Error Control Coding - Digital Communication: Principles and System Modelling - page 186

the decoder and the decoding fails unfortunately. This error is undetectable to the
decoder. This is also a case of false code acceptance. If X is received, the decoder
detects the error, but can't correct it as it is not inside any sphere. So decoding
fails. This is the case of detectable but not correctable error pattern. Based on this
explanation the error control code can be divided in 3 categories [ 1 , 4 , 5 ].

1. Undetectable
2. Detectable but not correctable
3. Detectable and correctable

9.2 Scope of Coding

Now a days the role of coding has expanded tremendously in various fields and
today coding can do the following:

Reduce the occurrence of undetected errors : This is the most important
advantage of coding. Today's error control codes are so effective that the
occurrence of undetectable errors is eliminated for all practical purposes.
Reduce the cost of communication systems : Coding can significantly reduce the
power needs of transmitter especially of satellite reducing the communica-
tion cost because signals received at thermal noise level can still be recovered
correctly.
Overcome jamming : Coding is one of the most effective techniques for reducing
the effects of jamming.
Eliminate interference : Error control coding is very effective to reduce the
effect of unintentional interference.

Despite all these features, there are some limitations of coding too. One of these
is the modulation technique of communication system. Coding must simultaneously
with the choice of modulation technique for the channel. Even the most powerful
codes cannot overcome the consequences of a poor modulation choice.
Another limitation is the inability to achieve Shannon's lower bound.

￿ Forward Error Correction

If we compare the sphere of code wards A and B in figure, we will see that the
error correcting capability of a code is given by d min = 1 (this is the minimum

separation that prevents overlapping spheres). In other words, a code with d min =

2 t +

3

or 5 can correct all patterns of 1 or 2 errors.