Methods and apparatus for signal modulation using lattice-based signal constellations

A method, comprising:

• receiving, at a processor, a bit string;
• identifying, via the processor, a plurality of binary strings based on the bit string;
• mapping, via the processor, each binary string from the plurality of binary strings to an element from a plurality of elements of a lattice-based signal constellation, without using a rectangular shaping region;
• identifying, via the processor, real-valued points from the plurality of elements based on the mapping;
• and
• causing transmission of a signal having a modulation based on the real-valued points.

A non-transitory, processor-readable medium storing instructions that, when executed by a processor, cause the processor to:

• receive, at a processor and from a transmitter, a signal encoding a bit string;
• identify, via the processor and based on the signal and a closest vector algorithm, a point of an n-dimensional lattice associated with the signal;
• multiply, via the processor, the point of the n-dimensional lattice by an inverse of a basis of the n-dimensional lattice, to identify an element from a plurality of elements of an n-dimensional matrix ℤn associated with the signal;
• and
• recover bits based on the signal, via the processor, by reducing components of the signal modulo m, to produce an element of a quotient ℤn/mℤn, where n is a positive integer, and m is a positive integer.