###### Abstract
The applications studied in the communications context lead from the design of channel output quantizers [9; 10; 11] over the decoding of low-density parity-check (LDPC) codes [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31] and polar codes [32; 33; 34] to entire receiver chains that include channel estimation and detection [35; 36; 37; 38]. Moreover, the information bottleneck method has been applied in joint source-channel coding, forwarding and relaying applications [39; 40; 41; 42; 43; 44; 45; 46; 47; 48] and in distributed sensor networks [49; 50; 51; 52; 53] successfully. Related works with a focus on inference with the distributiveness of data among multiple nodes and network learning aspects include [54; 55; 56]. It needs to be noted that some of the aforementioned works do not explicitly state themselves to be instances of the information bottleneck method. However, their fundamental ideas are in line with the key principle of the preservation of relevant information under compression. Please also note that even though the references provided above are numerous, we cannot claim to have mentioned all applications of the information bottleneck method and the related principles in communications here. Facing the huge variety of research on applications of the information bottleneck method in communications above, we note that a number of techniques have been proposed to apply information bottleneck signal processing lately. In this article, as a first contribution, we aim to give a quite general introduction to the ideas of receiver-side information bottleneck signal processing. For that purpose, we explain the general idea of the information bottleneck method and link it to the fundamental task of a communication receiver. To illustrate the applicability of the presented ideas to real-world communication receivers, we present and investigate a strongly quantized iterative receiver that is entirely designed with the information bottleneck method and compare its performance to a conventional receiver chain. The presented information bottleneck receiver implements all signal processing operations using lookup tables that are designed with an information bottleneck algorithm. Surprisingly, the presented quantized receiver that is designed with the information bottleneck method performs just as well as a double-precision reference receiver that employs state-of-the-art signal processing algorithms and uses much more costly signal processing operations. Some very fundamental ideas of information bottleneck signal processing were presented already in 2008 for LDPC decoding by [PERSON] et al. [12]. In fact, a special focus lies on the application of information bottleneck signal processing for the coarsely quantized message passing decoding of LDPC codes in the available literature [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. It needs to be appreciated that various authors have proposed very interesting ideas to solve this problem using the paradigm of maximizing the preserved relevant information under quantization with very few bits per message. The literature describes quantized decoders that replace the classical node operations of LDPC decoders completely with lookup tables [12; 14; 15; 16; 18; 20; 21; 23]. In addition, the hybrid min-LUT approach from [17; 22] uses lookup tables only for the variable node operations and a simple arithmetical operation for the check node operations. Moreover, computational domain approaches that pair relatively simple arithmetical operations with mutual information-maximizing quantizers to implement the node operations of LDPC decoders were studied in [24; 25; 30; 31]. Finally, the idea to learn and implement mutual information-maximizing node operations using neural networks was studied in [28; 29]. We note that the design goals of the mentioned methods for LDPC decoding are similar and mainly rely on the information bottleneck idea of maximizing the preserved relevant information.