Distance properties of trellis codes are of great importance for performance evaluation. In this paper, we use random coding analysis to study the average distance structures of trellis codes. The generating function enumerating the average number of error events of each distances is fully determined in the ensemble of time-varying trellis codes. The results obtained can be used to predict the growth rate of the number of error events at large distance and hence determine the signal-to-noise range in which the transfer function bound for error performance is convergent. Other applications of the average distance structure include a Gilbert-type lower bound on minimum distance.

In this paper, we propose a robust parameters estimation algorithm for channel coded systems based on the low-density parity-check (LDPC) code over fading channels with impulse noise. The estimated parameters are then used to generate bit log-likelihood ratios (LLRs) for a soft-inputLDPC decoder. The expectation-maximization (EM) algorithm is used to estimate the parameters, including the channel gain and the parameters of the Bernoulli-Gaussian (B-G) impulse noise model. The parameters can be estimated accurately and the average number of iterations of the proposed algorithm is acceptable. Simulation results show that over a wide range of impulse noise power, the proposed algorithm approaches the optimal performance under different Rician channel factors and even under Middleton class-A (M-CA) impulse noise models.