Space-Time Convolutional Codes over Finite Fields and Rings for Systems with Large Diversity Order

We propose a convolutional encoder over the finite ring of integers modulo pk ,Zpk , where p is a prime number and k is any positive integer, to generate a space-time convolutional code (STCC). Under this structure, we prove three properties related to the generator matrix of the convolutional code that can be used to simplify the code search procedure for STCCs over Zpk . Some STCCs of large diversity order (≥4) designed under the trace criterion for n = 2, 3, and 4 transmit antennas are presented for various PSK signal constellations.