Methods and apparatus for lattice-based signal modulation using a generalization of polar codes

A method comprising:

• receiving a bit string;
• identifying a plurality of binary strings based on the bit string;
• mapping each binary string from the plurality of binary strings to a first abelian group element from a plurality of first abelian group elements;
• applying a generalization of polar codes to the plurality of first abelian group elements to produce a plurality of second abelian group elements;
• mapping each second abelian group element from the plurality of second abelian group elements to an in-phase/quadrature (I/Q) point from a plurality of I/Q points;
• identifying a plurality of real-valued points based on the plurality of I/Q points, each real-valued point from the plurality of real-valued points representing an I/Q point from the plurality of I/Q points;
• and
• transmitting a signal having a modulation based on the plurality of real-valued points.

An apparatus comprising:

• a communication interface configured to transmit and receive wireless signals;
• and
• a processor configured to:
• receive a bit string;
• identify a plurality of binary strings based on the bit string,
• map each binary string from the plurality of binary strings to a first abelian group element from a plurality of first abelian group elements,
• apply a generalization of polar codes to the plurality of first abelian group elements to produce a plurality of second abelian group elements,
• map each second abelian group element from the plurality of second abelian group elements to an in-phase/quadrature (I/Q) point from a plurality of I/Q points;
• identify a plurality of real-valued points based on the plurality of I/Q points, each real-valued point from the plurality of real-valued points representing an I/Q point from the plurality of I/Q points;
• and
• cause the communication interface to transmit a signal having a modulation based on the plurality of real-valued points.