page_title: Differential coding
section_title: Conventional differential coding
hierarchical_section_title: Differential coding / Conventional differential coding
caption_attribution_description: English: Differential coding decoder with sign
context_page_description: In digital communications, differential coding is a technique used to provide unambiguous signal reception when using some types of modulation. It makes data to be transmitted to depend not only on the current signal state, but also on the previous one.
  The common types of modulation that require differential coding include phase shift keying and quadrature amplitude modulation.
context_section_description: 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.
caption: A differential decoder
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