Multicarrier modulation via finite-field transforms

Multicarrier modulation has rapidly become common in both wireline and wireless high speed digital communications applications. However, the large dynamic range of a multicarrier signal causes problems at both the transmitter and the receiver. Here, finite-field mathematics are examined as a means of controlling the signal´s dynamic range. A framework for multicarrier modulation with finite-field transforms is constructed, and equivalence to certain maximum distance separable error-correcting codes is demonstrated. Implications on the assumed digital channel model caused by using finite-field mathematics in the transmitter and receiver are also discussed.