Effect of binary modulation codes with rate R= 1/N on equivalent discrete-time models for channels with intersymbol interference

For a data transmission system with intersymbol interference and noise in which signaling occurs by means of nonoverlapping rectangular pulses, a relation between the equivalent discrete-time models for uncoded and coded transmission is derived. It applies to binary modulation codes with rate R = 1 / N, where N is a positive integer. Examples suggest that these models are often affected by coding in a manner that is incompatible with a commonly adopted definition of coding gain.