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New modulation formats are presented that increase the transmission rate over that of conventional systems, without degrading the bit error rate (BER) and with minimal bandwidth variation. A time-varying function called an "extra phase variation function" (EPVF) is added to the discrete phase of conventional modulation formats such as M-PSK and QAM to transmit additional data bits. A receiver configuration is presented that allows the decoding of information represented by the discrete and extra phases. It is shown that in an additive white Gaussian noise (AWGN) channel, the BER performance of the bits carried by the discrete phase and the extra phase in the modified format improves over the BER of conventional modulation formats.