Bounds on the Belief Propagation Threshold of Non-Binary LDPC Codes


We have a tendency to think about low-density parity-check (LDPC) code ensembles over non-binary Galois fields when used for transmission over arbitrary discrete memoryless channels. Belief propagation decoding for these codes has been shown to realize excellent results. But, computing the decoding threshold using density evolution is typically impractical, since one desires to propagate multi-dimensional likelihood distributions, and Monte Carlo simulations are required instead. By considering the evolution of the message Bhattacharyya parameter and the message expected price parameter, we have a tendency to derive a straightforward lower bound on the performance of the algorithm. This bound applies for both regular and irregular non-binary LDPC ensembles.

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