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Utilization of redundancy left in a channel coded sequence can improve channel decoding performance. Stronger improvement can usually be achieved with nonsystematic encoding. However, nonsystematic codes recently proposed for this problem are not robust to the statistical parameters governing a sequence and thus should not be used without prior knowledge of these parameters. In this work, decoders of nonsystematic quick-look-in turbo codes are adapted to extract and exploit redundancy left in coded data to improve channel decoding performance. Methods, based on universal compression and denoising, for extracting the governing statistical parameters for various source models are integrated into the channel decoder by also taking advantage of the code structure. Simulation results demonstrate significant performance gains over standard systematic codes that can be achieved with the new methods for a wide range of statistical models and governing parameters. In many cases, performance almost as good as that with perfect knowledge of the governing parameters is achievable.