Carriers are slowly creeping toward the day when they will no longer need old-fashioned 3G voice calls. AT&T is doing its part by updating another device with VoLTE functionality. The Galaxy S4 Mini should be getting an update right now with VoLTE baked in.
This update is only for the AT&T-branded S4 Mini (I257) and should arrive in standard OTA fashion. Here the AT&T changelog.
VoLTE inter-op call hold
SIM less 911 Dialing update
ISIM SQN re-sync for VoLTE reregistration
v4v6 for IMS PDN while roaming
VoLTE allows devices to place calls over the LTE network with improved quality and support for simultaneous voice and data. This OTA will clock in at 102-595MB, depending on the firmware version on the device.