HAMMING CODE

[kellin10]

Using bit 0, how can the Extended Hamming code can correct a single bit error and detect double bit error.

 

[Grimpeur]

By extending the Hamming code by one bit, you can ensure that the minimum Hamming distance between error syndromes (the XOR of the transmitted and generated parity vector) which identify an SBE is at least 2. That way, a DBE can not decode to look like a different SBE, but will still be non-zero, catching the error.

A hardware-friendly way to implement that is to ensure all of your SBE syndromes themselves have odd parity; then two errors occurring at the same time will cause an even-parity syndrome vector, which is a snap to detect.

This article goes into detail, but is a bit thick to read: https://en.wikipedia.org/wiki/Hamming_code