Human activity recognition is crucial for tactile internet, virtual reality, and digital-twin applications. Previous works have analyzed machine learning for this purpose but often need to pay more attention to typical challenges when deploying these machine learning models in production. First, data must be transmitted to the network node on which the machine-learning model is running. However, scaling human activity recognition by the number of devices and users puts additional constraints on the available transmission channel. While transmitting less data saves bandwidth, removing redundant information from the data can also benefit machine learning. This paper addresses the problem of transmitting wearable sensor data for human activity recognition. To this end, we analyze the extent to which wearable sensor data can be compressed via sparse coding without sacrificing loss in recognition performance. We empirically illustrate, on various datasets, that only a fraction of sensor information is relevant for human activity recognition.