In digital data transmission,a considerable galn in power efficiency can be obtained at constant bandwidth by extending the signal space of the modulator and coding the data.Most of the codes presented so far,however,are not suitable for channels with demanding requirements on the carrier phase synchronisation.The phase detector of a synchronisation circuit cannot uniquely detect phase errors greater than half the symmetry angle of the signal space.Therefore,to achieve fast acquisition and reacquisition after synchronisation failures,the coding should be transparent to phase errors of a multiple of the symmetry angle of the signal space,similar to a differentially precoded transmission of e.g.QPSK signals.In this paper a method is presented to design codes with the desired properties.In particular codes for mPSK transmission with reasonable coding gain and complexity are discussed.
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