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 111011110 11011111
01000000 11100100
11111000 01001111
11011000 01110100
00111111 11100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100110 00000100 001101010 10010100 1
00111110 10001111 0
00101000 00111010 0
00100101 00110001 0
11111111 00110100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000010 01000001 011001111 00011000 1
10101010 01001101 0
10010011 11111011 1
01101100 00010000 1
00011000 11101111 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:
11011110 11011111 1
01000000 11100100 1
11111000 01001111 0
11011000 01110100 0
00111111 11100100 0
10000001 11100100 0
1. The parity bits for the 16 columns is: 10000001 11100100
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (10,0):
10100110 00000100 0
01101010 10010100 1
00111110 10001111 0
00101000 00111010 0
00100101 00110001 0
11111111 00110100 1
For figure 3, the bit that was flipped is (11,1):
10000010 01000001 0
11001111 00011000 1
10101010 01001101 0
10010011 11111011 1
01101100 00010000 1
00011000 11101111 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: 1000000111100100
The answer was: 11000
The answer was: 0
The answer was: 10,0
The answer was: Yes