Purposes of Differential Coding
To demodulate BPSK one needs to make a local oscillator synchronous with the remote one. This is accomplished by a carrier recovery circuit. However, a carrier can be recovered in different ways, depending upon a valid phases count (2 for BPSK).
For this coding, if a carrier is recovered incorrectly, the received data are inverted.
Assuming that is a bit intended for transmission, and is a bit actually transmitted (differentially encoded), if
is transmitted, then on the decoding side
can be reconstructed, where indicates binary or modulo-2 addition.
Now depends only on a difference between and and not on their values. So, whether the data stream is inverted or not, the decoded data will always be correct.
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 data are inverted. There are several different line codes designed to be polarity insensitive -- 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.
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