Methods and devices are disclosed for encoding and transmitting data sequences for low data rate applications. An encoded data sequence is transformed and used to shape a multi-carrier pulse to create a narrow-band signal for transmission. Time domain tails of the narrow-band signal may be removed to decrease overhead. The data may be first encoded to create a sparse modulated data sequence. Multi-carrier pulse shaping may be carried out using frequency division multiplexing (FDM) or filter bank multi-carrier (FBMC) techniques. Alternatively, single carrier pulse shaping may be used to create the narrow-band signal.