A communication system is configured to use coded modulation architecture using sparse regression codes. A transmitter includes a plurality of antenna and processing circuitry configured to: divide a data signal into a plurality of layers, allocate power individually to each of the plurality layers, encode a subset of the plurality of layers, the subset comprising a number of layers less than the whole, and interleave the subset of the plurality of layers. A receiver includes a plurality of antenna and processing circuitry configured to divide a received data signal into a plurality of layers and perform layer-by-layer decoding on the received data and control signals.