Chapter 1.10, Problem 5QE

a.

Explanation of Solution

Decode the message $001111100100001100$.

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol	Value represented
A	$000000$
B	$001111$
C	$010011$
D	$011100$
E	$100110$
F	$101001$
G	$110101$
H	$111010$

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern

b.

Explanation of Solution

Decode the message $010001000000001011$.

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

• The pattern $010001$ matches with C of table 1 because $010001$ and $010011$ differ by one hamming distance

c.

Explanation of Solution

Decode the message $011010110110100000011100$.

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

• The pattern $011010$ matches with H of table 1 because $011010$ and $111010$ differ by one hamming distance.
• The pattern $110110$ matches with E of table 1 because $110110$ and $100110$ differ only by one hamming distance