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Optimality and duality of the turbo decoder : Two optimality criteria which underlie the turbo decoder are reconciled within: Turbo-information processing: Algorithms, implementations & applications
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Optimality and duality of the turbo decoder : Two optimality criteria which underlie the turbo decoder are reconciled within: Turbo-information processing: Algorithms, implementations & applications

Phillip A Regalia and John MACLAREN WALSH
Proceedings of the IEEE, v 95(6), pp 1362-1377
2007
DOI: https://doi.org/10.1109/JPROC.2007.896495

Abstract

Coding, codes Exact sciences and technology Information, signal and communications theory Signal and communications theory Telecommunications and information theory Applied Sciences
The near-optimal performance of the turbo decoder has been a source of intrigue among communications engineers and information theorists, given its ad hoc origins that were seemingly disconnected from optimization theory. Naturally one would inquire whether the favorable performance might be explained by characterizing the turbo decoder via some optimization criterion or performance index. Recently, two such characterizations have surfaced. One draws from statistical mechanics and aims to minimize the Bethe approximation to a free energy measure. The other characterization involves constrained likelihood estimation, a setting perhaps more familiar to communications engineers. The intent of this paper is to assemble a tutorial overview of these recent developments, and more importantly to identify the formal mathematical duality between the two viewpoints. The paper includes tutorial background material on the information geometry tools used in analyzing the turbo decoder, and the analysis accommodates both the parallel concatenation and serial concatenation schemes in a common framework.

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