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 111110111 10011010
11101101 01110010
11011011 10110000
01101110 10001100
00111000 11001100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010001 10010011 010001100 10000111 1
01111000 01010110 0
00011001 00100100 1
01110011 10000100 0
01011111 11100010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10001010 00001110 001111011 11011100 1
01010101 01001111 1
00111011 10110001 0
01110110 00110100 0
11101001 01010000 0
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:
11110111 10011010 1
11101101 01110010 0
11011011 10110000 1
01101110 10001100 0
00111000 11001100 1
10010111 00011000 1
1. The parity bits for the 16 columns is: 10010111 00011000
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,4):
11010001 10010011 0
10001100 10000111 1
01111000 01010110 0
00011001 00100100 1
01110011 10000100 0
01011111 11100010 0
For figure 3, the bits that were flipped are (12,3) and (9,5):
10001010 00001110 0
01111011 11011100 1
01010101 01001111 1
00111011 10110001 0
01110110 00110100 0
11101001 01010000 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 1001011100011000
The answer was: 10101
The answer was: 1
The answer was: 3,4
The answer was: No