Abstract: A method includes receiving a bit string at a processor, performing an error correction, and causing transmission of a modulated signal. The error correction includes identifying a set of binary strings based on the bit string, mapping each binary string from the set of binary strings to a first abelian group element from a set of first abelian group elements, and applying a generalization of polar codes to the set of first abelian group elements to produce a set of second abelian group elements. The error correction also includes mapping each of the second abelian group elements to an in-phase/quadrature (I/Q) point from a set of I/Q points and identifying real-valued points based on the set of I/Q points, each of the real-valued points representing an I/Q point from the set of I/Q points. The modulated signal has a modulation that is based on the real-valued points.

Abstract: A data modulation method includes receiving a bit string at a processor, and identifying a set of binary strings based on the bit string. Each binary string from the set of binary strings is mapped to an element from a set of elements of a lattice-based signal constellation, without using a lookup table. Real-valued points from the set of elements are identified based on the mapping. The method also includes causing transmission of a signal having a modulation based on the real-valued points.