A method is described for modifying classical N-dimensional trellis codes to provide baseband codes that combine a spectral null at DC with significant coding gain. The information rate of the classical code is decreased by one bit, and this extra redundancy is used to keep the running digital sum bounded. Equivalently, if the rate is held constant, then twice as many signal points are needed, causing a power penalty of 6/N dB. Baseband trellis codes are presented for several information rates together with complete spectral plots and performance comparisons. A method of constructing baseband codes with multiple spectral nulls is also described.>

Calderbank, Heegard, and Ozarow [1] have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. These codes are designed to exploit intersymbol interference. The standard method is to minimize intersymbol interference by constraining the input to the channel using run-length limited sequences. Calderbank, Heegard, and Ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function(1 - D^{N}) /2, where the channel inputs are constrained to be\pm 1. This problem is considered here. Channel inputs are generated using a nontrivial coset of a binary convolutional code. The coset is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.