Error Detection and Correction On-Board Nanosatellites Using Hamming Codes

Table 4

Bit layout of Hamming code (nonsystematic).

Bit position

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Encoded data bits

P1

P2

D1

P4

D2

D3

D4

P8

D5

D6

D7

D8

D9

D10

D11

P16

Encoded data coverage (nonsystematic) syndrome

P1

✗

✗

✗

✗

✗

✗

✗

✗

P2

✗

✗

✗

✗

✗

✗

✗

✗

P4

✗

✗

✗

✗

✗

✗

✗

✗

P8

✗

✗

✗

✗

✗

✗

✗

✗

P16

✗

The syndrome allows errors to be located and corrected. For example, if parity bits P1, P4, and P8 show an error, the location of the error can be found by 1(P1) + 4(P4) + 8(P8) = 13. Therefore, the error affected data bit 9 (D9) in position 13, shown in bold. The above explanation shows the general algorithm used when implementing Hamming code.