statton@bu-cs.bu.edu (Scott Statton) (04/25/89)
In a recent digest, Willis H. Ware writes asking questions about the
relation between baud rate and bit rate. There's a lot of hand-waving
about Baudot and character length and the like, but the basic question
was "what is baud rate vs. bit rate".
Definition #1: Baud rate is the reciprocal of the duration of the
shortest signalling element. Or, "elements-per-second".
Definiton #2: Bit rate is the number of data bits transmitted from
point A to point Z in one second.
Take the case of a Bell 103 FSK modem, (0 - 300 baud, asyncronous) at
300 baud/bits-per-second.
A one bit is transmitted as 3.333 mS of "mark tone" and a zero bit is
transmitted as 3.333 mS of "space tone" (where mark is either 2225 or
1270 for Answer or Originate respectively, and space is either, 2025
or 1070 for Answer/Originate). In this case, the "signalling element"
for either tone is 3.333 mS, for a "baud rate" of 300.
Now, for example, let's consider the Bell 212A 1200 bit-per-second
modem. This uses a carrier of 1800 Hz Answer, and 1200 Hz originate,
that is not frequency shift keyed, but instead is phase shifted.
There are four phase shifts (it's either { 0, 90, 180, 270 } or { 45,
135, 225, 315 } I confuse formats in my head ) each shift representing
two bits. For sake of argument, assume the following table (but I'm
sure it's wrong)
00 = 90 shift
01 = 180
10 = 0
11 = 270
In other words, each signalling element sends TWO bits, for a BAUD
rate of 600 (1200 bps / 2). In a APSK system, such as 9600 bd.
half-duplex, there are several phase/amplitude combinations,
representing 8 or 16 states, ergo 3 or 4 bits, and thus a baud rate of
3200 or 2400 (depending on complexity of the format).
In a transmission system, there are two constraints to "information
speed". These are (1) Bandwidth, and (2) Signal-to-Noise ratio. The
maximum BAUD rate is related (directly and linearly) to Bandwidth.
The maximum number of bits per baud (signalling element) is related
(logarithmically) to the S/NR. This is what prevents the development
of high-speed modems. The bandwidth of a phone line is hard limited
to approx. 2700 Hz. (300 Hz - 3.0 kHz) and there is a finite amount
of S/NR. (I'm at jsol's house, so I don't have my notes on all of
this).
For a more detailed discussion of the topic, go to your local library
and look up Claude Shannon, who pioneered the field of "information
theory" and proved mathematically why all of this works.