On Dec 26, 2015, krw wrote (in article):
Here is the missing bottom of my reply:
All these modems take an incoming bit stream and convert it to a series of line symbols on the wire (or fiber or radio wave). These line symbols are designed to be easy to tell apart, even after having been distorted and corrupted a bit on the line, so the receiving modem can tell with very high reliability which line symbol was sent, thus recovering the original bit stream.
Because only a known set of line symbols are sent, and nothing in between, the receiver can assume that the intended line symbol is that one that is closest to one of these known line symbols.
Design of such symbol sets is a career, and there is a large literature, but a good place to start is any college textbook on data communications.
Joe Gwinn