Hi David,
  I thought that You and the Gang here might be interested in this. I find
it ironic that I got this off a local BBS, who recieved it from another
User via the Internet, whom had found it on the FidoNet!  This is the text
of a white paper on the new 56Kbps dial-up modem technology by Rockwell.
------------------------------------------------------------------------
 
56 Kbps Communications Across the PSTN 
A new era in dial up communications 
 
- The Communications Path 
- Dealing with the communications path 
- Problems in the network 
- Shannon's limit 
- The upstream channel 
- Standardization 
- Connection limitations 
- Summary 
- Footnotes 
 
This paper describes the basics of the 56 Kbps modem technology recently 
announced by Rockwell Semiconductor Systems. 
 
The basic concept behind this communications technology is that the public 
switched telephone network (PSTN) is increasingly a digital network and
not an analog network.  Existing analog modems, such as V.34, view the
PSTN as an analog system, even though the signals are digitized for
communications throughout most of the network.
 
Figure 1:  The components of a modem connection in a digital network 
 
[-------]   [        ]                [       ]                 [-------] 
| MODEM |   | LINEAR | 2-WIRE TWISTED | m-LAW | 64K         64K | MODEM | 
|       |---|        |----------------|       |-----[delay]-----|       | 
|  DSP  |   | CODEC  |      PAIR      | CODEC |                 |  DSP  | 
[-------]   [        ]                [       ]                 [-------] 
 
Additionally, more and more, central site modems [1] are connected to the 
PSTN via digital connections (T1 in the Untied States and E1 in Europe [2] 
) and do not utilize a codec [3] .  The modem interprets this digital 
stream as the representation of the modem's analog signal. 
 
Rockwell's announced 56 Kbps technology looks at the PSTN as a digital 
network which just happens to have an impaired section in the 
communications path. That impaired section is, of course, the copper wire 
connection between the telephone central office and the user's home, 
usually referred to as the analog local loop. 
 
THE COMMUNICATIONS PATH 
 
When a user at his/her home calls a central site T1 connected modem, the 
network situation can be represented by Figure 1, below.  The user is 
connected to the network via a two wire twisted pair [4] copper line.  At 
the central office, this twisted pair line is terminated by a special type 
of transformer, called a hybrid, which converts from two wire to four wire 
[5] .  This four wire connection is then connected to a codec.  In the 
United States, this codec is called a mu-law codec, named for the
technique used to space the sample points (which are also called
quantization levels or quantization points).  In Europe, a different
technique is used for spacing these points, called A-law. The mu-law codec
is, in turn, connected to the digital network.  The full duple x digital
data, to and from the codec, is switched through the network to the
central site modem DSP, allowing the central site modem DSP to communicate
digitally with the mu-law codec.
 
The mu-law codec has 255 non-uniformly spaced quantization levels which
are closer together for small signal values and spread farther apart for
large signal values.  The modem DSP at the central site can generate any
quantization point voltage on the analog line simply by sending the 
appropriate eight bit sample to the mu-law codec.  Since the PCM codec 
sampling rate is 8-KHz, these voltage levels will be generated 8,000
times per second.
 
For the modem at the user's home, the major challenge is to be able to 
determine which quantization point was generated by the eight bits sent by 
the central site modem, and to do it 8,000 times per second. To do this, 
the modem in the home must synchronize its sample clock to the network 
codec's 8-KHz clock.  Clock recovery is done in existing analog modems and 
equivalent techniques are used to recover the network clock in this new 
application. 
 
Now let's look at how data is sent.  Assume that the modem DSP at the 
Internet service provider can send only two different sample values to the 
mu-law codec, say the values representing the two outermost points.  The 
two voltage levels on the analog line which result from sending these 
sample values can be used to represent two binary values (0 and 1).  These 
sample values will be sent 8,000 times per second, the network clock rate. 
Further assume that the modem in the home can discriminate between the two 
voltages, 8,000 times per second.  In this case, the central site modem
can send data to the user at 8,000 bits per second (bps).
 
Now let's assume that the modem DSP at the Internet service provider can 
send four different sample values, representing four different voltage 
levels. Since there will now be four different voltage levels on the
analog line, we can assign two bits to each voltage level (00, 01, 10,
and 11). Again, sample values will be sent 8,000 times per second.  If the
modem in the home can discriminate between these four different voltage
levels, 8,000 times per second, then 16,000 bps can be transmitted.
Table 1, following, shows how the data rate increases as more voltage
levels can be transmitted and discriminated.
 
                  Number of       Bits per      Line Rate 
                voltage levels    level          (bps) 
                ==============    ========      ========== 
                       2             1             8,000 
                       4             2            16,000 
                       8             3            24,000 
                      16             4            32,000 
                      32             5            40,000 
                      64             6            48,000 
                     128             7            56,000 
                     256             8            64,000 
 
Table 1:  The relationship between the number of voltage levels on the 
analog l ine, the number of bits communicated per voltage level and the 
resulting line rate. 
 
 
DEALING WITH THE COMMUNICATIONS PATH 
 
To make this technology work over the analog loop, the modem must 
"equalize" the line.  But this is easier said than done. 
 
Some of the problems encountered in equalizing the loop are caused by the 
central office codecs, which are designed for voice and not data.  Also, 
the transformer hybrids connecting the transmit and receive paths to the 
loop introduce spectral nulls at DC.  Some of the solutions developed by 
RSS engineers for these problems are being submitted as patent 
applications. 
 
Once these issues are dealt with, the quantization levels on the analog 
line are simply treated as symbols [6] in modem symbol space, in exactly 
the same way as combinations of amplitude an d phase are treated as
symbols in an analog modem QAM space [7] .  And once you're in symbol
space, you can use many of the techniques already developed for
traditional analog modems to improve the modem receiver's ability to
discriminate between quantization levels, thereby improving communications
accuracy and speed.
 
For example, new trellis8 codes, which recognize the non-uniform spacing
of the symbols, can be created and applied to allow better discrimination
between the quantization levels, especially those near the origin.  While 
not all of the existing modem coding techniques can be applied to this new 
communications technology, a great many can. 
 
PROBLEMS IN THE NETWORK 
 
If everything could be done perfectly, this technique would allow 
communications at 64 Kbps (8 bits per sample times 8,000 samples per 
second). However, there are a number of problems which prevent operation
at this speed.
 
First of all, in the United States, the link between the network and the 
central site modems can be a T1 line utilizing "robbed bit signaling" for 
call progress indication.  Robbed bit signaling "steals" the low order 
sample bit in two of the samples per frame to indicate the status of an 
incoming (or outgoing) call.  The use of this bit by the network means
that the central site modem cannot always access 8 bits per sample and
this reduces the achievable data rate.
 
Additionally, the codecs in the network are not perfect.  Many have a DC 
offset problem which limits the ability to utilize the quantization points 
near the origin.  There may also be a significant amount of nonlinear 
distortion in the circuit.  This further limits the achievable data rate. 
 
Finally, there is the problem of accurately determining the quantization 
point which was "sent" by the central site modem DSP.  Since the 
quantization points are closer together near the origin, it is more 
difficult to discriminate between these points.  Depending upon the 
channel, more or less of these points may have to be given up. 
Taken together, these limitations reduce the achievable data rate to about 
56,0 00 bps. 
 
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. 
 
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