Trellis precoding for channels with spectral nulls

Trellis-enhanced precoding for trellis-coded transmission over ISI channels allows coding and shaping gains to be achieved with minimal transmit power penalty for arbitrary signal constellations, provided the ISI channels are linearly invertible. If the channel exhibits spectral nulls, infinite error propagation can occur within the inverse precoder. We assume ISI channels with spectral nulls and possibly a rational transfer function. First, we investigate methods to stop error propagation in the inverse precoder. This is accomplished by exploiting knowledge about the signal region to which the transmit signal, which needs to be recovered in the inverse precoder, must be confined. Then, we consider combining the concept of feedback trellis encoding with Tomlinson-Harashima (1971, 1972) precoding, whereby error propagation is completely prevented, but only certain signal constellations are allowed. We demonstrate the effectiveness of the proposed methods for dual-duplex baseband data transmission at 100 Mbit/s over unshielded telephone-grade twisted-pair cables in office building environments