In
digital communications
Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
, differential coding is a technique used to provide ''unambiguous'' signal reception when using some types of
modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
. It makes data to be transmitted to depend not only on the current signal state (or symbol), but also on the previous one.
The common types of modulation that require differential coding include
phase-shift keying
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a ...
and
quadrature amplitude modulation
Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signa ...
.
Purposes of differential coding
When data is transmitted over twisted-pair wires, it is easy to accidentally insert an extra half-twist in the cable between the transmitter and the receiver. When this happens, the received signal is inverted.
Similarly for
BPSK
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at ...
. To demodulate BPSK, one needs to make a local oscillator ''synchronous'' with the remote one. This is accomplished by a
carrier recovery A carrier recovery system is a circuit used to estimate and compensate for frequency and phase differences between a received signal's carrier wave and the receiver's local oscillator for the purpose of coherent demodulation.
In the transmitter ...
circuit. However, the integer part of the recovered carrier is ambiguous. There are ''n'' valid but not equivalent phase shifts between the two oscillators. For BPSK, ''n'' = 2; the symbols appear inverted or not.
Differential encoding prevents inversion of the signal and symbols, respectively, from affecting the data.
Assuming that
is a bit intended for transmission and
was the symbol just transmitted, then the symbol to be transmitted for
is
where
indicates
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that ta ...
or
modulo-2 addition. On the decoding side,
is recovered as
That is,
depends only on a difference between the symbols
and
and not on their values (inverted or not).
There are several different
line code
In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained c ...
s designed to be polarity insensitive
"Spread spectrum direct sequence"
by Daniel Kraus -- whether the data stream is inverted or not, the decoded data will always be correct.
The line code
In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained c ...
s with this property include differential Manchester encoding
Differential Manchester encoding (DM) is a line code in digital frequency modulation in which data and clock signals are combined to form a single two-level self-synchronizing data stream. In various specific applications, this method is also call ...
, bipolar encoding
In telecommunication, bipolar encoding is a type of return-to-zero (RZ) line code, where two nonzero values are used, so that the three values are +, −, and zero. Such a signal is called a duobinary signal. Standard bipolar encodings are designed ...
, NRZI, biphase mark code
Differential Manchester encoding (DM) is a line code in digital frequency modulation in which data and clock signals are combined to form a single two-level self- synchronizing data stream. In various specific applications, this method is also ca ...
, coded mark inversion frame, CMI line coding
In telecommunication, coded mark inversion (CMI) is a non-return-to-zero (NRZ) line code. It encodes ''zero'' bits as a half bit time of zero followed by a half bit time of one, and while ''one'' bits are encoded as a full b ...
, and MLT-3 encoding
MLT-3 encoding (Multi-Level Transmit) is a line code (a signaling method used in a telecommunication system for transmission purposes) that uses three voltage levels. An MLT-3 interface emits less electromagnetic interference and requires less band ...
. coding ''
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
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at ...
).
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 filter
In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, t ...
s.
A ''differential encoder'' is similar to an analog integrator
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Integration is an importan ...
. It has an impulse response
:
and a transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...
:
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.
Generalized differential coding
Using the relation is not the only way of carrying out differential encoding. More generally, it can be any function provided that an equation has one and only one solution for any and .
Applications
Differential coding is widely used in satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope ...
and radio relay
Radio stations that cannot communicate directly due to distance, terrain or other difficulties sometimes use an intermediate radio relay station to relay the signals. A radio relay receives weak signals and retransmits them, often in a different di ...
communications together with PSK and QAM
Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signa ...
modulations.
Drawbacks
Differential coding has one significant drawback: it leads to error multiplication. That is, if one symbol such as was received incorrectly, two incorrect symbols and would be at the differential decoder's output, see:
and . This approximately doubles the BER
''Ziziphus mauritiana'', also known as Indian jujube, Indian plum, Chinese date, Chinese apple, ber, and dunks is a tropical fruit tree species belonging to the family Rhamnaceae. It is often confused with the closely related jujube, Chinese j ...
at signal-to-noise ratios for which errors rarely occur in consecutive symbols.
Other techniques to resolve a phase ambiguity
Differential coding is not the only way to deal with a phase ambiguity. The other popular technique is to use ''syncword
In computer networks, a syncword, sync character, sync sequence or preamble is used to synchronize a data transmission by indicating the end of header information and the start of data. The syncword is a known sequence of data used to identif ...
s'' for this purpose. That is, if a ''frame synchronizer'' detects repeated inverted sync-words, it inverts the whole stream. This method is used in DVB-S.
See also
* Phase-shift keying
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a ...
* Satellite modem
A satellite modem or satmodem is a modem used to establish data transfers using a communications satellite as a relay. A satellite modem's main function is to transform an input bitstream to a radio signal and vice versa.
There are some devices t ...
External links and references
{{Reflist
* INTELSAT
Intelsat S.A. (formerly INTEL-SAT, INTELSAT, Intelsat) is a multinational satellite services provider with corporate headquarters in Luxembourg and administrative headquarters in Tysons Corner, Virginia, United States. Originally formed as In ...
Earth Station Standard IESS-308
* DVB
Digital Video Broadcasting (DVB) is a set of international open standards for digital television. DVB standards are maintained by the DVB Project, an international industry consortium, and are published by a Joint Technical Committee (JTC) o ...
framing structure, channel coding and modulation for 11/12 GHz satellite services (EN 300 421)
Data transmission