Systems, methods and apparatuses for modulation-agnostic unitary braid division multiplexing signal transformation

1. A method, comprising:

selecting, via a processor of a communications system, a block size;

identifying, via the processor, a set of constellation points associated with a constellation diagram, based on a plurality of bits, the constellation diagram associated with a modulation scheme;

generating, via the processor, a plurality of symbol blocks based on the set of constellation points, each symbol block from the plurality of symbol blocks having a size equal to the block size and including a subset of constellation points from the set of constellation points;

applying, via the processor, a unitary braid division multiplexing (UBDM) transformation to each symbol block from the plurality of symbol blocks to produce a plurality of complex numbers; and

sending, via the processor, the plurality of complex numbers.

2. The method of claim 1 , wherein the communications system is configured to perform at least one of Quadrature Amplitude Modulation (QAM), Amplitude Phase Shift Keying (APSK) modulation, or Orthogonal Frequency-Division Multiplexing.

3. The method of claim 1 , wherein the communications system is a wireless communication system.

4. The method of claim 1 , wherein the communications system is a wired communication system.

5. The method of claim 1 , wherein the communications system is a fiber optic communication system.

6. The method of claim 1 , wherein identifying the set of constellation points includes mapping the received plurality of bits to the constellation diagram.

7. The method of claim 1 , wherein identifying the set of constellation points includes mapping the received plurality of bits to the constellation diagram using a gray code.

8. The method of claim 1 , further comprising causing transmission of at least one signal representing the plurality of complex numbers using the modulation scheme.

9. A method, comprising:

receiving, via a processor of a communications system, a plurality of input bits;

converting, via the processor, the plurality of input bits into a plurality of complex numbers by: (1) performing bit-to-symbol mapping based on the plurality of input bits and data associated with a constellation diagram to produce a plurality of symbols, the constellation diagram associated with a modulation scheme, and (2) applying a unitary braid division multiplexing (UBDM) transformation to the plurality of symbols to produce the plurality of complex numbers; and

sending the plurality of complex numbers, via the processor and using a predetermined modulation technique, for subsequent processing, the subsequent processing including performing the modulation scheme to transmit a signal including a representation of the complex numbers.

10. The method of claim 9 , wherein the UBDM transformation includes a plurality of nonlinear layers and a plurality of linear layers.

11. The method of claim 9 , wherein the predetermined modulation technique includes one of Quadrature Amplitude Modulation (QAM), Amplitude Phase Shift Keying (APSK) modulation, or Orthogonal Frequency-Division Multiplexing.

12. The method of claim 9 , wherein the communications system is a wireless communication system.

13. The method of claim 9 , wherein the communications system is a wired communication system.

14. The method of claim 9 , wherein the communications system is a fiber optic communication system.

15. The method of claim 9 , wherein the bit-to-symbol mapping is performed using a gray code.

16. The method of claim 9 , wherein the subsequent processing includes at least one of pulse shaping or the application of at least one filter.

17. The method of claim 9 , further comprising causing transmission of at least one signal representing the plurality of complex numbers using the modulation scheme.

18. A method for modulation-agnostic unitary braid division multiplexing (UBDM) signal transformation, the method including:

receiving a plurality of input bits;

mapping each input bit from the plurality of input bits using a bit-to-symbol map to identify a plurality of symbols;

grouping subsets of symbols from the plurality of symbols into a plurality of blocks, each block from the plurality of blocks having a size N, where N is a natural number;

applying a UBDM transformation to each block from the plurality of blocks to produce a plurality of complex numbers; and

sending the resulting complex numbers.

19. The method of claim 18 , wherein the sending the resulting complex numbers is to a downstream portion of the communication system for at least one of pulse shaping or filter application.

20. The method of claim 18 , wherein the method does not include the application of an inverse Fourier transform prior to sending the complex numbers.

21. The method of claim 18 , wherein the method does not include generating of spreading codes.

22. The method of claim 18 , wherein the bit-to-symbol map is a constellation diagram for a signal to be transmitted wirelessly, or through wired or fiber optic communication.