System and method for designing and using multidimensional constellations

A method for receiving data, the method comprising:

• receiving, by a receiving device, a codeword;
• and
• decoding, by the receiving device, the codeword to produce a first data using a multidimensional mother constellation, the multidimensional mother constellation generated from unitary rotations of at least two smaller constellations and generated from shuffling axes of the rotated at least two smaller constellations.

A transmitting device comprising:

• a processor configured to encode a first data using a multidimensional mother constellation to produce an encoded codeword, the multidimensional mother constellation generated from unitary rotations of at least two smaller constellations and generated from shuffling axes of the rotated at least two smaller constellations, and
• a transmitter operatively coupled to the processor, the transmitter configured to transmit the encoded codeword.

A receiving device comprising

• a receiver, configured to receive a codeword;
• and
• a processor operatively coupled to the receiver, the receiver configured to decode the codeword to produce a first data using a multidimensional mother constellation, the multidimensional mother constellation generated from unitary rotations of at least two smaller constellations and generated from shuffling axes of the rotated at least two smaller constellations.