A method includes generating a set of symbols based on an incoming data vector. The set of symbols includes K symbols, K being a positive integer. A first transformation matrix including an equiangular tight frame (ETF) transformation or a nearly equiangular tight frame (NETF) transformation is generated, having dimensions N×K, where N is a positive integer and has a value less than K. A second transformation matrix having dimensions K×K is generated based on the first transformation matrix. A third transformation matrix having dimensions K×K is generated by performing a series of unitary transformations on the second transformation matrix. A first data vector is transformed into a second data vector having a length N based on the third transformation matrix and the set of symbols. A signal representing the second data vector is sent to a transmitter for transmission of a signal representing the second data vector to a receiver.