Design of low-density parity-check codes for modulation and detection

Stephan Ten Brink, Gerhard Kramer, Alexei Ashikhmin

Research output: Contribution to journalArticlepeer-review

950 Scopus citations


A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

Original languageEnglish
Pages (from-to)670-678
Number of pages9
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 2004
Externally publishedYes


  • Fading
  • Iterative decoding
  • Low-density parity-check (LDPC) codes
  • Multiple-input
  • Multiple-output (MIMO) detection
  • Mutual information


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