Hamming SEC/DED extra parity bit

Question

I'm having some troubles with the SEC/DED error correction code. It seems I've found some cases in which the decoder thinks a double bit flip occured but only one really occured. I suppose I did somthing wrong, but I was not able to understand what. Let me show you an example.

Suppose I want to encode the 4 bits 1011 using a (7,4) code plus an extra bit needed to perform the two-error-detection. The coded word should be 00110011, where the most significant bit is the extra parity bit, the following two are p0 and p1 and so on.

Now, let's suppose that during a transmission the less significant bit is flipped; thus the received word will be 00110010. The receiver will extract from this code the four received data bits 1010 and will construct a new code which will result 01011010. Finally the receiver will perform a bitwise xor of the two codes obtaining 0111. The last three bits says that bit 7 has been flipped (which is right), but the first bit is 0 and, as far as i know, the decoder should consider this situation as if more than a bit flip has occured.

What did I do wrong?

Answer 1

I think I've solved the problem.

In the example above I calculate the syndrome and then I compute a new overall parity bit of the resultant codeword. Instead, I should check the overall parity of the received word and set the error_happened boolean to that value; then calculate the syndrome.