On robust stability of the belief propagation algorithm for LDPC decoding

Title: On robust stability of the belief propagation algorithm for LDPC decoding
Creator: Rüffer, Björn S.; Dower, Peter M.; Kellett, Christopher M.; Weller, Steven R.
Relation: 19th International Symposium on Mathematical Theory Networks Systems (MTNS 2010). MTNS 2010: 19th International Symposium on Mathematical Theory Networks Systems. Proceedings (Budapest, Hungary 5-9 July, 2010)
Relation: http://www.conferences.hu/mtns2010
Publisher: MTNS
Resource Type: conference paper
Date: 2010
Description: The exact nonlinear loop gain of the belief propagation algorithm (BPA) in its log-likelihood ratio (LLR) formulation is computed. The nonlinear gains for regular lowdensity parity-check (LDPC) error correcting codes can be computed exactly using a simple formula. It is shown that in some neighborhood of the origin this gain is actually much smaller than the identity. Using a small-gain argument, this implies that the BPA is in fact locally input-to-state stable and produces bounded outputs for small-in-norm input LLR vectors. In a larger domain the algorithm produces at least bounded trajectories. Further it is shown that, as the block length increases, these regions exponentially shrink.
Subject: iterative decoding; LDPC codes; dynamical system; convergence; belief propagation; small-gain theorem
Identifier: http://hdl.handle.net/1959.13/935878
Identifier: uon:12156
Identifier: ISBN:9789633113707
Language: eng

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