{'fraction_non_alphanumeric': 0.01824212271973466, 'fraction_numerical': 0.0, 'mean_word_length': 5.631868131868132, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the bit-error probability of differentially encoded QPSK and offset QPSK in the presence of carrier synchronization

We investigate the differences between allowable differential encoding strategies and their associated bit-error probability performances for quadrature phase-shift keying (QPSK) and offset QPSK modulations when the carrier demodulation reference signals are supplied by the optimum (motivated by maximum a posteriori estimation of carrier phase) carrier-tracking loop suitable for that modulation. In particular, we show that in the presence of carrier-synchronization phase ambiguity but an otherwise ideal loop, both the symbol and bit-error probabilities in the presence of differential encoding are identical for the two modulations. On the other hand, when in addition the phase error introduced by the loop's finite signal-to-noise ratio is taken into account, it is shown that the two differentially encoded modulations behave differently, and their performances are no longer equivalent. A similar statement has previously been demonstrated for the same modulations when the phase ambiguity was assumed to have been perfectly resolved by means other than differential encoding.