Rick Fritschek

Muah Kim, Rick Fritschek, Rafael F. Schaefer

Strong generative models can accurately learn channel distributions. This could save recurring costs for physical measurements of the channel. Moreover, the resulting differentiable channel model supports training neural encoders by enabling gradient-based optimization. The initial approach in the literature draws upon the modern advancements in image generation, utilizing generative adversarial networks (GANs) or their enhanced variants to generate channel distributions. In this paper, we address this channel approximation challenge with diffusion models (DMs), which have demonstrated high sample quality and mode coverage in image generation. In addition to testing the generative performance of the channel distributions, we use an end-to-end (E2E) coded-modulation framework underpinned by DMs and propose an efficient training algorithm. Our simulations with various channel models show that a DM can accurately learn channel distributions, enabling an E2E framework to achieve near-optimal symbol error rates (SERs). Furthermore, we examine the trade-off between mode coverage and sampling speed through skipped sampling using sliced Wasserstein distance (SWD) and the E2E SER. We investigate the effect of noise scheduling on this trade-off, demonstrating that with an appropriate choice of parameters and techniques, sampling time can be significantly reduced with a minor increase in SWD and SER. Finally, we show that the DM can generate a correlated fading channel, whereas a strong GAN variant fails to learn the covariance. This paper highlights the potential benefits of using DMs for learning channel distributions, which could be further investigated for various channels and advanced techniques of DMs.

Onur Günlü, Rick Fritschek, Rafael F. Schaefer

Small neural networks (NNs) used for error correction were shown to improve on classic channel codes and to address channel model changes. We extend the code dimension of any such structure by using the same NN under one-hot encoding multiple times, then serially-concatenated with an outer classic code. We design NNs with the same network parameters, where each Reed-Solomon codeword symbol is an input to a different NN. Significant improvements in block error probabilities for an additive Gaussian noise channel as compared to the small neural code are illustrated, as well as robustness to channel model changes.

Rick Fritschek, Rafael F. Schaefer

Early neural channel coding approaches leveraged dense neural networks with one-hot encodings to design adaptive encoder-decoder pairs, improving block error rate (BLER) and automating the design process. However, these methods struggled with scalability as the size of message sets and block lengths increased. TurboAE addressed this challenge by focusing on bit-sequence inputs rather than symbol-level representations, transforming the scalability issue associated with large message sets into a sequence modeling problem. While recurrent neural networks (RNNs) were a natural fit for sequence processing, their reliance on sequential computations made them computationally expensive and inefficient for long sequences. As a result, TurboAE adopted convolutional network blocks, which were faster to train and more scalable, but lacked the sequential modeling advantages of RNNs. Recent advances in efficient RNN architectures, such as minGRU and minLSTM, and structured state space models (SSMs) like S4 and S6, overcome these limitations by significantly reducing memory and computational overhead. These models enable scalable sequence processing, making RNNs competitive for long-sequence tasks. In this work, we revisit RNNs for Turbo autoencoders by integrating the lightweight minGRU model with a Mamba block from SSMs into a parallel Turbo autoencoder framework. Our results demonstrate that this hybrid design matches the performance of convolutional network-based Turbo autoencoder approaches for short sequences while significantly improving scalability and training efficiency for long block lengths. This highlights the potential of efficient RNNs in advancing neural channel coding for long-sequence scenarios.

Muah Kim, Rick Fritschek, Rafael F. Schaefer

It is a known problem that deep-learning-based end-to-end (E2E) channel coding systems depend on a known and differentiable channel model, due to the learning process and based on the gradient-descent optimization methods. This places the challenge to approximate or generate the channel or its derivative from samples generated by pilot signaling in real-world scenarios. Currently, there are two prevalent methods to solve this problem. One is to generate the channel via a generative adversarial network (GAN), and the other is to, in essence, approximate the gradient via reinforcement learning methods. Other methods include using score-based methods, variational autoencoders, or mutual-information-based methods. In this paper, we focus on generative models and, in particular, on a new promising method called diffusion models, which have shown a higher quality of generation in image-based tasks. We will show that diffusion models can be used in wireless E2E scenarios and that they work as good as Wasserstein GANs while having a more stable training procedure and a better generalization ability in testing.

Gerhard Wunder, Benedikt Groß, Rick Fritschek et al.

The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric means or the Hölder inequality. In a probabilistic setting, the Jensen inequality describes the relationship between a convex function and the expected value. In this work, we want to look at the probabilistic setting from the reverse direction of the inequality. We show that under minimal constraints and with a proper scaling, the Jensen inequality can be reversed. We believe that the resulting tool can be helpful for many applications and provide a variational estimation of mutual information, where the reverse inequality leads to a new estimator with superior training behavior compared to current estimators.

Rick Fritschek, Rafael F. Schaefer, Gerhard Wunder

The use of deep learning-based techniques for approximating secure encoding functions has attracted considerable interest in wireless communications due to impressive results obtained for general coding and decoding tasks for wireless communication systems. Of particular importance is the development of model-free techniques that work without knowledge about the underlying channel. Such techniques utilize for example generative adversarial networks to estimate and model the conditional channel distribution, mutual information estimation as a reward function, or reinforcement learning. In this paper, the approach of reinforcement learning is studied and, in particular, the policy gradient method for a model-free approach of neural network-based secure encoding is investigated. Previously developed techniques for enforcing a certain co-set structure on the encoding process can be combined with recent reinforcement learning approaches. This new approach is evaluated by extensive simulations, and it is demonstrated that the resulting decoding performance of an eavesdropper is capped at a certain error level.

Rick Fritschek, Rafael F. Schaefer, Gerhard Wunder

End-to-end deep learning for communication systems, i.e., systems whose encoder and decoder are learned, has attracted significant interest recently, due to its performance which comes close to well-developed classical encoder-decoder designs. However, one of the drawbacks of current learning approaches is that a differentiable channel model is needed for the training of the underlying neural networks. In real-world scenarios, such a channel model is hardly available and often the channel density is not even known at all. Some works, therefore, focus on a generative approach, i.e., generating the channel from samples, or rely on reinforcement learning to circumvent this problem. We present a novel approach which utilizes a recently proposed neural estimator of mutual information. We use this estimator to optimize the encoder for a maximized mutual information, only relying on channel samples. Moreover, we show that our approach achieves the same performance as state-of-the-art end-to-end learning with perfect channel model knowledge.