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 110011101 01110000
11000000 10011011
01100010 11010010
00001101 11111000
10111010 01000100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00100011 11111000 000101111 11010011 0
00010100 00101001 0
10001000 10010001 1
10110101 11001011 0
00100101 11011000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100100 00011001 111011010 00000111 0
00111100 10001110 0
10101010 11111010 1
10011010 10011011 1
00100010 11110001 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:
10011101 01110000 0
11000000 10011011 1
01100010 11010010 1
00001101 11111000 0
10111010 01000100 1
10001000 10000101 1
1. The parity bits for the 16 columns is: 10001000 10000101
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,2):
00100011 11111000 0
00101111 11010011 0
00010100 00101001 0
10001000 10010001 1
10110101 11001011 0
00100101 11011000 1
For figure 3, the bit that was flipped is (3,3):
11100100 00011001 1
11011010 00000111 0
00111100 10001110 0
10101010 11111010 1
10011010 10011011 1
00100010 11110001 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: 1000100010000101
The answer was: 01101
The answer was: 1
The answer was: 8,2
The answer was: Yes