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G1002 Pages: 2

Find the capacity of a channel with infinite bandwidth. Discuss Shannon’s limit.
The parity matrix of a (6, 3) linear systematic block code is given below.
1 0 1
P= | 1 1
0 1 1

Find all the possible code vectors.
a) Find out the minimum distance of the code.
b) How many errors can be detected and corrected by this code?

Explain the properties of a field. Cite any two examples.

Alphanumeric data are entered into a computer from a remote terminal through a
voice grade telephone channel. The channel has a bandwidth of 3.4 KHz and
output signal to noise power ratio of 20 dB. The terminal has a total of 128
symbols which may be assumed to occur with equal probability and that the
successive transmissions are statistically independent.

a) Calculate the channel capacity.

b) Calculate the maximum symbol rate for which error free transmission over

the channel is possible.
PART C
Answer any two full questions, each carries 20 marks.

Draw a (2, 1, 2) convolutional encoder with the feedback polynomials as

gi(X)=1+X+X? and go(X)= 1+X?. Draw Trellis and find the output sequence for
input sequence [1 0 0 1 1]. Do Viterbi decoding on this trellis for the received
sequence (01, 10, 10, 11, 01, 01, 11} and obtain the estimate of the transmitted
sequence and the message sequence.

A channel encoder uses a (7, 4) linear systematic cyclic code in the systematic
form, generator polynomial being ‏ت×‎ + X + 1. Determine the correct codeword
transmitted if the received word is

(i) 1011011 (ii) 1101111

Draw a (3,2,1) convolutional encoder with impulse responses given as 2101)= [1.1],
gi =[1,0], 8/0-[1,0], go=[0,1], 22 =[ 1,1], go =[0,0].

Mention the parameters of BCH codes.

Discuss the procedure for generation of a systematic cyclic code. Draw and
explain the systematic cyclic encoder circuit for a (15, 9) cyclic code with
generator polynomial g(X)= 14 X*+ X*+ X>+ X°®.

Draw a (2,1,2) convolutional encoder with the feedback polynomials as
gi(X)=1+X+X? and go(X)= 1+X*. Draw the code tree and trace output for input
sequence 10011.

What are Reed Solomon Codes? Discuss properties.

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