Question

In: Other

Find the shortest encoded bit string of the following source sequence: Source sequence: ABCCDEAFABCBEDFABCBBAEFFEBCEFF (a) using...

Find the shortest encoded bit string of the following source sequence: Source sequence: ABCCDEAFABCBEDFABCBBAEFFEBCEFF

(a) using extended Huffman coding to encode the string where k=2


(b) using arithmetic coding.
For this case, you can ignore the termination issue ina a decoder, and output the shortestbit string of the first 5 symbols only, while the probability distribution is based on the whole sequence.


(c) Using adaptive Huffman coding to encode the first 10 symbols of the string. The initial code assignment is given below

  • New : 0

  • A : 00001

  • B : 00010

  • C : 00011

  • D : 00100

  • E : 00101

  • F : 00110

Solutions

Expert Solution

Answer: Following are the LT properties

a) \(P=\varnothing^{\emptyset}\)

b) \(\mathrm{P}=\left\{A O, A 1, A 2 \ldots \in 2 A P w / x O \in A O^{A_{0}}, A_{1}, A_{2} \ldots \in\left(2^{A P}\right)^{w} \mid x_{0} \in A_{0}\right\}\)

c) \(\mathrm{P}=\left\{A O, A 1, A 2 \ldots \in 2 A P w / x O \notin A C A_{0}, A_{1}, A_{2} \ldots \in\left(2^{A P}\right)^{w} \mid x_{0} \notin A_{0}\right\}\)

d) \(P=\left\{A O, A 1, A 2 \ldots \in 2 A P w / x O \notin A O \wedge \exists A_{0}, A_{1}, A_{2} \ldots \in\left(2^{A P}\right)^{w} \mid x_{0} \notin A_{0} \wedge \exists_{i}:(x>i) \in A_{i} \wedge i>0\right\}\)

e) \(\mathrm{P}=\left\{A O, A 1, A 2 \ldots \in 2 A P_{W} A_{0}, A_{1}, A_{2} \ldots \in\left(2^{A^{p}}\right)^{w} \mid \exists_{i} \geq \geq 0: \forall j \geq i,(x>i) \notin A_{j}\right\}\)

f) \(P=\left\{A O, A 1, A 2 \ldots \in 2 A P w^{A_{0}}, A_{1}, A_{2} \ldots . \in\left(2^{A P}\right)^{w} \mid \forall i \geq 0: \exists_{j} \geq 1,(x>i) \in A_{j}\right\}\)

g) \(P=\left\{A O, A 1, A 2 \ldots \in 2 A P w^{A}_{0}, A_{1}, A_{2} \ldots . \in\left(2^{A P}\right)^{w} \mid \forall(x=0)^{\forall}(x=0) \in^{\epsilon} A_{1} A_{i} \wedge^{\wedge}(x>1) \in^{\epsilon} A i+1^{A}_{i+1} \wedge^{\wedge} i m o d z^{m o d}_{2}\right.\)

\(=0\) ) \(v\)

h) \(\mathrm{P}=2 \mathrm{APW}^{\left(2^{A P}\right)^{w}}\)

Safety property is a behavior in which "nothing bad happens".

Here, \(d, g\) is a safety property, as a bad prefix is for instance.


Related Solutions

Recall that a 5-bit string is a bit strings of length 5, and a bit string...
Recall that a 5-bit string is a bit strings of length 5, and a bit string of weight 3, say, is one with exactly three 1’s. a. How many 5-bit strings are there? b. How many 5-bit strings have weight 0? c. How many 5-bit strings have weight 1? d. How many 5-bit strings have weight 2? e. How many 5-bit strings have weight 4? f. How many 5-bit strings have weight 5? g. How many 5-bit strings have weight...
Stream Cipher. A message is encoded by exclusive-or’ing each bit with a random bit stream. (In...
Stream Cipher. A message is encoded by exclusive-or’ing each bit with a random bit stream. (In exclusive or, 0⊕0 = 0, 1⊕0 = 1, 0⊕1 = 1, and 1⊕1 = 0.) a. Recover the original message from the random stream and encrypted stream, by filling in the blanks in the “Recovered” and “ASCII” rows. (In the ASCII column, interpret the byte as an ASCII character and write the value in that row.) Message: ? ? ? ? ? ? ?...
An n-bit binary string is a sequence of length n over the alphabet {0,1}. How many...
An n-bit binary string is a sequence of length n over the alphabet {0,1}. How many n-bit binary strings are there? How many n-bit binary strings b1,…,bn are there such that b1b2≠00? In other words, how many n-bit binary strings don't begin with 00? How many n-bit binary strings b1,…,bn are there such that b1b2≠00 and b2b3≠11? How many n-bit binary strings b1,…,bn are there such that b1b2≠00 and such that b2b3≠01?
perfrome bit destuffing for the following sequence: 11101111101111100111110
perfrome bit destuffing for the following sequence: 11101111101111100111110
Write an essay in which you explain how the sequence of proteins is encoded in the...
Write an essay in which you explain how the sequence of proteins is encoded in the mRNA and how it is translated at the ribosome. Also using a drawing give a detailed description of how initiation, elongation and termination occur in bacteria. explain how the sequence of proteins is encoded in the mRNA and how it is translated at the ribosome. using a drawing give a detailed description of how initiation, elongation and termination occur in bacteria.
In c++, using stack structure, write a program that will take a sequence of characters (string)...
In c++, using stack structure, write a program that will take a sequence of characters (string) and determine whether it is a palindrome. Use the linked version of the stack.
Design a transducer to convert a binary string into octal. For example the bit string 001101110...
Design a transducer to convert a binary string into octal. For example the bit string 001101110 should produce 156. Please complete the code to account for the 7 cases of 3 digit binary strings. //Function binaryToOctal takes a char array digits of length 3 //Pre: digits contains 3 binary digits. //Post: function returns the octal number equivalent to the 3 binary digits int binaryToOctal( char digits[], int 3){ int number; if(digits[0]=='0') if (digits[1]=='1') if (digits[2]=='0') return 2;//found "010" else return...
Suppose that you pick a bit string from the set of all bit strings of length...
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that the bit string has exactly two 1s; the bit string begins and ends with 0; the bit string has the sum of its digits equal to seven; the bit string has more 0s than 1s; the bit string has exactly two 1s, given that the string begins with a 1.
Suppose that you pick a bit string from the set of all bit strings of length...
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that the bit string has exactly two 1s; the bit string begins and ends with 0; the bit string has the sum of its digits equal to seven; the bit string has more 0s than 1s; the bit string has exactly two 1s, given that the string begins with a 1.
Assume that you had just received the bit sequence "10000011". Given the first bit is a...
Assume that you had just received the bit sequence "10000011". Given the first bit is a parity bit, which parity system would indicate that there has been a 1 bit transmission error? Justify your answer. Enter your answer below.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT