# Genetic Algorithms to Maximize the Relevant Mutual Information in Communication Receivers +
###### Abstract
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons. and polar codes to entire baseband receiver chains that include channel estimation and detection [5; 6; 7; 8; 9; 10; 11; 12; 13]. Fundamentally, the idea of most aforementioned applications of the method in communications is to design deterministic compression mappings \(t=f(y)\) that replace the classical arithmetical operations in the baseband signal processing algorithms. These mappings are typically considered as lookup tables that store the respective \(t\) for each possible \(y\). The lookup table approach sketched above is well-suited for many of the baseband signal processing problems already studied in communications. In some other applications, however, it is desirable to have an arithmetical rule or a sequence of processing steps in an algorithm which maps an observed realization \(y\) onto the compressed \(t\). This is the case, for example, when the cardinality of \(\Upsilon\) and, therefore, the resulting lookup table implementing \(t=f(y)\) becomes fairly large. As a result, it is meaningful to consider parametrized compression mappings \(t=f_{\theta}(y)\) with \(M\) parameters \(\mathbf{\theta}=[\theta_{0},\theta_{1},\ldots,\theta_{M-1}]\) that preserve a desired large amount of mutual information \(\mathrm{I}(\mathcal{X};\mathcal{T})\). In this article, we develop parametrized mappings for communication receivers that only need few parameters and simple signal processing operations to preserve significant amounts of relevant information. The mappings investigated use exact or approximate nearest neighbor search algorithms [14; 15]. Other approaches to designing parametrized systems exist in the literature. Some of the most popular use neural networks [16; 17; 18]. Our motivation to study the proposed nearest neighbor search-based systems instead is that they offer a very simple implementation with a small number of mathematical operations to determine the system output \(t\). This is an important aspect for their practical use in communication receivers. Finding optimum parameters \(\mathbf{\theta}\), however, is cumbersome for the proposed parametrized mappings, especially if approximate nearest neighbor search algorithms are used. Therefore, we use genetic algorithms for the required optimization of the parameters \(\mathbf{\theta}\). Genetic algorithms are very generic and powerful optimization algorithms that are inspired by the natural evolution of the species [19; 20]. Their general idea is to create a population of candidate solutions to an optimization problem. Then, a so-called fitness of each individual in the population is evaluated with respect to the target function. The members of the population breed novel generations by combining their genetic information using simple crossover operators. In this process, the Darwinistic principle of promoting solutions with higher fitness is applied and also mutations happen. Fascinatingly, like this genetic algorithms can in fact find very good solutions to very complicated optimization tasks [19; 20; 21; 22]. The above motivates us to apply genetic algorithms to optimize parametrized compression mappings that aim for maximum preservation of relevant information. Such mappings have numerous applications in learning and also in the baseband signal processing of communication receivers. This article investigates the receiver-sided channel output quantization in communication receivers based on nearest neighbor search algorithms, similar to the original conference version of this article [23].