Path: utzoo!utgpu!news-server.csri.toronto.edu!mailrus!accuvax.nwu.edu!nucsrl!telecom-request From: Rob Warnock Newsgroups: comp.dcom.telecom Subject: Re: Data Access Lines Message-ID: <8683@accuvax.nwu.edu> Date: 5 Jun 90 08:48:16 GMT Sender: news@accuvax.nwu.edu Reply-To: Rob Warnock Organization: Silicon Graphics Inc., Mountain View, CA Lines: 89 Approved: Telecom@eecs.nwu.edu X-Submissions-To: telecom@eecs.nwu.edu X-Administrivia-To: telecom-request@eecs.nwu.edu X-Telecom-Digest: Volume 10, Issue 415, Message 2 of 8 In article <8574@accuvax.nwu.edu> mtndew!friedl@uunet.uu.net (Stephen J. Friedl) writes: | > If PEP is modulated only at 7.35 or 88.26 baud, it should be no | > difficulty for the local lines to carry it, unless shoving so many | > bits into so few bauds requires so many carrier pitches that local | > telco lines might not be reliably able to discriminate that fine. | PEP is modulated at 7.35 or 88.26 baud PER CARRIER, and to get the | baud for the whole signal one must multiple by the number of carriers | in use. A PEP line is easily thousands of baud for a clean line, and | for phone line requirements, the 7.35 or 88.26 number is meaningless. Sorry, you have a slight misunderstanding of the term "baud". The signaling rate in "baud" is defined as "the reciprocal of the smallest signalling interval", that is, the peak number of "symbols" or state changes per second. All of the sub-carriers change at the same time. Thus the PEP protocol is indeed 7 or 88 baud. However, each sub-carrier is only using about (3000 - 300) / 511 = 5.28 Hz of bandwidth. (Pushing a 7 baud signal through a 5 Hz pipe is quite good! The theoretical maximum is 2 baud/Hz: one state for each half-cycle of bandwidth.) Since each sub-carrier encodes 2, 4, or 6 bits per baud, or 14.7, 29.4, or 44.1 bits/second, respectively, at the 7.35 baud rate, that is 2.78, 5.57, or 8.35 bits/second per Hertz of bandwidth. From the Shannon limit: BitsPerSecond < Bandwidth * log2((S/N) + 1) That implies that the signal-to-noise has to be at least: bps/Hertz S/N (dB) > 10 * log(2 - 1) or: S/N > 7.69 dB (min.), for 2 bits/baud (a 14.7 bit/s sub-channel) S/N >16.67 dB (min.), for 4 bits/baud (a 29.4 bit/s sub-channel) S/N >25.12 dB (min.), for 6 bits/baud (a 44.1 bit/s sub-channel) Of course, these are theoretical minima, and don't account for noise to to adjacent sub-channel interference, or loss due to imperfect coding, so the line has to be a good deal better than this. Still, if only 400 channels could get the highest rate, that's still 17,600 bits/second (before subtracting for the 20% CRC and packetizing overhead). In case anyone is still confused, note that sending 6 bits/baud means that you have to be able to send any one of 64 (= 2^6) "symbols" at each state change. Symbols can be encoded as amplitude difference, frequency difference (although not in this case), or phase difference. The PEP scheme, which is actually called DAMQAM or Dynamically Adaptive Multicarrier Quadrature Amplitude Modulation at this level, uses a combination of amplitude and phase modulation on each sub-carrier. Note that if you only used AM, 64 symbols means 64 different voltage levels, which means that (*very* crudely speaking) to avoid error the noise level has to be less than 1/2 the difference between two adjacent levels, so the noise doesn't turn one into the other, or 1/128 the maximum level. Thus, you need a S/N of 20*log(128) or 42 dB. (The "20" is because we are comparing *amplitude*, not *power*, as above.) That this doesn't match the 25 dB "Shannon limit" given above is due to (1) my example was crude indeed, (2) pure AM is not nearly as efficient as QAM, and (3) the Shannon limit -- a *minimum* bound -- assumes that you are employing "perfect" encoding. The actual S/N needed is somewhere between the two, and closer to the upper. Anyway, you get the idea... So the limit to PEP operation is the signal-to-noise of each of a large number of very narrow, slow channels, any of which can be down-graded or dropped from use if needed if *that particular* sub-channel is too noisy. Non-linearities and phase-slopes which would blow away a higher baud-rate modem are shrugged off, since they has much less affect on a 5 Hz (sub)channel. In case anyone's curious about the fact that the quantizing into levels by PCM (T-carrier) puts an upper limit of something like 20*log(128/0.5) = 48 dB on the S/N if 7 bits/sample are being used, note that at 7.35 baud there are 8000 / 7.35 = 1088 samples/baud. A lot of the quantizing noise can thus be averaged out. Rob Warnock, MS-9U/510 rpw3@sgi.com rpw3@pei.com Silicon Graphics, Inc. (415)335-1673 Protocol Engines, Inc. 2011 N. Shoreline Blvd. Mountain View, CA 94039-7311