Communication systems and methods in accordance with various embodiments of the invention utilize modulation on zeros. Carrier frequency offsets (CFO) can result in an unknown rotation of all zeros of a received signal's z-transform. Therefore, a binary MOCZ scheme (BMOCZ) can be utilized in which the modulated binary data is encoded using a cycling register code (e.g. CPC or ACPC), enabling receivers to determine cyclic shifts in the BMOCZ symbol resulting from a CFO. Receivers in accordance with several embodiments of the invention include decoders capable of decoding information bits from received discrete-time baseband signals by: estimating a timing offset for the received signal; determining a plurality of zeros of a z-transform of the received symbol; identifying zeros from. the plurality of zeros that encode received bits by correcting fractional rotations resulting from the CFO; and decoding information bits based upon the received bits using a cycling register code.