System and methods for mapping and demapping digitized signals for optical transmission

A mapping unit for an optical transmission link, comprising:

• a processor in operable communication with the optical transmission link;
• and
• a memory device in operable communication with the processor, and including computer-executable instructions stored therein, which, when executed by the processor, cause the processor to:
• (i) receive an input series of symbols having a first Gaussian distribution of symbol amplitude values;
• (ii) digitize the input series of symbols into a digitized series of symbols having a second Gaussian distribution different from the first Gaussian distribution, wherein the digitized series of symbols includes (i) a first symbol having a first symbol amplitude value, and (ii) a second symbol having a second symbol amplitude value greater than the first symbol amplitude value;
• (iii) map the second symbol to the first symbol and the first symbol to the second symbol to generate a mapped signal;
• and
• (iv) modulate the mapped signal into a digitized output signal for transmission over the optical transmission link.