The Birdman of DeepShip 12 was a legendary prisoner who raised homing pigeons in his cell for months.
He then hatched a scheme in which he'd write notes and attach them to the pigeons and send the pigeons out the window in search of help. Naturally, the birds would immediately explode upon being released into outer space, but he never gave up.
When he was released, he was heavily recruited by SOL, Inc.
The Birdman confirms the (prior?) existence of a DeepShip 12 (although it's also possible that it's just a story or Roger doesn't remember it too accurately).
"The Birdman of DeepShip 12" is a reference to The Birdman of Alcatraz.