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10000EC401122101

Define Ring and give two examples
Parity matrix of a (7,4) systematic linear block code (LBC) is given as
1 0 1
‏ا۔م‎ ٤
1 1 1
1) Find the generator and parity check matrices.
2) Draw the syndrome calculation circuit.
3) Explain the decoding using the syndrome of a received vector.
Construct standard array of an Linear Block Code with generator matrix,

1 0 11 0 0
6-1 100 1 0
0 1 1 0 0 1

Find the transmitted codeword corresponding to the received vector, ‘111110’.

A continuous channel has a bandwidth of 4.8 KHz. For a signal to noise ratio of
20dB, calculate the channel capacity. Also, calculate the minimum SNR in dB
required to support information transmission at the rate of 4800 bits/sec through
the channel.
PART C
Answer any two full questions, each carries 20 marks.

For a (7,4) cyclic code in systematic form with generator polynomial 1+X+X?

1) Find the codewords in systematic form corresponding to the message

vectors (1010) and (1100).

2) Find the generator matrix corresponding to the systematic cyclic code.

3) Draw the encoder circuit and explain encoding of the message (1010)
With the help of a block diagram, explain the decoding of cyclic codes.
Discuss minimum free distance of a convolutional code.
Draw the state diagram and trellis diagram of a (3,1,2) convolution encoder with
ഇട )1 0 1(, ‏ددع‎ )1 10), 2“ = (1 1 1).
Discuss the encoding and decoding of Hamming codes with a suitable example.
Draw a (2, 1,3) convolutional encoder with [1, 0, 0, 1] and [1, 1, 0, 1] as the
impulse responses. Find the output of the convolutional encoder for input
sequence 11001.

What are Reed Solomon codes? Discuss its properties.

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