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Here are the most common data modem signalling standards. Note that the descriptions are not complete technical descriptions, and only cover the major feature of the standard (i.e. no discussion is made of fallback data rates etc.)
There are also numerous standard for error correction and data transmission. MNP (Microcom Networking Protocol) is a family of protocols with various levels. MNP levels 1 through 4 denote error correction schemes of increasing sophistication. MNP level 4 is the most common MNP error correction level; while there are higher levels, they are not terribly widespread. You may never see your modem report an MNP level 4 connection if you have data compression enabled; it will report level 5 instead. MNP level 5 is usually considered a 2:1 compressor, meaning that it will generally compress your data by up to a factor of 2 (though it can exceed this on some data and not reach it on other data). Note that it does not check to ensure that it can actually compress the data; if you send precompressed data through it, it will actually increase the amount of data which must be transferred between modems, thereby decreasing throughput.
V.42 is another error correction standard; unlike MNP, it is non-proprietary. Its primary error-control protocol is called LAP-M. It also includes a provision for falling back to MNP level 4 error correction should the remote modem not support V.42. V.42bis is the corresponding data compression standard. It is both more efficient than MNP level 5, providing up to a 4:1 rate (even higher on particularly repetitive data), and more intelligent, in that it can recognize whether or not it can compress data and send the data uncompressed if this makes the most sense.
For further information on modems, see the newsgroup comp.dcom.modems.
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