Efficient and reliable transmission of information from sparse sources over wireless channels in wireless signal networks (WSNs). WSN nodes employ an “integrated signal representation-to-modulation” scheme to describe a sparse signal acquired from a sensor so as to ensure robustness against channel errors across a wide range of signal to noise (SNR) values in a rateless fashion. In one example, sparse signal samples are linearly transformed such that the total number of bits representing the sparse signal is reduced. The linearly-transformed signal samples are directly mapped to a modulation constellation to provide a succession of modulation symbols. A carrier wave is modulated in phase and/or frequency according to the succession of the modulation symbols to generate an encoded carrier wave representing the sparse analog signal. In one aspect, an order of the modulation constellation is based on the precision (e.g., number of bits) of each of the linearly-transformed signal samples.