Information Theory and Coding (EC-702 (B)) - Important Questions

Derive the expression for channel capacity when bandwidth tends to infinity from the channel capacity theorem and explain it.

Explain the decoder for cyclic codes with the help of a block diagram and error correction procedure.

A zero memory source has source alphabet S = {s1, s2, s3} with P = {0.5, 0.3, 0.2}. Find the entropy of the source. Find the entropy of its second extension and verify.

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) = 1 + X^3 + X^4 + X^5 + X^6.

A channel encoder uses a (7, 4) linear systematic cyclic code in systematic form with generator polynomial X^3 + X + 1. Determine the correct codeword transmitted if the received word is given. Explain syndrome computation for error correction.

Consider message ensemble S = {s1, s2, s3, s4, s5, s6, s7} with probabilities P = {0.45, 0.15, 0.12, 0.08, 0.08, 0.08, 0.04}. Construct a binary code using Shannon-Fano encoding algorithm and determine its efficiency.

Design an (n, k) Hamming code with message length k = 4 and minimum distance dmin = 3. Give its generator matrix and parity-check matrix and comment on its error correction capability and applications.

Explain maximum likelihood decoding of convolutional codes using the Viterbi algorithm.

State and prove Shannon-Hartley theorem on channel capacity.

Show how a 4-bit stage shift register can generate a convolution code for an input train 11001. Explain the convolution encoder operation.

What is the significance of the syndromes of a (6, 3) systematic cyclic code? Give a complete list of codes and syndromes.

Explain matrix description of linear block codes. Explain the structure of block codes and systematic block codes with generator matrix and parity-check matrix.

Define uncertainty, information and entropy and discuss its properties, including that entropy is maximum when all messages are equiprobable.

Construct the Huffman code with minimum code variance for the probabilities {0.25, 0.25, 0.125, 0.125, 0.125, 0.0625, 0.0625} and determine the code variance and code efficiency.

Write short notes on (any four): (i) Binary Symmetric Channel and Binary Erasure Channel (ii) Parity check polynomial (iii) Minimum distance and error detection/correction (iv) BCH codes (v) Transform domain approach of convolutional encoder (vi) Mutual information.