(SEM IV) THEORY EXAMINATION 2017-18 INFORMATION THEORY AND CODING

B.Tech – Semester IV | Total Marks: 70 | Time: 3 Hours

This question paper checks a student’s understanding of information theory, entropy, coding techniques, error detection & correction, channel capacity, block codes, Huffman/Shannon coding, BSC/BEC channels, and convolution/Hamming codes.

The paper has three sections:
Short concepts (A)
Medium-level problems (B)
Long analytical/coding questions (C)

SECTION A — Short Answer Questions (2 × 7 = 14 Marks)

This section contains 7 short questions covering basics of information theory & codes.

Topics include:

Information=0 if receiver already knows message     Entropy

Kraft–McMillan inequality                                           BSC (Binary Symmetric Channel) matrix & diagram

Channel capacity theorem                                          Advantages of cyclic codes

Golay codes (short note)

These test basic concepts, definitions, and core theories of information systems.
 

SECTION B — Medium-Length Analytical Questions (7 × 3 = 21 Marks)

Attempt ANY 3 out of 5.

Topics include:

(a) Noiseless Channel Entropy

Prove:

H(X)=H(Y)H(X)=H(Y)H(X)=H(Y)                            H(Y∣X)=0H(Y|X)=0H(Y∣X)=0

(b) Shannon–Fano Coding

For a given 7-symbol DMS, construct code and calculate code efficiency.

(c) Mutual Information for BSC

Derive mutual information equation                  Calculate I(X;Y) for α=0.5 and p=0.1

(d) Linear Block Code (7,4)

Using parity-check matrix H, find:

Generator matrix G                              All code vectors

Minimum distance                              Error-detecting & correcting capability

(e) Coding Techniques

Explain:

BCH codes                                           Reed–Solomon codes

Shortened cyclic codes

This section tests mathematical reasoning, probability, and coding construction skills.
 

SECTION C — Long / Analytical Questions (7 marks each)

Each question has two choices (a or b).
These require full derivations, coding steps, numerical results, or theoretical explanation.

Q3 – Information Rate / Mutual Information

(a) Calculate information rate of telegraph source
OR
(b) Mutual information and its properties (with examples)

Q4 – Huffman Coding / Block Codes

(a) Construct Huffman code for 6-symbol DMS and find code efficiency
OR
(b) Explain block codes and their properties

Q5 – Channel Capacity / Channel Types

(a) Find channel capacity of Binary Erasure Channel
OR
(b) Explain different channels with their channel matrix & diagram

Q6 – Error Detection / Linear Block Code

(a) Different error detection methods with examples
OR
(b) Given (6,3) code & G matrix → find transmitted data word from received word

Q7 – Convolution / Hamming Codes

(a) Convolution codes + generator matrix
OR
(b) Hamming code (7,4) using polynomial g(x) — find syndrome and error polynomial

These questions test coding design, decoding, channel analysis, error control methods, and polynomial-based coding theory.
 

OVERALL PURPOSE OF THE EXAM

The question paper evaluates whether the student can:

Understand entropy, information, and source coding

Construct Shannon–Fano & Huffman codes

Compute mutual information, conditional entropy, and channel capacity

Build and decode linear block codes

Analyze BSC/BEC channels

Understand cyclic, BCH, Reed–Solomon, and convolutional codes

Perform error detection & correction

Work with generator/parity-check matrices and syndrome decoding

Apply coding theory in reliable communication systems

This paper focuses on mathematical fundamentals + coding design + theoretical reasoning, essential for communication engineering.