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00000EC401121902

For a systematic (7,4) linear block code, the parity matrix P is given by

1 1 1

1 1 0
P=

1 0 1

0 1 1

(i) Find all possible valid code vectors. (ii) Draw the encoder circuit. (iii) Draw
the syndrome calculation circuit.
If V is a valid code vector, prove that VH’ = 0, where H is parity check matrix.
State and prove Shannon — Hartley theorem.
PART C

Answer any two full questions, each carries 20 marks.
Draw a (2,1,3) encoder with impulse sequences 8 = 1011 and ഉ = 1111.
Find the generator matrix for the given encoder. Also find the code vector for the
message 11010 by time and frequency domain approaches.
What is a BCH code? Find the generator polynomial for single, double and triple
error correcting BCH code of block length, 7 = 15.
What are the properties to be satisfied by a cyclic code?

For a non-systematic rate 1% code given by ‏"اع‎ = 111 and ‏اع‎ =101. Draw the
graph, trellis and state diagram.
What are the features of Reed-Solomon codes?

Explain how systematic encoding is achieved in cyclic codes. For a systematic
(7, 4) cyclic code, find the code vector corresponding to message u(x) = 1 + x,
generated by g(x) =1+x+ x

For a convolutional encoder with generator sequences 2” =100 ೩7068 =101,
if the received code word is 00100000010000, find the transmitted code word
using Viterbi algorithm.

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