Digital Signal Processing Reference
In-Depth Information
Chapter 12
Digital transmission technology ll: channel encoding
If a device transmits a continuous stream of bit patterns it should arrive without distortion
at the receiver. This is also true of the retrieval of data from a storage medium. The
yardstick par excellence for the quality of transmission or storage is the so-called bit error
probability.
Error protection encoding for the reduction of bit error probability
In what way can a signal be transmitted as safely as possible via a noisy or distorted
channel? The
theory of error-correction encoding
attempts to provide answers to this
question. Research into this problem has many direct effects on Communications and
computer technology.
While this is clear as far as communications technology is concerned it is perhaps not so
clear for computer technology as such. But, think for example of the storage and compres-
sion of data. Storage can be understood as a kind of temporary data transmission. The
transmission of data is equivalent to writing in a storage medium and receiving data is
equivalent to reading. In between time passes in which the storage medium may be
scratched or changed in some other way. Error protection encoding can also be
advantageous in the storage of data.
In retrospect there have always been transmission errors in the past which could be hardly
avoided with the means available. In the case of a telephone call over a noisy and
crackling line you can still usually understand the gist of what the person you are talking
to says even if you can only hear half of it. And if you can't undestand you can ask him
to repeat. Obviously, language is highly redundant and this appears to be the true source
of error correction.
For the storing of a longer straightforward text file it would scarcely be necessary to take
precautions. If some bytes are erroneous they only make themselves felt as a kind of
typing error. It is possible usually to correct the errors from the context as a result of
redundancy.
The situation is very different with a packed zip file. The compression is achieved by
eliminating redundant data and a single erroneous sign could make the the entire file
unusable. Think for instance of the packed
∗
.exe file of a program.
As already mentioned the strategy of modern transmission technology is as follows (see
Illustration 221):
• In
source encoding
data are compressed via the elimination of redundancies.
• In
entropy encoding
the attempt is made independent of the type of source signal to
optimise the code of the source encoder with respect to compactness.
• In
channel encoding
redundancy in the form of additional bits (check data) is added
systematically according to a particular plan in order to recognise and eliminate errors
more effectively.
