingly can be trained online and adapt to channel dynamics. To demonstrate the performance of our framework, we combine it with recent neural decoders and show improved performance compared to the original models and traditional decoding algorithms on various codes.

The Bayesian online change point detection (BOCPD) algorithm provides an efficient way to do exact inference when the parameters of an underlying model may suddenly change over time. BOCPD requires computation of the underlying model's posterior predictives, which can only be computed online in $O(1)$ time and memory for exponential family models. We develop variational approximations to the posterior on change point times (formulated as run lengths) for efficient inference when the underlying model is not in the exponential family, and does not have tractable posterior predictive distributions. In doing so, we develop improvements to online variational inference. We apply our methodology to a tracking problem using radar data with a signal-to-noise feature that is Rice distributed. We also develop a variational method for inferring the parameters of the (non-exponential family) Rice distribution.