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Coherence is a property of information-carrying signals. There are two types of coherence: Fully-coherent and differentially-coherent.

Fully-coherent signals are signals where the information mapped directly onto a property of the carrier signal. For instance, amplitude modulation is almost always fully-coherent; a high amplitude corresponds to the bit '1', a low amplitude corresponds to a bit '0' (or vice-versa).

Differentially-coherent signals are signals where the information is encoded onto changes in the carrier signal. Phase modulation more often uses differential coherence, because two systems with different clocks may not be able to easily agree (long-term) on what a reference phase is, but either or both should be able to recognise a change in phase when it happens.

For example, imagine there are two states for a transmitter to be in: A and B. Fully-coherent transmission of data might map the value '0' to state A, and the value '1' to the state B (of course, it can be done the other way: B for '0' and A for '1'). Differentially-coherent transmission of data might leave the transmitter in the same state whenever there's a '0' in the data stream, and flip state when there's a '1' (this can also be done the other way, but it's nicer in some ways when '1' is associated with change and '0' with no change). An example follows.

```Fully-coherent example:
000011110101010011
AAAABBBBABABABAABB

Differentially-coherent example (starting in state A):
000011110101010011
AAAABABAABBAABBBAB
```

I've seen another nifty instance of differential coherence where the modulated signal had a period of three times a base clock. For a '0' bit, the phase of the transmitted signal was retarded by one-third (i.e. one tick of the base clock), for a '1' bit, the phase was advanced by one-third. This had the extra advantage of being self-clocking; the transmitter never stays in the same state for more than a bit period, so drift between the transmitter's clock and the receiver's clock never becomes a problem.

The relationship between fully-coherent signals and differentially-coherent signals is the same as the relationship between binary numbers and gray code. Binary data transmitted with differentially-coherent (change-on-1) frequency modulation, for example, is identical to the same data transmitted in gray code with fully-coherent frequency modulation.