Deep learning based physical layer design, i.e., using dense neural networks as encoders and decoders, has received considerable interest recently. However, while such an approach is naturally training data-driven, actions of the wireless channel are mimicked using standard channel models, which only partially reflect the physical ground truth. Very recently, neural network based mutual information (MI) estimators have been proposed that directly extract channel actions from the input-output measurements and feed these outputs into the channel encoder. This is a promising direction as such a new design paradigm is fully adaptive and training data-based. This paper implements further recent improvements of such MI estimators, analyzes theoretically their suitability for the channel coding problem, and compares their performance. To this end, a new MI estimator using a "reverse Jensen" approach is proposed.