Iterative Decoding and Turbo Equalization: The Z-Crease Phenomenon

TL;DR

This paper models iterative decoding as a nonlinear dynamical system and uncovers a universal Z-crease phenomenon, revealing fluctuations in per-block errors during turbo decoding, and proposes a heuristic stopping criterion to improve performance.

Contribution

It introduces a nonlinear dynamical system model for iterative decoding, revealing the Z-crease phenomenon and proposing a heuristic stopping criterion to optimize decoding iterations.

Findings

Identification of the Z-crease phenomenon in iterative decoding.

Correlation of Z-crease with pseudo codewords and trapping sets.

Effective heuristic stopping criterion reduces iterations and controls errors.

Abstract

Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the iterative approach inevitably use the statistical and information-theoretical tools that bear ensemble-average flavors. This paper consider the per-block error rate performance, and analyzes it using nonlinear dynamical theory. By modeling the iterative processor as a nonlinear dynamical system, we report a universal "Z-crease phenomenon:" the zig-zag or up-and-down fluctuation -- rather than the monotonic decrease -- of the per-block errors, as the number of iteration increases. Using the turbo decoder as an example, we also report several interesting motion phenomenons which were not previously reported, and which appear to correspond well with the notion of "pseudo codewords" and "stopping/trapping sets." We further propose a heuristic stopping criterion to control Z-crease and identify the best iteration. Our stopping criterion is most useful for controlling the worst-case per-block errors, and helps to significantly reduce the average-iteration numbers.