Constellation shaping for pragmatic turbo-coded modulation with high spectral efficiency

Dan Raphaeli*, Assaf Gurevitz

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

94 Scopus citations


We propose a new turbo-encoding scheme for high spectral efficiency with performance close to the Gaussian channel capacity. The scheme combines nonuniform signaling on a Gaussian channel with pragmatic turbo-coded modulation (TCM) for simple and flexible implementation. A variable-rate turbo code is followed by a Huffmann code mapping onto nonequiprobable points in a quadrature amplitude modulation constellation. The rate of the turbo code is matched to the Huffmann code by variable puncturing, such that both the input bit rate and the output symbol rate are constant. It is shown that the new scheme provides shaping gains of 0.6 and 0.9 dB, at rates 2 and 3 b/dimension, respectively, compared with the equiprobable pragmatic TCM, and reach about 1 dB from the continuous input Gaussian channel capacity.

Original languageEnglish
Pages (from-to)341-345
Number of pages5
JournalIEEE Transactions on Communications
Issue number3
StatePublished - Mar 2004


  • High spectral efficiency modulation
  • Signal shaping
  • Turbo codes


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