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CTT Q3

The document discusses coding theory and techniques topics for an exam, including: calculating entropy for random variables, designing a Huffman code and determining channel capacity, explaining error control strategies and constructing block codes, standard error detection for linear block codes, error-trapping decoding for cyclic codes, properties of convolutional codes, applications of Viterbi and sequential decoding, BCH codes including generator polynomials and decoding.

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Shiva Glenn
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20 views2 pages

CTT Q3

The document discusses coding theory and techniques topics for an exam, including: calculating entropy for random variables, designing a Huffman code and determining channel capacity, explaining error control strategies and constructing block codes, standard error detection for linear block codes, error-trapping decoding for cyclic codes, properties of convolutional codes, applications of Viterbi and sequential decoding, BCH codes including generator polynomials and decoding.

Uploaded by

Shiva Glenn
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Code No: 137BE R16

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD


B. Tech IV Year I Semester Examinations, March - 2021
CODING THEORY AND TECHNIQUES
(Electronics and Communication Engineering)
JN
Time: 3 Hours Max. Marks: 75
Answer any Five Questions
All Questions Carry Equal Marks
---
TU
1.a) Two binary random variables X and Y are distributed according to the joint distributions
P(X = Y = 0) = P(X = 0, Y = 1) = P(X = Y = 1) = 1/ 3. Compute H(X), H(Y ), H(X|Y ),
2H3
H(Y|X), and H(X, Y ).
b) A discrete memoryless source produces outputs {a1, a2, a3, a4, a5, a6, a7, a8}. The
corresponding output probabilities are 0.05, 0.07, 0.08, 0.1, 0.1, 0.15, 0.2, 0.25.
i) Design a binary Huffman code for the source. Find the average codeword length.
U-0
Compare it to the minimum possible average codeword length.
ii) What is the minimum channel capacity required to transmit this source reliably? Can
S3E
this source be reliably transmitted via a binary symmetric channel? [8+7]
-2D
2.a) Explain the types of errors and error control strategies for reliable data transmission.
b) Construct an extended (8, 4) code from the (7, 4) Hamming code by specifying the
generator matrix and the parity check matrix. [8+7]
02P
3.a) Explain error detecting and correcting capabilities of block codes.
b) Construct the standard array for the (7, 3) code with generator matrix
1a
pPeM
and determine the correctable patterns and their corresponding syndromes. [8+7]

4.a) Explain standard error and syndrome detection of linear block codes
b) The polynomial g(X) = X4 + X + 1
r-2
is the generator for the (15, 11) Hamming binary code.
i) Determine a generator matrix G for this code in systematic form.
ii) Determine the generator polynomial for the dual code. [8+7]
02
5.a) Explain about error-trapping logic decoding for cyclic codes.
b) Determine the correctable error patterns (of least weight) and their syndromes for the
systematic (7, 4) cyclic Hamming code. [8+7]
1
6. A convolutional code is described by
g1 = [101], g2 = [111], g3 = [111]
a) Draw the encoder corresponding to this code.
b) Draw the state-transition diagram for this code.
c) Draw the trellis diagram for this code.
d) Find the transfer function and the free distance of this code.
e) Verify whether or not this code is catastrophic. [15]
7.a) Explain the applications of Viterbi decoding and sequential decoding.
b) Determine the generator polynomial and the rate of a double-error-correcting BCH code
with block length n = 31. [8+7]
JN
8.a) Explain the decoding procedure of BCH codes.
b) Devise a syndrome computation circuit for the binary double error correcting (31,21) BCH
code. [8+7]
TU
--ooOoo--
2H3
U-0
S3E
-2D
02P
1a
pPeM
r-2
02
1

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