At 3:24 PM 9/13/96, Enzo Michelangeli wrote:

On Fri, 13 Sep 1996, Asgaard wrote:

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U.S. Robotics and Rockwell International are planning new modems with speeds up to 56 kbps a second, almost double the speed of the fastest rate now available. The new devices should be available by the end of the year, although their top speed initially may be less than 56 kbps. (Wall Street Journal 12 Sep 96 B11)

People who seemed to know used to say that 'the Shannon limit' set an absolute upper limit around 40 kbps. Has Shannon been proven wrong, or what?

Well, it all depends on the signal-to-noise ratio. Also, if the noise is not white gaussian the situation can be even better.

No, this is not what's important in this case. (Besides, the "upper limit" is really more about the Nyquist Limit. Shannon's Theorem says that even in the presence of noise, this limit can be approached if proper coding schemes and whatnot are used.) While it is true that a noisy channel can reduce the effective channel capacity to something less than its capacity (for some particular coding scheme), the upper limit on channel capacity is whatever it is. As to the original question about modems and 40 kbps vs. 56 kpbs rates, this depends on "tricks" involving definitions of a "symbol" (a la the familiar argument about baud vs. bits per second). "Trellis coding," for example. I'm not a modem designer, but I'm not surprised to see these incremental improvements...none involve huge gains, and none involve getting, say, a megabit per second through a 6 kHz (or whatever) audio line--now that _would_ violate Shannon's Theorem, the Nyquist Limit, etc. --Tim May We got computers, we're tapping phone lines, I know that that ain't allowed. ---------:---------:---------:---------:---------:---------:---------:---- Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay@got.net 408-728-0152 | anonymous networks, digital pseudonyms, zero W.A.S.T.E.: Corralitos, CA | knowledge, reputations, information markets, Higher Power: 2^1,257,787-1 | black markets, collapse of governments. "National borders aren't even speed bumps on the information superhighway."