Maxwell Construction: The Hidden Bridge between Iterative and Maximum a Posteriori Decoding

Cyril Measson , Andrea Montanari (1, 2) , Ruediger Urbanke

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 Department of Electrical Engineering and Statistics

There is a fundamental relationship between belief propagation and maximum a posteriori decoding. A decoding algorithm, which we call the Maxwell decoder, is introduced and provides a constructive description of this relationship. Both, the algorithm itself and the analysis of the new decoder are reminiscent of the Maxwell construction in thermodynamics. This paper investigates in detail the case of transmission over the binary erasure channel, while the extension to general binary memoryless channels is discussed in a companion paper.

Domaines: Autre [cond-mat.other]

Cyril Measson, Andrea Montanari, Ruediger Urbanke. Maxwell Construction: The Hidden Bridge between Iterative and Maximum a Posteriori Decoding. 2005. ⟨hal-00290624⟩