System and methods for multi-level signal transmission

A method for transmitting a digitized signal over a communication channel as a series of transmitted symbols having a distribution of symbol amplitude values, the method comprising the steps of:

• generating a channel matrix for the series of transmitted symbols based upon a time response of the communication channel;
• decomposing the communication channel into a plurality of orthogonal subsets;
• precoding the digitized signal according to an eigenvalue distribution of the channel matrix and the plurality of orthogonal subsets;
• and
• shaping the precoded digitized signal into the distribution of symbol amplitude values.

A transmitter for an optical network, comprising:

• a processor configured to receive an input digitized stream of symbols;
• and
• a memory device including computer-executable instructions stored therein, which, when executed by the processor, cause the processor to:
• (i) generate an eigenvalue channel matrix for the input digitized stream of symbols based on a communication channel of the optical network;
• (ii) decompose the communication channel into a plurality of orthogonal subsets;
• (iii) precode the input digitized stream of symbols into a precoded symbol stream based on elements from the generated eigenvalue matrix;
• (iv) shape the precoded symbol stream according to a distribution function;
• and
• (v) transmit the shaped symbol stream over a digital communication link to a remote receiver, such that the remote receiver is enabled to recover the shaped symbol stream, decompose from the recovered symbol stream eigenvalues of the eigenvalue channel matrix, and decode the symbol stream using the decomposed eigenvalues.