Conventional Differential Coding
A method illustrated above can deal with a data stream inversion (it is called 180° ambiguity). Sometimes it is enough (e.g. if BPSK is used or if other ambiguities are detected by other circuits, such as a Viterbi decoder or a frame synchronizer) and sometimes it isn't.
Generally speaking, a differential coding applies to symbols (these are not necessary the same symbols as used in the modulator). To resolve 180° ambiguity only, bits are used as these symbols. When dealing with 90° ambiguity, pairs of bits are used, and triplets of bits are used to resolve 45° ambiguity (e.g. in 8PSK).
A differential encoder provides the operation, a differential decoder - the operation.
Both differential encoder and differential decoder are discrete linear time-invariant systems. The former is recursive and IIR, the latter is non-recursive and thus FIR. They can be analyzed as digital filters.
A differential encoder is similar to an analog integrator. It has an impulse response
and a transfer function
A differential decoder is thus similar to an analog differentiator, its impulse response being
and its transfer function
Note that in binary (modulo-2) arithmetic, addition and subtraction (and positive and negative numbers) are equivalent.
Read more about this topic: Differential Coding
Famous quotes containing the words conventional and/or differential:
“One of the reasons, surely, why women have been credited with less perfect veracity than men is that the burden of conventional falsehood falls chiefly on them.”
—Katharine Fullerton Gerould (1879–1944)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)