Remember that experiment Google did with a few Android manufacturers, where they took their flagship devices, threw stock Android on them and sold them in Google Play at full retail? Well if you were one of the few that bought the first of those, being the Samsung Galaxy S4 Google Play Edition, your Android 5.1 update is now pushing out. The initial promise of the Google Play Edition devices were, that they would get updates quickly. But not quicker than a Nexus. So it would go Nexus, then Google Play Edition and then everyone else. Well Android 5.1 is on a slew of other devices already, that aren't a Nexus, and the Galaxy S4 GPe is just now getting its update. Although it is a bit surprising to see it still getting updated, to be honest.
Android 5.1 started rolling out back in February. With the biggest change actually affecting Android One devices. As Android 5.1 brought in support for Dual-SIM. Something that is very popular in emerging markets that Android One is targeting. Android 5.1 of course brought in loads of other bug fixes and performance enhancements, but as far as new features, there's not much.
The OTA for the Galaxy S4 GPe is going to take you build LMY47O. That is Android 5.1, and not 5.1.1. Which means it's still not on the latest version of Android. We have the OTA link if you want to sideload it. But remember, you need to be on build LRX21P, which was Android 5.0.
Google Play Edition was a cool experiment, and it appears to not have worked out so well for Google. As they have moved on and it's been over a year since the last Google Play Edition device was announced and made available. Having said that, while we did get the Android 5.1 update here for the Galaxy S4 Google Play Edition, it's very likely that this could be the last official update from Google and Samsung. Of course, there will be plenty of custom ROMs. Actually there already are, if you know where to look. Maybe Android Silver will finally come to light this year, as GPe was supposed to be the predecessor to Silver.