US Patent 9819530 Constellation designs with non-gray bit mapping

Methods and systems for communication with an optimized constellation include coding an input data stream to a symbol stream according to an optimized constellation that has a non-Gray bit mapping and that has neighboring points having more than one bit difference farther apart than neighboring points having one bit difference. The symbol stream is modulated onto a transmission signal and subsequently demodulated at a receiver to produce a received symbol stream. The received symbol stream is decoded to a bitstream according to an optimized constellation that has a non-Gray bit mapping and that has neighboring points having more than one bit difference farther apart than neighboring points having one bit difference.