[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/differential-coding-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/differential-coding-wikipedia\/","headline":"Differential coding – Wikipedia","name":"Differential coding – Wikipedia","description":"before-content-x4 In digital communications, differential coding is a technique used to provide unambiguous signal reception when using some types of","datePublished":"2022-12-27","dateModified":"2022-12-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e87000dd6142b81d041896a30fe58f0c3acb2158","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e87000dd6142b81d041896a30fe58f0c3acb2158","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/en\/differential-coding-wikipedia\/","wordCount":4238,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4In 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 (or symbol), but also on the previous one.       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4The common types of modulation that require differential coding include phase-shift keying and quadrature amplitude modulation.Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Purposes of differential coding[edit]Conventional differential coding[edit]Generalized differential coding[edit]Applications[edit]Drawbacks[edit]Other techniques to resolve a phase ambiguity[edit]See also[edit]External links and references[edit]Purposes of differential coding[edit]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. To demodulate BPSK, one needs to make a local oscillator synchronous with the remote one. This is accomplished by a carrier recovery 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        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4xi{displaystyle x_{i}} is a bit intended for transmission and yi\u22121{displaystyle y_{i-1}} was the symbol just transmitted, then the symbol to be transmitted for xi{displaystyle x_{i}} isyi=yi\u22121\u2295xi,{displaystyle y_{i}=y_{i-1}oplus x_{i},}(1)where \u2295{displaystyle oplus {}} indicates binary or modulo-2 addition. On the decoding side, xi{displaystyle x_{i}} is recovered asxi=yi\u2295yi\u22121.{displaystyle x_{i}=y_{i}oplus y_{i-1}.}(2)That is, xi{displaystyle x_{i}} depends only on a difference between the symbols yi{displaystyle y_{i}} and yi\u22121{displaystyle y_{i-1}} and not on their values (inverted or not).There are several different line codes designed to be polarity insensitive[1] — whether the data stream is inverted or not, the decoded data will always be correct.The line codes with this property include differential Manchester encoding, bipolar encoding, NRZI, biphase mark code, coded mark inversion, and MLT-3 encoding. coding Conventional differential coding[edit]    A method illustrated above can deal with a data stream inversion (it is called 180\u00b0 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\u00b0 ambiguity only, bits are used as these symbols. When dealing with 90\u00b0 ambiguity, pairs of bits are used, and triplets of bits are used to resolve 45\u00b0 ambiguity (e.g. in 8PSK).A differential encoder provides the (1) operation, a differential decoder – the (2) 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 responseh(k)={1,if\u00a0k\u226500,if\u00a0k1.{displaystyle H(z)={frac {1}{1-z^{-1}}}.}A differential decoder is thus similar to an analog differentiator, its impulse response beingh(k)={1,if\u00a0k=0\u22121,if\u00a0k=10,otherwise{displaystyle h(k)={begin{cases}1,&{mbox{if }}k=0\\-1,&{mbox{if }}k=1\\0,&{mbox{otherwise}}end{cases}}}and its transfer functionH(z)=1\u2212z\u22121.{displaystyle H(z)=1-z^{-1}.}Note that in binary (modulo-2) arithmetic, addition and subtraction (and positive and negative numbers) are equivalent.Generalized differential coding[edit]Using the relation yi\u22121\u2295xi=yi{displaystyle y_{i-1}oplus x_{i}=y_{i}} is not the only way of carrying out differential encoding. More generally, it can be any function u=F(y,x){displaystyle u=F(y,x)} provided that an equation u0=F(y0,x){displaystyle u_{0}=F(y_{0},x)} has one and only one solution for any y0{displaystyle y_{0}} and u0{displaystyle u_{0}}.Applications[edit]Differential coding is widely used in satellite and radio relay communications together with PSK and QAM modulations.Drawbacks[edit]Differential coding has one significant drawback: it leads to error multiplication. That is, if one symbol such as yi{displaystyle y_{i}} was received incorrectly, two incorrect symbols xi{displaystyle x_{i}} and xi+1{displaystyle x_{i+1}} would be at the differential decoder’s output, see:xi=yi\u2295yi\u22121{displaystyle x_{i}=y_{i}oplus y_{i-1}} and xi+1=yi+1\u2295yi{displaystyle x_{i+1}=y_{i+1}oplus y_{i}}. This approximately doubles the BER at signal-to-noise ratios for which errors rarely occur in consecutive symbols.Other techniques to resolve a phase ambiguity[edit]Differential coding is not the only way to deal with a phase ambiguity. The other popular technique is to use syncwords 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[edit]External links and references[edit]INTELSAT Earth Station Standard IESS-308DVB framing structure, channel coding and modulation for 11\/12\u00a0GHz satellite services (EN 300 421)     (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/differential-coding-wikipedia\/#breadcrumbitem","name":"Differential coding – Wikipedia"}}]}]