EXIT chart analysis and performance of precoded turbo equalisation systems for long block lengths

The authors investigate the effect that the precoders´ weights have on the convergence of turbo equalisation systems for long block lengths. A comparison is made between the trellis code capacities and the independent and identically distributed channel capacity. The extrinsic information transfer chart is used to analyse four precoded turbo equalisation systems. It is observed that the gradient of the transfer function at high input mutual information values, relating to the maximum a posteriori equalisation of a precoded channel, plays a greater role than the initial loss of information in determining the convergence of precoded turbo equalisation systems. Simulation results demonstrate that a low weight precoder converges at a lower signal-to-noise ratio in comparison to a high weight precoder. Further, it is noticed that the system trajectories only follow the bounds of the transfer functions on the extrinsic information transfer chart during the early iterations. The Kolmogorov-Smirnov test is used to study probability density function shapes of the extrinsic log-likelihood ratios during the iterative equalisation/decoding process. The authors also show that the extrinsic information transfer chart can be used to compute the trellis code capacity of a precoded channel.