## 4 Conclusions  
In this article, we first gave an overview of the information bottleneck method and explained how it can be linked to the fundamental task of a digital communication receiver. The application of the information bottleneck method for receiver-side signal processing in this context effectively allows building quantized signal processing units that aim to maximize the relevant information that flows through them. This concept is fundamentally different from conventional quantized signal processing approaches, which typically aim to minimize an expected error measure, such as the mean squared error. Based on the principle of maximizing the preserved relevant information under quantization, we presented and investigated an iterative receiver structure for a frequency-flat fading channel that employs advanced signal processing concepts for iterative LDPC decoding, decision feedback-aided channel estimation and detection. All signal processing units in this receiver were designed using the information bottleneck principle of maximizing the preserved relevant information under quantization. The corresponding signal processing operations applied in the constructed receiver were implemented as static lookup tables that were designed offline with the information bottleneck method. Despite this fact, the designed receiver did not suffer from any mentionable performance degradation in comparison with a conventional receiver with double-precision signal processing and belief propagation decoding. After having studied the fundamental idea and the lookup table-based implementation of information bottleneck signal processing units in the receiver implementation, other methods for learning and implementing mutual information-maximizing signal processing units for LDPC decoders were also recalled from the literature and investigated. Our main conclusion is that the considered approaches to information bottleneck signal processing, including the one based on lookup tables, effectively aim to learn the parameters \(\mathbf{\theta}\) of trainable functions \(f_{\mathbf{\theta}}(\mathbf{y})\) that are tuned to maximize the preserved relevant information \(\mathrm{I}(\mathrm{X};f_{\mathbf{\theta}}(\mathbf{Y}))\) under a constraint for the cardinality of the value set of \(f_{\mathbf{\theta}}(\mathbf{y})\). We note that the ways to learn the respective parameters differ depending on the kind of function that is designed to preserve the relevant information. While the lookup table based approaches typically employ information bottleneck algorithms, the computational domain approach from [24; 25] uses a quantizer design algorithm to determine the optimum quantization thresholds. The neural network-based approaches from [28; 29] mimic lookup tables or directly use gradient-based algorithms to maximize the preserved relevant information. Even more ideas that use nearest neighbor search algorithms to implement information bottleneck signal processing units and genetic algorithms to tune their parameters were proposed in the literature [64; 65]. Finally, what all these approaches have in common is the learning of trainable parameters to maximize the preserved relevant information under quantization. A lot of very interesting open research questions on information bottleneck signal processing arise from the problem of finding powerful and, at the same time, simple trainable functions for different signal processing applications that allow preserving huge amounts of relevant information. Moreover, exploring the methods for efficient training of the involved parameters, such as using genetic algorithms or gradient-based schemes, is interesting. **Author Contributions:** Conceptualization, J.L., G.B. and M.S. ; methodology, J.L. and M.S. ; software, J.L. and M.S. ; validation, J.L., G.B. and M.S. ; formal analysis, J.L., G.B. and M.S. ; investigation, J.L., G.B. and M.S. ; resources, J.L. ; writing--original draft preparation, J.L. ; writing--review and editing, J.L., G.B. and M.S. ; visualization, J.L., G.B. and M.S.