The invention relates to a system for low data-rate communication over a modulated direct carrier current, having one or more communication transmitters (6, 8), a communication receiver (10), and a wire bus (12) forming a shared transmission channel. Each communication transmitter (6, 8) is configured to form a first raw staggered transmission frame according to a second staggered transmission frame, said staggered transmission frames using a set of separate basic chip-encoding sequences. The basic encoding sequences for staggering the symbols used by all the communication transmitters (4, 6) are identical, and the times of the initial transmission of the second staggered frames produced by each transmitter (6, 8) are autonomously and freely determined by each transmitter (6, 8), without taking into account any synchronization signal external to the transmitter (6, 8).