Iterative turbo decoder analysis based on density evolution

摘要

We track the density of extrinsic information in iterative turbondecoders by actual density evolution, and also approximate it bynsymmetric Gaussian density functions. The approximate model is verifiednby experimental measurements. We view the evolution of these densitynfunctions through an iterative decoder as a nonlinear dynamical systemnwith feedback. Iterative decoding of turbo codes and of seriallynconcatenated codes is analyzed by examining whether a signal-to-noisenratio (SNR) for the extrinsic information keeps growing with iterations.nWe define a “noise figure” for the iterative decoder, suchnthat the turbo decoder will converge to the correct codeword if thennoise figure is bounded by a number below zero dB. By decomposing thencode's noise figure into individual curves of output SNR versus inputnSNR corresponding to the individual constituent codes, we gain many newninsights into the performance of the iterative decoder for differentnconstituents. Many mysteries of turbo codes are explained based on thisnanalysis. For example, we show why certain codes converge better withniterative decoding than more powerful codes which are only suitable fornmaximum likelihood decoding. The roles of systematic bits and ofnrecursive convolutional codes as constituents of turbo codes arencrystallized. The analysis is generalized to serial concatenations ofnmixtures of complementary outer and inner constituent codes. Designnexamples are given to optimize mixture codes to achieve low iterativendecoding thresholds on the signal-to-noise ratio of the channel