Finite alphabet iterative decoders-Part I: Decoding beyond belief propagation on the binary symmetric channel

Shiva Kumar Planjery, David Declercq, Ludovic Danjean, Bane Vasic

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the proposed finite alphabet iterative decoders (FAIDs) do not propagate quantized probabilities or log-likelihoods and the variable node update functions do not mimic the BP decoder. Rather, the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code, thereby rendering these decoders capable of outperforming the BP in the error floor region. On certain column-weight-three codes of practical interest, we show that there exist {FAIDs that surpass the floating-point BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages}. Hence, FAIDs are able to achieve a superior performance at much lower complexity. We also provide a methodology for the selection of FAIDs that is not code-specific, but gives a set of candidate FAIDs containing potentially good decoders in the error floor region for any column-weight-three code. We validate the code generality of our methodology by providing particularly good three-bit precision FAIDs for a variety of codes with different rates and lengths.

Original languageEnglish (US)
Article number6600695
Pages (from-to)4033-4045
Number of pages13
JournalIEEE Transactions on Communications
Issue number10
StatePublished - Oct 2013


  • Low-density parity-check codes
  • belief propagation
  • binary symmetric channel
  • error floor
  • finite precision iterative decoding
  • trapping sets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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