Example communication systems and methods are described. In one implementation, a method receives a first chaotic sequence of a first temporal length, and a second chaotic sequence of a second temporal length. The method also receives a data symbol for communication to a destination. Based on the data symbol, the second chaotic sequence is temporally shifted and combined with the first chaotic sequence to generate a composite chaotic sequence. The first chaotic sequence functions as a reference chaotic sequence while the second chaotic sequence functions as a data-carrying auxiliary chaotic sequence.