56 Kbps data transmission across the PSTN. How does it work?

On September 10, 1996, Rockwell Semiconductor Systems shocked the communications industry with its announcement of a revolutionary new dial up modem technology for communicating across the public switched telephone network (PSTN) at rates up to 56 Kbps. Since that time, Rockwell's 56 Kbps technology has been supported and adopted by most of the communications related companies in the world as the way to communicate at rates up to 56 Kbps. Prior to this announcement, the modem communications industry had convinced itself that communications across the PSTN were limited by Shannon's theorem to rates below 35 Kbps. Although Rockwell published a white paper describing its 56 Kbps technology shortly after the public announcement, and submitted its technology for standardization to both the ITU and the ANSI TR30 committees, there have been continual requests for an in-depth discussion of how the technology works, with particular emphasis on how this technology gets around the so-called Shannon limit. This paper attempts to address these issues.