Rayleigh Fading BER Analysis Task Constraints:

1) Implement `DeepFadeSampler` class that inherits from `SamplerBase`.
2) Implement `simulate_variance_controlled()` method with the required signature.
3) The method must return a tuple or dict with: (errors_log, weights_log, err_ratio, total_samples, actual_std, converged).
4) Use importance sampling to bias channel gain distribution toward deep fade events.
5) The solution should estimate average BER accurately and efficiently under Rayleigh fading.

