Example 10.10 textbook: data communications and networkings by behrouz forouzan

Question

Example 10.10

textbook: data communications and networkings by behrouz forouzan 4th edition
capter 10
Example:
Let us see if the two codes we defined in Table 10.1 and Table 10.2 belong to the class of linear
block codes.
1. The scheme in Table 10.1 is a linear block code because the result of XORing any codeword
with any other codeword is a valid codeword. For example, the XORing of the second and
third codewords creates the fourth one.
2. The scheme in Table 10.2 is also a linear block code. We can create all four codewords by
XORing two other codewords.


Example 10.12
Let us look at some transmission scenarios. Assume the sender sends the dataword 1011. The codeword
created from this dataword is 10111, which is sent to the receiver. We examine five cases:
1. No error occurs; the received codeword is 10111. The syndrome is O. The dataword 1011 is
created.
2. One single-bit error changes aI' The received codeword is 10011. The syndrome is 1. No
dataword is created.
3. One single-bit error changes roo The received codeword is 10110. The syndrome is 1. No dataword
is created. Note that although none of the dataword bits are corrupted, no dataword is
created because the code is not sophisticated enough to show the position of the corrupted bit.
4. An error changes ro and a second error changes a3' The received codeword is 00110. The syndrome
is O. The dataword 0011 is created at the receiver. Note that here the dataword is
wrongly created due to the syndrome value. The simple parity-check decoder cannot detect an
even number of errors. The errors cancel each other out and give the syndrome a value of O.
5. Three bits-a3, az, and aI-are changed by errors. The received codeword is 01011. The
syndrome is 1. The dataword is not created. This shows that the simple parity check, guaranteed
to detect one single error, can also find any odd number of errors.


Questions:
13. In Table 10.1, the sender sends dataword 10. A 3-bit burst error corrupts the codeword.
Can the receiver detect the error? Defend your answer.

14. In Table 10.2, the sender sends dataword 10. If a 3-bit burst en-or con-upts the first
three bits of the codeword, can the receiver detect the error? Defend your answer

17. Using the code in Table 10.2, what is the dataword if one of the following codewords
is received?
a. 01011
b. 11111
c. 00000
d. 11011


29. Assuming even parity, find the parity bit for each of the following data units.
a. 1001011
b. 0001100
c. 1000000
d. 1110111

Chapter 5
9. Which characteristics of an analog signal are changed to represent the lowpass analog
signal in each of the following analog-to-analog conversions?
a. AM
b. FM
c. PM


11. Calculate the baud rate for the given bit rate and type of modulation.
a. 2000 bps, FSK
b. 4000 bps, ASK


12. Calculate the bit rate for the given baud rate and type of modulation.
a. 1000 baud, FSK
b. 1000 baud, ASK
c. 1000 baud, BPSK


13. What is the number of bits per baud for the following techniques?
a. ASK with four different amplitudes
b. FSK with 8 different frequencies
c. PSK with four different phases

Explanation / Answer

1) Consider Table 10.1 dataword (000,011,101,110)
Then perform XOR operation on 000 and 011
       1 0 1
XOR 0 1 1
---------------
       1 1 0
---------------
Therefore we perform XOR operation on second(011) and third(101) datawords then we get fourth(110).So the table 10.1 is a linear block code.

Consider Table 10.2 dataword (00000,01011,10101,11110)
Then perform XOR operation on 000 and 011
       0 1 0 1 1
XOR 1 0 1 0 1
-------------------
       1 1 1 1 0
--------------------
Therefore we perform XOR operation on second(01011) and third(101) datawords then we get fourth(11110).So the table 10.2 is also a linear block code.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.