### 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*

01010011 10000000

01010000 10101010

10000011 01100110

01010100 10011011

11010111 11101100

*Figure 2*

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

10101110 11101110 100010010 00011111 1

00101111 11000010 0

11111100 00110100 1

00000101 01011100 0

01001010 01011011 1

*Figure 3*

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

10000111 11100011 000111110 01110010 1

01011100 11111101 1

00011011 11100111 0

00100100 11010100 1

11001010 01011111 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:

01010011 10000000 1

01010000 10101010 0

10000011 01100110 1

01010100 10011011 0

11010111 11101100 1

00000011 00111011 1

1. The parity bits for the 16 columns is: 00000011 00111011

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 (2,5):

10101110 11101110 1

00010010 00011111 1

00101111 11000010 0

11111100 00110100 1

00000101 01011100 0

01001010 01011011 1

For figure 3, the bits that were flipped are (16,0) and (3,4):

10000111 11100011 0

00111110 01110010 1

01011100 11111101 1

00011011 11100111 0

00100100 11010100 1

11001010 01011111 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: 0000001100111011

The answer was: 10101

The answer was: 1

The answer was: 2,5

The answer was: No