Iterative turbo decoder analysis based on Gaussian density evolution

We model the density of extrinsic information in iterative turbo decoders by Gaussian density functions. This model is verified by experimental measurements. We consider evolution of these density functions through the iterative turbo decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes are analyzed based on this method. We define a “noise figure” for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded below 0 dB. Many mysteries of turbo codes can be explained based on this analysis. For example we can explain why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are explained based on this analysis