Outage Probability and Constrained Capacity of Moderate-Length Codes for Gaussian Mixture Over AWGN Channel

We study the outage probability and constrained capacity of moderate-length forward error correcting (FEC) codes for Gaussian mixture under additive white Gaussian noise (AWGN) channel. There is no closed form expression for the average mutual information between a discrete MPSK uniform random variable and a Gaussian mixture output. We use an approximation and a numerical integration of constrained capacity to estimate the average mutual information. Using constrained capacity, we estimate the mutual information rate, which is used to estimate the outage probability. The outage probability is the probability that the mutual information rate random variable is less than the code rate. The outage probability provides a theoretical benchmark for various code rates with moderate-length over AWGN channel. Computer simulation investigates the performance of Protected Tactical Waveform (PTW) using Second Generation Digital Video Broadcasting Satellite FEC with various code rates.