Iterative Decoding and Turbo Equalization: The Z-Crease Phenomenon

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.Comment: 6 page

Approximate MIMO Iterative Processing with Adjustable Complexity Requirements

Targeting always the best achievable bit error rate (BER) performance in iterative receivers operating over multiple-input multiple-output (MIMO) channels may result in significant waste of resources, especially when the achievable BER is orders of magnitude better than the target performance (e.g., under good channel conditions and at high signal-to-noise ratio (SNR)). In contrast to the typical iterative schemes, a practical iterative decoding framework that approximates the soft-information exchange is proposed which allows reduced complexity sphere and channel decoding, adjustable to the transmission conditions and the required bit error rate. With the proposed approximate soft information exchange the performance of the exact soft information can still be reached with significant complexity gains.Comment: The final version of this paper appears in IEEE Transactions on Vehicular Technolog

Low Complexity Belief Propagation Polar Code Decoders

Since its invention, polar code has received a lot of attention because of its capacity-achieving performance and low encoding and decoding complexity. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two of the most popular approaches for decoding polar codes. SCD is able to achieve good error-correcting performance and is less computationally expensive as compared to BPD. However SCDs suffer from long latency and low throughput due to the serial nature of the successive cancellation algorithm. BPD is parallel in nature and hence is more attractive for high throughput applications. However since it is iterative in nature, the required latency and energy dissipation increases linearly with the number of iterations. In this work, we borrow the idea of SCD and propose a novel scheme based on sub-factor-graph freezing to reduce the average number of computations as well as the average number of iterations required by BPD, which directly translates into lower latency and energy dissipation. Simulation results show that the proposed scheme has no performance degradation and achieves significant reduction in computation complexity over the existing methods.Comment: 6 page

Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200