Error correcting codes have been used in power limited digital communication systems to improve the system error probability performance. This performance improvement is obtained at the price of an expanded occupied bandwidth or a lower rate of information transmission. Integrated coding and modulation techniques allow an increased performance without this bandwitdt expansion. In this thesis, a digital computer simulation analysis of the performance of communication systems which incorporates Multi-h codes, a bandwidth efficient modulation, is carried out. The simulated system consider a band-limited non-linear channel perturbed by additive, white Gaussian noise. The simulation technique selected uses a base-band signal represented by it´s time domain samples equally spaced. The band limiting effect is obtained with Butterworth digital filters. The performance of codes with small number of states ( = < 16) and error probability range greater than 10 exp(-4) is analised. A computer program to calculate the normalized mínimum Euclidean distance, d min, of Multi-h codes was developped. The distance d min is used to establish an upper bound on the bit error probability for transmission over additive, white Gaussian noise channels. Codes with larger dmin have a better performance, been dmin, thus, an indication of good codes. A program developped to calculate power spectrum density of Multi-h codes is also presented. To reduce decoder complexity the number of trellis states should be small. By properly selecting a set of modulation indices codes with good performance, reduced complexity and small spectral occupation is obtained. A restriction on the set of indices to get a reduce complexity decoder is to have indices d which are integer ratios nk/q. Other related aspects are discussed in this work. In particular, a condition to get a number of trellis state equal to q is proposed. A discussion on the structed of the trellis is also presented.