522 Chapter 16
Moreover, the fact that the parity bits of column q and row e both have even parity means
that, in this example, the parity bits themselves are correct. If the error had occurred
instead in one of the parity bits, as in Figure 16.17(d) , this would have shown up by
the fact that the loss of parity occurred only in a single row—not in both a row and a
column.
So far, the addition of redundant parity bit information has offered the possibility of
detecting and correcting single bit “ random ” errors, but this would not be of assistance
in correcting longer duration “ burst ” errors, comprising one or more words. This can be
done by “ interleaving, ” the name given to the deliberate and methodical scrambling of
words, or the bits within words, by selectively delaying them and then reinserting them
into the bit sequence at later points, as shown in Figure 16.18. This has the effect of
converting a burst error, after deinterleaving, into a scattered group of random errors, a
type of fault that is much easier to correct.
A further step toward the correction of larger duration errors can be made by the use
of a technique known as “ cross-interleaving. ” This is done by reassembling scrambled
data into 8-bit groups without descrambling. (It is customary to refer to these groups of
bits as “ symbols ” rather than words because they are unrelated to the signal.) Following
this, these symbols are themselves mixed up in their order by removal and reinsertion
at different delay intervals. In order to do this it is necessary to have large bit-capacity
shift registers, as well as a fast microprocessor, which can manipulate the information
needed to direct the fi nal descrambling sequences and generate and insert the restored and
corrected signal words.
To summarize, errors in signals in digital form can be corrected by a variety of
procedures. In particular, errors in individual bits can be corrected by the appropriate
addition of parity bits, and burst errors affecting words, or groups of words, can be
corrected by interleaving and deinterleaving the signal before and after transmission—a
process that separates and redistributes the errors as random bit faults, correctable by
parity techniques.
A variety of strategies has been devised for this process, aimed at achieving the greatest
degree of error removal for the lowest necessary number of added parity bits. The CIRC
error correction process used for CDs is very effi cient in this respect, as it only demands
an increase in transmitted data of 33.3% and yet can correct burst errors up to 3500