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Block transmission systems with guard periods are used for high rate transmissions over wireless channels. Removing the guard periods would increase the throughput at the price of higher computational complexity. Here a method called overlapping is presented that retains the algebraic structure of the block processing stages while the insertion of guard periods can be omitted. The necessary computations of the overlapping method can be performed in the receiver. If they are transferred to the transmitter side, a new system with block wise pre-equalization and optional error correction in the receiver is obtained.