### 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 1*

11111011 11100001

11001011 01100000

10101001 10110001

00110000 10001011

10110010 01111010

*Figure 2*

Both the payload and parity bits are shown. One of these bits is flipped.

01011110 11111101 001111001 00001001 1

11010101 11101011 1

11111001 01000010 0

00001110 01111100 1

00000101 00000001 1

*Figure 3*

Both the payload and parity bits are shown; Either one or two of the bits have been flipped.

10111100 11011000 101100011 01101110 0

11010000 11111011 0

01010010 00110010 0

00111000 11100111 0

01100101 10001010 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:

11111011 11100001 1

11001011 01100000 1

10101001 10110001 0

00110000 10001011 0

10110010 01111010 1

00011011 11000001 1

1. The parity bits for the 16 columns is: 00011011 11000001

2. The parity bits for the 5 rows is: 11001

3. The parity bit for the parity row is: 1

4. The bit that was flipped in figure 2 is (10,4):

01011110 11111101 0

01111001 00001001 1

11010101 11101011 1

11111001 01000010 0

00001110 01111100 1

00000101 00000001 1

For figure 3, the bits that were flipped are (11,4) and (14,1):

10111100 11011000 1

01100011 01101110 0

11010000 11111011 0

01010010 00110010 0

00111000 11100111 0

01100101 10001010 1

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: 0001101111000001

The answer was: 11001

The answer was: 1

The answer was: 10,4

The answer was: No