An L-frequency trellis coding scheme designed for fading channels that provides diversity up to order L is described. L-frequency coding is advantageous over channel coding schemes that achieve implicit time-diversity through trellis coding in conjunction with time-interleaving because it requires negligible end-to-end delay. The authors derive an upper-bound for the probability of symbol error of the L-frequency code. Based on this upper-bound, they then deduce the design criteria for optimum L-frequency codes. A numerical approximation to this upper-bound and the design of a two-state and two four-state, two-frequency codes are presented. Through simulations, it was found that relative to the traditional dual frequency diversity approach, the two-state and four-state codes achieve 3- and 4-dB coding gains, respectively. This energy efficiency gain can be translated into a spectral efficiency gain. A brief discussion on the difference in code design techniques for the Gaussian channel and the fading channel is also presented.>