I just started learning about hamming codes and they're pretty awesome. I was just wondering though, are the check bits able to detect error in the check bits, as in, if one of the check bits is received erroneously can that be detected? Or is some other method required?
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1The best way to understand is to look at the codewords of the error correction scheme. Codewords can be tabulated like a truth table. This is something you can generate programmatically, or found on internet websites. In general most error correction schemes are already covered extensively by articles on Wikipedia. For example, to see whether the error can be detected if some of the check bits are wrong, you can write a program to flip a specific number of those check bits, and see the result for yourself. Some basic laws apply, like pigeonhole– rwongCommented Dec 2, 2017 at 13:25
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1 Answer
The actual error detection and error correction for hamming codes does not treat parity bits (I guess that is what you mean by "check bits") different than any other bits in a code word. If one bit gets lost during a transmission, it can be recovered (by finding the "nearest neighbour" among valid words), if two bits get lost, the error can still be detected (since words differing two bits from a valid word are always invalid). If these bits are parity bits or other bits does not matter.
answered Dec 2, 2017 at 15:20
