Error Detection and Correction: Two Dimensional Parity
Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):
Figure 111000111 01000001
00100000 11101011
01110111 11101100
01000100 00101101
00101111 10101101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110101 10101011 011001011 10000010 1
10010010 01110111 1
01000100 10101101 1
00100000 00110010 0
11001000 11001001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110110 00111011 010100100 00000000 1
00001011 00011010 0
11001010 10001011 1
01010010 10110111 1
10000001 00010101 1
Question List
1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string
2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string
3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.
4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0
5. For figure 3, is it possible to detect and correct the bit flips? Yes or No
Solution
The full solution for figure 1 is shown below:
11000111 01000001 1
00100000 11101011 1
01110111 11101100 1
01000100 00101101 0
00101111 10101101 0
11111011 11000110 1
1. The parity bits for the 16 columns is: 11111011 11000110
2. The parity bits for the 5 rows is: 11100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,0):
11110101 10101011 0
11001011 10000010 1
10010010 01110111 1
01000100 10101101 1
00100000 00110010 0
11001000 11001001 1
For figure 3, the bit that was flipped is (12,3):
10110110 00111011 0
10100100 00000000 1
00001011 00011010 0
11001010 10001011 1
01010010 10110111 1
10000001 00010101 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1111101111000110
The answer was: 11100
The answer was: 1
The answer was: 12,0
The answer was: Yes