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 101001110 00010100
01100000 00101101
00000100 10000010
11001100 01011101
00001011 11001010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110010 00010011 111011100 00011000 1
01010111 11111110 0
10000011 00010100 1
00101010 01100010 0
00010000 10000001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001110 01011101 111100000 01010000 1
10111110 00111000 1
11111100 01000100 0
10000000 10011110 0
01101101 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:
01001110 00010100 0
01100000 00101101 0
00000100 10000010 1
11001100 01011101 1
00001011 11001010 1
11101101 00101100 1
1. The parity bits for the 16 columns is: 11101101 00101100
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,0):
00110010 00010011 1
11011100 00011000 1
01010111 11111110 0
10000011 00010100 1
00101010 01100010 0
00010000 10000001 1
For figure 3, the bit that was flipped is (7,5):
01001110 01011101 1
11100000 01010000 1
10111110 00111000 1
11111100 01000100 0
10000000 10011110 0
01101101 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: 1110110100101100
The answer was: 00111
The answer was: 1
The answer was: 14,0
The answer was: Yes