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A Cross-Entropy Based Method to Analyse Iterative Decoding

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Iterative decoding provides a practical solution for the approaching of Shannon limit with acceptable complexity. By decoding in an iterative fashion, the decoding complexity is spread over time domain while the overall optimality is still approachable.

Ever since its successful application in turbo codes in 1993, people keep trying to discover the secrets behind iterative decoding. Till now, BER bounds, density evolution, EXIT chart, Gaussian approximation are several most famous methods that proves to be helpful for the analysis of the behavior of iterative decoders. However, restrictions like subject sequence must be Gaussian distributed, transmitted sequence must be known, applicable region is either BER floor or BER clip only, etc., greatly limit the applications of these methods.

In this talk, a new, universal method for the analysis of iterative decoding based on cross-entropy will be discussed. We prove that the maximum a posteriori probability (MAP) decoding algorithm minimizes the cross-entropy between the a priori and the extrinsic information subject to given coding constraints, and the error correcting ability of each step of decoding can be evaluated with this cross-entropy for a converging turbo decoder. Based on this proof, the analysis of turbo decoding on convergence rate, derivation of Eb/N0 convergence threshold, evaluation of error performance in “error floor” region, and design of asymmetric turbo codes are carried out. Unlike most conventional analysis methods which rely heavily on either Gaussian approximation of distribution of the a priori/extrinsic information or a full knowledge of source bits, or even both, the new method provides analysis in a totally blind fashion.

This talk is part of the Inference Group series.

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