[sdiy] Information Content of Signals

[Magnus Danielson]

From: Neil Johnson <nej22 at hermes.cam.ac.uk>
Subject: Re: [sdiy] Information Content of Signals
Date: Sat, 17 May 2003 13:42:31 +0100 (BST)

> 
> Easy one...
> 
> Tim Ressel wrote:
> > I want to know how they can get 53kbps on a phone line with 3khz
> > bandwidth. Oh I know they use this funky phase-constellation thingie.
> 
> Remember that "baud" != "bits per second".  The proper definition goes
> something like "symbols per second".

The propper definition of 1 Baud is number of symbols per second. This unit is
named after Baudot who invented the original Telex-system. Each such symbol
can be manifested in many ways, it may be a 2-level signal (which we quickly
interprent as a bit) or it may be a multi-level signal. For instance, many
telecommunication signals use a trinary signal, i.e. an n-ary signal with n=3
meaning three levels. What people don't realize is that good old trusty RS-232
is really a trinary system. The third level means "BREAK" on the Rx and Tx
lines.

> "bits per second" is a special case of baud, where each symbol represents
> only two states (1 or 0).  If we give each symbol 4 states, then we can
> encode two bits per symbol.  As DSP gets better, we can decode many more
> states per symbol.

Bits per second (a.k.a. b/s or more popularly but more incorrect bps) is a
measure of amount of information flow per timeunit. The base unit for amount of
information is bit and the base unit for time is second, so there you are.

Then for transmission systems we measure the amount of bits per symbol, so we
can convert the symbol rate to information rate.

> Take your phone line, and lets say we have an upper limit of 3,000 symbols
> per second.  Now leys say we have 16 states per symbol, which we can
> encode 4 bits per symbol.  Now the bit rate is 16 x 3,000 = 48kb/s.

Right. If you take a "19,2 kBd" fax or modem, it uses a phase-amplitude scheme
having 16 phase-amplitude positions (which when plotted forms a 4x4 grid in the
I-Q (In-phase, Quadrature-phase) diagram. The actual symbol rate on the
modulated side is 1200 symbols per second, so it's really just a 1,2 kBd system
but with a information rate of up to 19,2 kb/s. The reason it's called 19,2 kBd
is because this is the speed of the RS-232 line, nothing else.

That people (here I talk about suppossedly skilled engineers designing
data/tele-com equipment) still haven't understood even the most basic aspects
of Shannons findings is actually a bit upsetting.

Cheers,
Magnus