Decoding turbo codes based on their parity-check matrices

Fan Jiang, Eric Psota, Lance C. Pérez

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


The turbo iterative decoding algorithm only performs well for turbo codes with relatively small memories. Moreover, its decoding complexity becomes prohibitively large when the turbo encoders have very large memories. The sumproduct and linear programming decoding algorithms are based on the parity-check matrices of the codes. They are widely used to decode low-density parity-check codes. These algorithms do not suffer the limitations of the turbo iterative decoding algorithm. In order to apply them to the turbo codes, the parity-check matrices of turbo codes must be found. By treating turbo codes as serially concatenated codes, the generator and paritycheck matrices of the turbo codes are derived in this paper. Turbo codes with low-density parity-check matrices are then designed based on the derived results. Provided these matrices, turbo codes are decoded using the sum-product algorithms. Preliminary results show that the sum-product decoding of turbo codes performs slightly worse than sum-product decoding of conventional low-density parity-check codes. However, since the encoding of turbo codes has less complexity than the straightforward encoding of low-density parity-check codes, this loss in performance may be justified by the drastically decreased encoding complexity. The availability of the parity-check matrices of turbo codes also makes them ready to be decoded by the linear programming decoding algorithm which is optimum for the given linear constraints.

Original languageEnglish (US)
Title of host publicationProceedings of the Thirty-Ninth Southeastern Symposium on System Theory, SSST
Number of pages4
StatePublished - 2007
Event2007 39th Southeastern Symposium on System Theory, SSST - Macon, GA, United States
Duration: Mar 4 2007Mar 6 2007

Publication series

NameProceedings of the Annual Southeastern Symposium on System Theory


Other2007 39th Southeastern Symposium on System Theory, SSST
Country/TerritoryUnited States
CityMacon, GA

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Mathematics


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