Reference : Tree expectation propagation for ml decoding of LDPC codes over the BEC
Scientific journals : Article
Engineering, computing & technology : Electrical & electronics engineering
Tree expectation propagation for ml decoding of LDPC codes over the BEC
Salamanca Mino, Luis mailto [University of Sevilla > Signal theory and communications]
Olmos, P. M. [University of Sevilla > Signal theory and communications]
Murillo-Fuentes, J. J. [University of Sevilla > Signal theory and communications]
Perez-Cruz, F. [Universidad Carlos III de Madrid > Signal theory and communications]
IEEE Transactions on Communications
[en] ML decoding ; LDPC codes ; tree-structured ex- pectation propagation ; graphical models ; binary erasure channel
[en] We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the bi- nary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.

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