A method of encoding data includes identifying multiple complex number pairs of a data vector and generating a transformed data vector by applying a non-linear transformation to each complex number pair from the multiple complex number pairs. The non-linear transformation includes modifying a phase of a first complex number from each complex number pair. The phase modification is based on a value associated with a second complex number from each complex number pair. A signal representing the transformed data vector is sent to multiple transmitters for transmission to multiple receivers. A signal representing the non-linear transformation is sent to a compute device for transmission of the non-linear transformation to the multiple receivers prior to transmission of the signal representing the transformed data vector from the multiple transmitters to the multiple receivers, for recovery of the data vector at the multiple receivers.