[C2]=[1011001] 1- Find hamming distance for the three code words [C1]=[1011100] [C3]=[1011000].
[C2]=[1011001] 1- Find hamming distance for the three code words [C1]=[1011100] [C3]=[1011000].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![[C2]=[1011001] ,
1- Find hamming distance for the three code words [C1]=[1011100] ,
[C3]=[1011000].
2- Find the generator matrix for the following H matrix of LBC
r1
1
1-
1
1
1
1
1
1
[H] =
1
%3D
0 0
1
1]
3- For (7,4) code, with [H] for the previous problem
a- Find the corrected word at the receiver, if the received word [R]=[1001111].
b. Find the syndrome vector
c. Draw the decoder circuit used to find [S].
double errors occur at first and last positions
[1 0 0 1 1 0 1 1 0 0]
01101 1
4- [G]=
Find the following:
0 10
0 010 0 1 1 1 0 1
a- Find the [H] matrix.
b- Find the code table, hamming weight and the error correction capability.
c- If the received word is [R]=[1011110011], find the corrected word at the receiver.
5- Write down the code table for the (7,4) multiplication cyclic code with generator polynomial
g(p) = p3 +p+1
6- Using g(p) = p3 + p? + 1, find the output codeword for [D]=[0011] and [D]=[0010]
7- Find the code table for (7,4) division cyclic code generated by
g(p) = p3 + p? + 1
8- For the given message sequence with their probabilities, Apply a) Fano coding b)Shannon coding
c) Huffman coding, calculate the code efficiency in all types of source coding.
[x] = [x1
x2
x3
X5 х6 х7
х8]
1/16 1/16 1/4 1/16 1/8]
x4
[P] = [1/4 1/8
1/16
9- Repeat previous problem for the following
[x]%3D[x1 х2 х3
[P] = [0.4 0.2. 0.12 0.08 0.08 0.08 0.04]
х4
x5 хб
x7 ]
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Transcribed Image Text:[C2]=[1011001] ,
1- Find hamming distance for the three code words [C1]=[1011100] ,
[C3]=[1011000].
2- Find the generator matrix for the following H matrix of LBC
r1
1
1-
1
1
1
1
1
1
[H] =
1
%3D
0 0
1
1]
3- For (7,4) code, with [H] for the previous problem
a- Find the corrected word at the receiver, if the received word [R]=[1001111].
b. Find the syndrome vector
c. Draw the decoder circuit used to find [S].
double errors occur at first and last positions
[1 0 0 1 1 0 1 1 0 0]
01101 1
4- [G]=
Find the following:
0 10
0 010 0 1 1 1 0 1
a- Find the [H] matrix.
b- Find the code table, hamming weight and the error correction capability.
c- If the received word is [R]=[1011110011], find the corrected word at the receiver.
5- Write down the code table for the (7,4) multiplication cyclic code with generator polynomial
g(p) = p3 +p+1
6- Using g(p) = p3 + p? + 1, find the output codeword for [D]=[0011] and [D]=[0010]
7- Find the code table for (7,4) division cyclic code generated by
g(p) = p3 + p? + 1
8- For the given message sequence with their probabilities, Apply a) Fano coding b)Shannon coding
c) Huffman coding, calculate the code efficiency in all types of source coding.
[x] = [x1
x2
x3
X5 х6 х7
х8]
1/16 1/16 1/4 1/16 1/8]
x4
[P] = [1/4 1/8
1/16
9- Repeat previous problem for the following
[x]%3D[x1 х2 х3
[P] = [0.4 0.2. 0.12 0.08 0.08 0.08 0.04]
х4
x5 хб
x7 ]
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