Kola codes: A constructive technique for trellis codes with large d _free

We present a novel method for constructing trellis codes, based on recursive nonlinear equations. Using this method, trellis codes having good code rates (A = k/n) can be constructed. At the same time, the method allows the code-designer to construct a trellis with a large free distance, d _free, at the cost of a larger number of states in the trellis. It has been shown in this paper that for the code rate, R, less than a critical rate, R_c, the free distance can be made as large as desired for large n. This design methodology provides the freedom to play with the code performance and the code rate of the trellis code. Using this method, a rate 3/4 trellis code has been constructed with d_free = 12.