Question 1

Assume the following polynomial is the generator for a cyclic code and design a syndrome testing circuit using shift registers.

G(X) = 1 + X + X4 + X6

Question 2

The generator polynomial of a (15,11) Hamming code is defined as

g(X) = 1 + X + X4

(i) Design a feedback register encoder implementing this coding scheme.

(ii) Illustrate the encoding procedure with the message 11001101011, by listing the successive states of the registers.

Question 3

Consider a systematic block code that forms it’s codewords by adding to the bits mi of the messages, the parity bits pi defined by the following equations:

p1 =m1 +m2 +m4

p2 =m1 +m3 +m4

p3 =m1 +m2 +m3

p4 =m2 +m3 +m4

a) Find the generator matrix and the parity check matrix for the code.

b) How many errors can the codeword correct?

c) Is 10101010 a valid codeword?

d) Is 01011100 a valid codeword?

Question 4

The maximum and minimum values taken by the envelope of an AM signal are 3.5 and 0.5 Volts. What is the modulation index? The radio transmitter radiates 10kW. How much is the carrier power?

Question 5

An angle-modulated wave is described as:

V(t) = 10cos(2p(10^8)t + sin(3142t))

Determine:

a) The modulation index

b) The frequency deviation

c) The frequency components of the spectrum using Bessel function tables

Thank you very much for taking the time to read this, and for any help.