Secrecy gain of trellis codes: The other side of the union bound

Secrecy gain has been proposed as a criterion to design wiretap lattice codes. Its analysis relies on the theta series of a lattice, which is closely related to the union bound on the decoding error probability. In this paper, theta series of trellis codes are computed by using a modified transfer function originally for the union bound. We find that the low SNR region of the union bound dominates the secrecy gain. Numerical results show that trellis codes can achieve a similar or higher secrecy gain with less complexity compared to unimodular lattice codes.