- 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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