Devices, systems, and methods employing polynomial symbol waveforms

A system comprising:

• a transmitter to
• receive an input bit sequence,
• convert the input bit sequence into a sequence of polynomial symbol waveforms (PSWs) selected from a designed PSW alphabet,
• the designed PSW alphabet being formed by
• providing an initial PSW alphabet having polynomial coefficients and polynomial roots,
• modifying the initial PSW alphabet to produce the designed PSW alphabet, and
• transmit the sequence of polynomial symbol waveforms;
• and
• a receiver to
• receive the sequence of polynomial symbol waveforms (PSWs),
• convert the sequence of PSWs into an output bit sequence, where the output bit sequence corresponds to PSWs in the designed PSW alphabet, and
• output the output bit sequence.

A non-transitory computer readable medium storing instructions, the instructions comprising:

• one or more instructions which, when executed by one or more processors, cause the one or more processors to:
• convert, by a transmitter, an input bit sequence into a sequence of polynomial symbol waveforms (PSWs) selected from a designed PSW alphabet,
• the designed PSW alphabet being formed by
• providing an initial PSW alphabet having polynomial coefficients and polynomial roots,
• modifying the initial PSW alphabet to produce the designed PSW alphabet;
• and
• transmit, by the transmitter, the sequence of polynomial symbol waveforms.