The information bottleneck method is a generic clustering framework from the fieldof machine learning which allows compressing an observed quantity while retaining as much ofthe mutual information it shares with the quantity of primary relevance as possible. The frameworkwas recently used to design message-passing decoders for low-density parity-check codes in whichall the arithmetic operations on log-likelihood ratios are replaced by table lookups of unsignedintegers. This paper presents, in detail, the application of the information bottleneck method to polarcodes, where the framework is used to compress the virtual bit channels defined in the code structureand show that the benefits are twofold. On the one hand, the compression restricts the outputalphabet of the bit channels to a manageable size. This facilitates computing the capacities of the bitchannels in order to identify the ones with larger capacities. On the other hand, the intermediatesteps of the compression process can be used to replace the log-likelihood ratio computations inthe decoder with table lookups of unsigned integers. Hence, a single procedure produces a polarencoder as well as its tailored, quantized decoder. Moreover, we also use a technique called messagealignment to reduce the space complexity of the quantized decoder obtained using the informationbottleneck framework.