What is the correct name of this error correction method (it is similar to Hamming Code)

Question

What is the correct name of this error correction method? It is quite similar to Hamming Code, but much more simple. I also cannot find it in the literature any more. The only internet sources, I'm now able to find, which describes the method, are this:

http://www.mathcs.emory.edu/~cheung/Courses/455/Syllabus/2-physical/errors-Hamming.html

And the german-language Wikipedia.

http://de.wikipedia.org/w/index.php?title=Fehlerkorrekturverfahren

In the Wikipedia article, the method is called Hamming-ECC method. But I'm not 100% sure, this is correct.

Here is an example, which describes the way the method works.

Payload: 10011010

Step 1: Determine parity bit positions. Bits, which are powers of 2 (1, 2, 4, 8, 16, etc.) are parity bits:

Position:               1 2 3 4 5 6 7 8 9 10 11 12
Data to be transmitted: ? ? 1 ? 0 0 1 ? 1  0  1  0

Step 2: Calculate parity bit values. Each bit position in the transmission is assigned to a position number. In this example, the position number is a 4-digit number, because we have 4 parity bits. Calculate XOR of the values of those positions (in 4-digit format), where the payload is a 1 bit in the transmission:

    0011 Position 3
    0111 Position 7
    1001 Position 9
XOR 1011 Position 11
--------------------
    0110 = parity bit values

Step 3: Insert parity bit values into the transmission:

Position:               1 2 3 4 5 6 7 8 9 10 11 12
Data to be transmitted: 0 1 1 1 0 0 1 0 1  0  1  0

Is is quite simple to verify, if a received message was transmitted correctly and single-bit errors can be corrected. Here is an example. The receiver calulates XOR of the calculated and received payload bits where the value is a 1 bit. Is the result is 0, there the transmission is error-free. Otherwise the result contains the position of the bit with the wrong value.

Received message: 0001101100101101

Position:      1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Received data: 0 0 0 1 1 0 1 1 0 0  1  0  1  1  0  1
Parity bits:   X X   X       X                     X


    00101 Position 5
    00111 Position 7
    01011 Position 11
    01101 Position 13
XOR 01110 Position 14
--------------------
    01010 Parity bits calculated
XOR 00111 Parity bits received
--------------------
    01101 => Bit 13 ist defective!

I hope, anybody here knows the correct name of the method.

Thanks for any help.

Jens Jens · Accepted Answer · 2015-02-02T19:07:08

This looks like a complicated implementation of the Hamming(15,11) encoding & decoding algorithm.

Interleaving the parity bits with the information bits does not change the behaviour (or performance) of the code. Your description only uses 8 information bits, where the Hamming(15,11) corrects all single bit errors even with 11 information bits being transmitted.

Your description does not explain how the transmitted 12-bit message gets extended to a 16-bit message on the receive side.

What is the correct name of this error correction method (it is similar to Hamming Code)

1 Answers