Communication system and method using layered construction of arbitrary unitary matrices

A system, comprising:

• a plurality of signal receivers;
• a plurality of signal transmitters;
• and
• at least one processor operably coupled to the plurality of signal transmitters, the at least one processor configured to:
• generate a plurality of symbols based on an incoming data,
• decompose a unitary transformation matrix of size N×N, N being a positive integer, into a set of layers, each layer including a permutation and at least one primitive transformation matrix of size M×M, M being a positive integer having a value smaller than or equal to N,
• encode each symbol from the plurality of symbols using at least one layer from the set of layers to produce a plurality of transformed symbols, and
• send a signal representing the plurality of transformed symbols to the plurality of transmitters for transmission of a signal representing the plurality of transformed symbols from the plurality of transmitters to the plurality of signal receivers.

A method, comprising:

• generating, via a first processor of a first compute device, a plurality of symbols;
• applying an arbitrary transformation of size N×N, N being a positive integer to each symbol from the plurality of symbols to produce a plurality of transformed symbols, the arbitrary transformation including an iterative process, each iteration of which includes:
• 1) a permutation followed by 2) an application of at least one primitive transformation matrix of size M×M, M being a positive integer having a value smaller than or equal to N;
• sending a signal representing the plurality of transformed symbols to a plurality of transmitters for transmission of a signal representing the plurality of transformed symbols from the plurality of transmitters to a plurality of receivers;
• and
• sending a signal representing the arbitrary transformation to a second compute device for transmission of the arbitrary transformation to the plurality of signal receivers prior to transmission of the plurality of transformed symbols, for recovery of the plurality of symbols at the plurality of signal receivers.