MIKE FARRILL wrote the following to CRAIG FORD, and I quote (in part):
-=> Note: Copied from HS_MODEMS by WIMM/2 1.31
  -> Aetherworks is the only outfit besides Lucent that I am aware of that
  -> making noises about upstream PCM, and none violate the
  -> Shannon/Hartley Theorem.
 MF> What is the exact Theorem, didn't it say that the maximum data
 MF> speed over analogue lines was 35k?
[Excerpted from the COMM Echo Primer] -
SHANNON/HARTLEY THEOREM - further refines Nyquist Theory by taking into    
account the signal-to-noise ratio of the communications channel in addition
to the bandwidth. It is expressed as follows:                              
                                                                           
Maximum bits    Available                                                  
per second   =  bandwidth  x  LOGbase2 ( 1 + Signal-to-noise ratio )       
                                                                           
NYQUIST THEOREM - a fundamental dictum of data communications that governs
channel capacity. In simple terms it states that frequencies can only be  
accurately reproduced at up to half the sampling rate. Stated differently,
the maximum theoretical signaling speed of a channel in baud is twice its 
bandwidth.                                                                
[end excerpt]
[Excerpted from USR X2 Q&A]
Q. How can you receive data at 56Kbps when the theoretical limit of Shannon's 
   Law is about 35 Kbps?               
                                                                   
A. Shannon's limit is theoretically determined by the impairments (noise) in 
the telephone link. This new technique relies on a reduced noise environment  
 due to a digital connection to the network by the service provider and a new 
encoding technique.                                                         
[end excerpt]
[Excerpted from Rockwell 56K White Paper]
SHANNON'S LIMIT                                                            
                                                                           
Shannon's limit is determined by a number of parameters but for ordinary   
telephone channels it is, to a large degree, determined by the channel's   
signal to noise ratio.                                                     
                                                                           
Conventional modems treat the telephone network as a pure analog channel,  
so the analog signals generated by these modems see a PCM codec            
quantization distortion of about 36 dB.  This distortion represents a      
significant impairment as data rates are increased and limits the channel  
to about 35 Kbps. The effects of PCM quantization distortion are avoided by
using a form of amplitude modulation in which the amplitude levels are     
chosen to be the quantization levels of the PCM codec in the central       
office.  The user's data is encoded into this quantization-level symbol    
alphabet and transmitted across the local loop in digital form.            
                                                                           
The problem then is to equalize the local loop such that the signal samples
seen by the user's modem are equivalent to the quantization levels at the  
central office codec.  This equalization problem is significantly reduced  
by limiting the data transmission to a single local loop.  With this       
approach of "hooking" into the middle of the channel and avoiding one of   
the encoding or decoding PCM steps, the PCM quantization distortion can be 
treated as a deterministic impairment, and not as a random noise source,   
which is the case for the conventional analog modem.  This raises the      
theoretical Shannon's limit very close to 64 Kbps, depending upon the local
loop.                                                                      
                                                                           
THE UPSTREAM CHANNEL                                                       
                                                                           
It is more difficult to equalize the upstream channel, and therefore more  
difficult to achieve the same high data rates as are achieved in the       
downstream channel.  However, for Internet access, the data rate in the    
upstream direction is less important than downstream, since the upstream   
channel transmits mostly "key strokes and mouse clicks".  At present, a    
data rate of around 30 Kbps can be attained in the upstream direction, but 
research continues toward increasing the rate.                             
[end excerpt]
Regards....
Craig
aka: cford@ix.netcom.com
   : craig.ford@2001.conchbbs.com
--- timEd/2 1.10+
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