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

Leonid Geller, David Burshtein

Research output: Contribution to journalArticlepeer-review


We consider 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 achieve excellent results. However, computing the decoding threshold using density evolution is usually impractical, since one needs to propagate multi-dimensional probability distributions, and Monte Carlo simulations are required instead. By considering the evolution of the message Bhattacharyya parameter and the message expected value parameter, we derive a simple lower bound on the performance of the algorithm. This bound applies for both regular and irregular non-binary LDPC ensembles.

Original languageEnglish
Article number7429784
Pages (from-to)2639-2657
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2016


  • Low-density parity-check (LDPC) codes
  • belief propagation decoding
  • non-binary codes


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