Reports are trickling in to Google Support that Galaxy Nexus users who upgraded to the most recent version of Android ICS are experiencing unexpected signal strength issues, causing them not to be able to text message or send/receive calls. While there has been speculation that the issue has to do with how 4.0.4 enters sleep mode, there has been no official cause analysis or resolution at this time.
Android ICS 4.0.4 was made available for the GSM variant of the Galaxy Nexus only, so if you are a Verizon LTE Galaxy Nexus user, it is business as usual for now.
