###### Abstract  
Digital communication receivers extract information about the transmitted data from the received signal in subsequent processing steps, such as synchronization, demodulation and channel decoding. Technically, the receiver-side signal processing for conducting these tasks is complex and hence causes bottleneck situations in terms of power, delay and chip area. Typically, many bits per sample are required to represent and process the received signal in the digital receiver hardware accurately. In addition, demanding arithmetical operations are required in the signal processing algorithms. A popular recent trend is designing entire receiver chains or some of their crucial building blocks from an information theoretical perspective. Signal processing blocks with very simple mathematical operations can be designed to directly maximize the relevant information that flows through them. At the same time, a strong quantization reduces the number of bits processed in the receiver to further lower the complexity. The described system design approach follows the principle of the information bottleneck method. Different authors proposed various ideas to design and implement mutual information-maximizing signal processing units. The first important aim of this article is to explain the fundamental similarities between the information bottleneck method and the functionalities of communication receivers. Based on that, we present and investigate new results on an entire receiver chain that is designed following the information bottleneck design principle. Afterwards, we give an overview of different techniques following the information bottleneck design paradigm from the literature, mainly dealing with channel decoding applications. We analyze the similarities of the different approaches for information bottleneck signal processing. This comparison leads to a general view on information bottleneck signal processing which goes back to the learning of parameters of trainable functions that maximize the relevant mutual information under compression. information bottleneck; mutual information; machine learning 202224972249722497  
Interestingly, the concept of a relevant random variable was also introduced by [PERSON] et al. in [2] in a very generic information theoretical setup termed the information bottleneck method. Conceptually, this method is not directly linked to the communication problem considered above. The elementary idea of the information bottleneck method is to compress an observed random variable \(Y\) to a compressed variable \(T\) using a compression rule. The compression rule is tailored to preserve relevant mutual information \(I(X;T)\), where \(I(X;T)\leq I(X;Y)\). In this problem formulation, \(X\) is a chosen random variable of interest. This variable defines which features of the observation \(Y\) are relevant and should be preserved under the invoked compression. Hence, this concept can be understood as defining relevance through another variable [2]. The information bottleneck method already has numerous very successful applications, such as in image and speech processing, astronomy and neuroscience [3; 4; 5; 6]. A comprehensive tutorial on the information bottleneck method, its applications in source coding and its connections to inference and representation learning problems can be found in [7]. In addition, a survey on the applicability and usefulness of the information bottleneck for machine learning is provided in [8]. In the past few years, the information bottleneck method gained massive popularity in the communications community. Various authors brought up different ideas to design and implement receiver subsystems and other parts of communcation systems using the information bottleneck principle of maximizing the preserved relevant information.