It seems like once again this 8071053D is plaguing the PlayStation community again. After doing a bit of reading, it seems like the error is stems from a power / internet issue. While this fix does not seem to be 100%, it seems to work for the majority who attempt it. Taken from the PS3Blog:
“8071053D – Hard boot the PS3, turn off the PS3 to stand-by, flip off the back switch and remove the power cord. Then shut off your modem/router, for about 5 minutes, then turn the modem back up first and let it sync, then turn the router back on(if using one) and let it sync. Reconnect your power cable and flip the back switch up again. Then make a new network connection.”
That same link contains fixes to other PS3 error codes, search which one you are having and see if the fix helps you.