System and method for communications with reduced peak to average power ratio

A method for transmitting data includes modulating data bits with a constellation to produce modulated data symbols, precoding the modulated data symbols to obtain ns groups of precoded samples, where ns is equal to a number of non-zero terms in a sparse code associated with the transmitting device, mapping the ns groups of precoded samples to groups of subcarriers in accordance with the sparse code associated with the transmitting device, to obtain a plurality of subcarrier-mapped samples, transforming the plurality of subcarrier-mapped samples into encoded data symbols, and transmitting the encoded data symbols.