Final Information Theory Base PDF

1.\_\_\_\_\_\_ indicate(s) an error in a received combination. A\) Parity bits **B) Error syndrome** C\) Data bits D\) None of the given 2\. \... is a measure of uncertainty A\) Encoding **B) Entropy** C\) Information D\) Redundancy 3\. A code has two allowable combinations 101 and 010. Wh...

1.\_\_\_\_\_\_ indicate(s) an error in a received combination. A\) Parity bits **B) Error syndrome** C\) Data bits D\) None of the given 2\. \... is a measure of uncertainty A\) Encoding **B) Entropy** C\) Information D\) Redundancy 3\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 001? **A) 101** B\) 010 C\) 001 D\) None 4\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 100? **A) 101** B\) 010 C\) 100 D\) None 5\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 000? **A) 010** B\) 101 C\) 000 D\) None 6\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 111? **A) 101** B\) 010 C\) 111 D\) None 7\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 011? **A) 010** B\) 101 C\) 011 D\) None 8\. A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 110? **A) 010** B\) 101 C\) 110 D\) None 9\. A codeword of the Hamming code consists of \_\_\_\_\_\_\_\_ and \_\_\_\_\_\_\_\_ bits. **A) data; parity** B\) with errors; without errors C\) allowable; not allowable D\) none of the given 10\. A Huffman code is a = 1, b = 000, c = 001, d = 01. Probabilities are p(a) = 0.4, p(b) = 0.1, p(c) = 0.2, p(d) = 0.3. The average length of codewords q is A\) 2.1 bit **B) 1.9 bit** C\) 2.0 bit D\) 8.0 bit 11\. A redundancy of a code S = \... **A) 1 - Iavr/Imax** B\) Iavr/Imax C\) 1 + Iavr/Imax D\) Imax/Iavr 12\. An average length of codewords qavr = \... **A) ∑ (pi\*qi)** B\) ∑ (pi/qi) C\) ∑pi / n D\) ∑qi / n 13\. An efficiency of a code E = \... **A) Iavr/Imax** B\) Imax/Iavr C\) Iavr/100 D\) Imax - Iavr 14\. ASCII code is a A\) Variable length code **B) Fixed length code** C\) Error-correction code D\) None of the given 15\. By the Bayes\' rule for conditional entropy H(Y\|X) = \... **A) H(X\|Y) - H(X) + H(Y)** B\) \[P(A)\] /P(B) C\) H(X\|Y) - H(X) D\) H(X\|Y)+ H(Y) 16\. By the Bayes\' theorem \... A\) P(B\|A) = P(A and B)/P(A) **B) P(A\|B) = \[P(B\|A)\]\[P(A)\] /P(B)** C\) P(B\|A) = P(A and B)\*P(A) D\) P(A\|B) = \[P(B\|A)\]\[P(A)\] \* P(B) 17\. By the Chain rule H(X,Y) = H(Y\|X) + \... **A) H(X)** B\) H(Y) C\) H(Y\|X) D\) H(X\|Y) 18\. By the Hartley\'s formula the amount of information I = \... **A) I = n\*log m** B\) I = m\*n C\) I = log (m/n) D\) I = log (m\*n) 19\. By the Hartley\'s formula the entropy H = \... A\) H = - ∑(pi\*log pi) B\) H = - ∑ (log pi) **C) H = log m** D\) H = - ∑ (pi/log pi) 20\. By the property of joint entropy H(X,Y) \= H(X) and H(X,Y) \= H(X) and H(X,Y) \>= H(Y)** D\) H(X,Y) \>= H(X) + H(Y) 22\. By the Shannon\'s formula the amount of information I = \... **A) H = - n \* ∑(pi\*log pi)** B\) H = - n \* ∑ (log pi) C\) H = - n \* ∑ pi D\) H = - n \* ∑ (pi/log pi) 23\. By the Shannon\'s formula the entropy H = \... **A) H = - ∑(pi\*log pi)** B\) H = - ∑ (log pi) C\) H = - ∑ pi D\) H = - ∑ (pi/log pi) 24\. Calculate the code rate for Hamming (15,11) code A\) 1 **B) 0,733** C\) 0,571 D\) 0,839 25\. Calculate the code rate for Hamming (31,26) code A\) 1 **B) 0,839** C\) 0,733 D\) 0,571 26\. Calculate the code rate for Hamming (7,4) code A\) 1 **B) 0,571** C\) 0,733 D\) 0,839 27\. Calculate the **efficiency** of the language if it has 32 letters and its I average is 1 bit. A\) 0,8 **B) 0,2** C\) 5 D\) 1 28\. Calculate the **redundancy** of the language if it has 32 letters and its I average is 1 bit. **A) 0,8** B\) 0,2 C\) 5 D\) 1 29\. Choose an example of block code A\) Shannon-Fano code B\) Huffman code **C) Hamming code** D\) None of the given 30\. Choose conditions of an optimal coding (p -- probability, l -- length of a code word) **A) pi \< pj and li\ pj and li\ pj and li\>=lj D\) none of the given 31\. Choose the formula to create the Hamming code **A) (n, k) = (2r - 1, 2r - 1 - r)** B\) (n, k) = (2r, 2r - 1 - r) C\) (n, k) = (2r - 1, 2r - r) D\) (n, k) = (2r - 1, 2r - 1 + r) 32\. Choose the formula to determine the number N of possible messages with length n if the message source alphabet consists of m characters, each of which can be an element of the message. **A) N = mn** B\) N = nm C\) N = m\*n D\) N = log m **Правильный ответ N = m\^n** 33\. Code has dmin = 1. How many errors can be **corrected** by this code? A\) 2 B\) 3 **C) 0** D\) 1 34\. Code has dmin = 1. How many errors can be **detected** by this code? A\) 2 B\) 3 **C) 0** D\) 1 35\. Code has dmin = 10. How many errors can be **detected** by this code? A\) 4 B\) 8 **C) 9** D\) 10 36\. Code has dmin = 11. How many errors can be **corrected** by this code? A\) 11 B\) 7 **C) 5** D\) 10 37\. Code has dmin = 11. How many errors can be **detected** by this code? A\) 5 B\) 9 **C) 10** D\) 11 38\. Code has dmin = 12. How many errors can be **detected** by this code? A\) 5 B\) 10 **C) 11** D\) 12 39\. Code has dmin = 2. How many errors can be **corrected** by this code? A\) 2 B\) 3 **C) 0** D\) 1 40\. Code has dmin = 2. How many errors can be **detected** by this code? A\) 2 B\) 3 **C) 1** D\) 0 41\. Code has dmin = 3. How many errors can be **corrected** by this code? A\) 2 B\) 3 D\) 4 42\. Code has dmin = 3. How many errors can be **detected** by this code? A\) 1 B\) 3 **C) 2** D\) 4 43\. Code has dmin = 4. How many errors can be **detected** by this code? A\) 5 B\) 1 **C) 3** D\) 4 44\. Code has dmin = 5. How many errors can be **corrected** by this code? A\) 5 B\) 3 **C) 2** D\) 4 45\. Code has dmin = 5. How many errors can be **detected** by this code? A\) 6 B\) 2 **C) 4** D\) 5 46\. Code has dmin = 6. How many errors can be **detected** by this code? A\) 6 B\) 2 **C) 5** D\) 4 47\. Code has dmin = 7. How many errors can be **corrected** by this code? A\) 5 B\) 6 **C) 3** D\) 4 48\. Code has dmin = 7. How many errors can be **detected** by this code? A\) 7 B\) 3 **C) 6** D\) 5 49\. Code has dmin = 8. How many errors can be **detected** by this code? A\) 8 B\) 6 **C) 7** D\) 3 50\. Code has dmin = 9. How many errors can be **corrected** by this code? A\) 5 B\) 7 **C) 4** D\) 8