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Just got a Galaxy Nexus / 4.0.2, also encountered this problem, and would like to add some information :

- I notice that whenever the screen is turned off, pinging GN on a local network varies between 60-1200ms. Once the screen is turned back on, ping is back to < 10ms instantly.

- WiFi connection remains intact throughout the process. Just very bad ping when the screen is turned off.

Look forward to seeing a fix for this problem soon. I have to fall back to my N1 for XiiaLive needs.