Western University

Faculty of Engineering

Department of Electrical and Computer Engineering

ECE 4433: Digital Communication Systems

EXERCISE-06

Try these problems (you need not submit solutions)

1. Consider a (7,4) code whose generator matrix is

1000011

0100110

0010101

0001111

G

i. Find all the code vectors of the code

ii. Find the parity check matrix of the code.

iii. Compute the syndrome for the received vector 1101101. Is this a valid

code vector?

iv. What is the error correcting capability of the code?

v. What is the error-detecting capability of the code?

2. The parity bits of a (8, 4) block code are generated by:

3100 mmmb

2101 mmmb

3202 mmmb

3213 mmmb

(a) Find the generator matrix and the parity check matrix for this code

(b) Find the minimum weight of this code

(c) Find the error-detecting capability of this code

(d) Show through an example that this code can detect three errors/codeword.