JNTU
JNTU B.Tech III ERROR CORRECTING CODES Previous Question Paper (January/February - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
PART A
What is mean by Forward Error Correction codes?
Answer
Forward Error Correction (FEC) is a digital communication technique where the transmitter adds redundant data to a message, allowing the receiver to detect and correct errors without requiring a retransmission of the original data. By embedding extra bits into the transmitted signal, the receiver uses a decoding algorithm to identify and fix errors caused by noise or interference in the communication channel, thereby improving reliability in real-time or one-way transmission systems.
Derive the condition for block codes to be a linear code.
Answer
A block code C of length n over a finite field GF(q) is defined as a linear code if and only if it satisfies the following two conditions:
- The code C is a subspace of the vector space V = GF(q)n.
- The sum of any two codewords is also a codeword in C. That is, for any c1, c2 ∈ C, their vector sum c1 + c2 ∈ C.
Mathematically, a code is linear if it is closed under vector addition and scalar multiplication. Specifically, for any two codewords c1 and c2 and any scalars a, b ∈ GF(q), the linear combination ac1 + bc2 must also be a codeword in C. A necessary consequence of this property is that the all-zero vector must be present in every linear block code.
What are the advantages of shortened cyclic codes?
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An (n,k) linear code C is called a cyclic code if every cyclic shift of a code vector in C is also a code vector in C.
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How majority logic decoding differ from other decoding methods of convolutional codes?
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How convolutional codes are used in ARQ systems?
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Define a log prior ration for turbo codes.
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Compare parallel and serial concatenation in turbo codes.
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What are the advantages of Alamouti code?
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How Trellis codes provide diversity?
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PART B
For a BSC with crossover probability p having input X and output Y, let the probability of the inputs be P(X=0) = q and P(X=1) = 1-q. Find the mutual information?
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Show that H(X) ≥ H(X/Y).
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Prove that the minimum distance of a linear block code is equal to the minimum weight of its nonzero code words.
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Consider an (n,k) linear code C whose generator matrix G contains no zero column. Arrange all the code vectors of C as rows of a 2^k-by-n array. Show that no column of array contains only zeros.
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Design a decoding circuit for a single-error-correcting and double-error-detecting cyclic Hamming code and explain its working with example.
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For a cyclic code, if an error pattern e(X) is detectable, show that its ith cyclic shift e^(i)(X) is also detectable.
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Let C1 and C2 be two cyclic codes of length n which are generated by g1(X) and g2(X), respectively. Show that the code polynomials common to both C1 and C2 also form a cyclic code C3. Determine the generator polynomial of C3.
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Consider the (3, 1, 2) convolutional code with g^(1) = (1 0 1 0), g^(2) = (1 1 1 0), g^(3) = (1 1 1 1)
- Draw the encoder block diagram
- Find the generator matrix G
- Find the code word V corresponding to the information sequence u= (1 1 1 0 0) using tree diagram?
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Write Viterbi algorithm and explain how it is used for decoding of convolutional codes.
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Draw the diagram of a log likelihood turbo decoder and explain its working.
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Show that the log likelihood of the sequence log p(r) = log p(r0^N-1) can be written as the given sum expression.
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For the provided parity check matrix A:
- Construct the Tanner graph for the code.
- Determine the girth of the minimum-girth cycle.
- Determine the number of cycles of length 6.
- Determine a generator matrix for this code.
- Express the N and M lists describing this parity check matrix.
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How a delay diversity coder may also written as a space-time block code?
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For the given set of space-time codes A1, A2, A3, A4, find diversity order of each code, assuming transmitted symbols are selected from 40 QAM and receiver has a single antenna.
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Explain the following:
- BLAST detection
- Multi-layer detection schemes.
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