This paper investigates the performance of trellis coding when it is applied to a spread-spectrum multiple-access system. A system model is proposed that allows one to apply both trellis coding and a PN spreading sequence to the data symbols to be transmitted. Rate n/n + 1, trellis codes employing 2n+ 1 point MPSK signal constellations are investigated when Gold sequences are employed for purposes of PN spreading. Performance in an additive white Gaussian noise (AWGN) channel is investigated, with 5-20 users transmitting simultaneously. Using criteria of equal complexity and throughput, the performance of the trellis codes in a SSMA environment is compared to that of medium to low rate convolutional codes through the use of a generalized transfer function bound. The average degradation due to the interuser interference is determined by employing the method of moments. The validity of approximating the interuser interference as a Gaussian random variable is also investigated. The numerical results illustrate that for a given complexity, chip rate and throughput, that low rate convolutional codes provide the best performance in a SSMA system. As lower rate convolutional codes are employed, there is an increase in the effective interuser interference due to the greater cross-correlation effects from using shorter PN sequences, or alternatively from the effects of partial cross-correlation. However, this increased degradation is more than overcome by the increased distance properties of the low rate codes. The coding gains for the codes that were considered range from 1-6 dB (depending on the type and complexity of the code) over the corresponding uncoded performances of SSMA in an AWGN channel.

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Journal IEEE Journal on Selected Areas in Communications
Boudreau, G.D. (Gary D.), Falconer, D.D, & Mahmoud, S.A. (Samy A.). (1990). A Comparison of Trellis Coded Versus Convolutionally Coded Spread-Spectrum Multiple-Access Systems. IEEE Journal on Selected Areas in Communications, 8(4), 628–640. doi:10.1109/49.54459