The Shannon formula, and in particular the error free condition, is only valid for gaussian noise. It is not valid for, for example, impulsive noise. It also only strictly applies when the coding delay goes to infinity. (If the "noise" is predictable, it can exceed the Shannon limit. One also has to be careful with the signal bit rate, e.g. contest exchanges tend to have quite a low bit rate, because so much of them is predictable.)
Currently I think we are within a few percent of the Shannon limit, but no real system actually reaches it. 56kbps modems don't rely on source coding, except, possibly, in as much as all modems, other than FSK ones, require scrambling. The enabling technology for 56 kbps modems is actually echo cancellation. They work because there isn't really a modem at all at the ISP side, and the link from the local exchange, where the the D/A happens, to the subscriber, is relatively noise free, so the receiver can actually identify all 256 D/A convertor output levels (this is complicated by the levels being non-linear, low ones are closer together than high ones). The ISP end put "PCM" codes directly onto the digital wire. No clever coding is needed for this, but you do need to accurately subtract out the uplink signal, so it requires good echo cancellation. The actual SNR at the input to a subscriber modem is much worse than the Shannon limit allows, but the input "noise" is not random, so not really noise, and can be predicted and subtracted out. Top quoted for policy, not effectiveness. Kok Chen wrote > > Channel capacity in bits/sec is equal to W, the bandwidth, multiplied by the > log(base 2) of the (S+N)/N ratio. > > With appropriate modulation and error correction coding, [Shannon shows that] > you can transmit a digital signal, with *any* arbitrarily small, non-zero > error bound that you wish to set, at a data rate up to the channel capacity. > > A practical modem from the 1980s can do 28.8 and 33.6 kbits/second through a > 3 kHz telephone circuit. The 56 kbits/sec modems achieve the higher rate by > using source coding in addition to channel coding, but they cannot maintain > 56 kb/s with completely random binary data. > -- David Woolley "we do not overly restrict the subject matter on the list, and we encourage postings on a wide range of amateur radio related topics" List Guidelines <http://www.elecraft.com/elecraft_list_guidelines.htm> ______________________________________________________________ Elecraft mailing list Home: http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/mmfaq.htm Post: mailto:Elecraft@mailman.qth.net This list hosted by: http://www.qsl.net Please help support this email list: http://www.qsl.net/donate.html
