The communication system has a first modem having a digital port for communicating a first data block in a first format between a first transmission channel and the digital port and a second modem having a digital port for communicating a second data block in a second format between a second transmission channel and the digital port. The first data block has a header block and a message block. The controller/processing device comprises a first interface means, a second interface means and a conversion means. The first interface means is adapted for receiving the first data block in the first format from the first digital port. The conversion means is coupled to the first interface means. The conversion means converts the first data block in the first format to the second data block in the second format. The second interface means is coupled to the conversion means. The second interface means is adapted for sending the second data block in the second format to the second digital port. The second interface means starts sending the second data block after said the interface means has received the header block and before it has received the message block.