Discrete Mathematics

186 DISCRETE

MATHEMATIC...__

________________________

_

a sequence

of

three binary digits. A possible code is given in the table on the previous page.

If

a message

carried by a channel in this example is changed owing to disturbances

or

noise, then the receiver will make an

uncorrectable and undetectable mistake because any interchange

of

0

or

1 in a particular code sequence

results in a different code sequence. For example,

if

the sequence 000 for A is changed by noise to 100, then

it will be decoded as

E.

We shall now modify our code by adding one extra or redundant digit to each sequence

of

3 bits as

shown in the table on the previous ...