LDPC Convolutional Codes

  • Giovanni CancellieriEmail author
Part of the Signals and Communication Technology book series (SCT)


The best results on LDPC convolutional codes are summarized. Such results have been obtained, up to now, after proper transformations of good LDPC block codes. Unwrapping assures better performance with respect to that of the original parent block code. Irregular codes appear to be preferable. Modified H-extension offers good possibilities starting from BPG block codes. Nevertheless the parity check constraint length is extremely high. The direct design of LDPC convolutional codes with very short constraint length is outlined, starting from the case of code rate 1/2. A parity check matrix not in minimal form is typically employed, especially when the code is regular. Irregular codes allow to obtain good performance with shorter constraint lengths. The case of high-rate convolutional code is treated deriving their properties from those of 1/2-rate codes. Low-rate convolutional codes require a more involved treatment, since some vertical separations between 1-symbols in their syndrome former sub-matrix can be reused. The case of period length and number of information symbols per period not co-prime is analyzed. Some interesting 2/4-rate codes are presented. Regular and irregular codes are compared, fixing the code rate and minimum distance, in search for the minimum parity check constraint length. Hints for a direct design of LDPC convolutional codes with short constraint length are given. The concept of doubly convolutional codes is revisited.


Code Rate Block Code LDPC Code Parity Check Convolutional Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Baldi M, Bambozzi F, Chiaraluce F (2011) On a family of circulant matrices for quasi-cyclic low-density generator matrix codes. IEEE Trans Inf Th 57:6052–6067CrossRefMathSciNetGoogle Scholar
  2. Baldi M, Bianchi M, Cancellieri G, Chiaraluce F (2012) Progressive differences convolutional low-density parity check codes. IEEE Comm Lett 16:1848–1851CrossRefGoogle Scholar
  3. Baldi M, Cancellieri G, Chiaraluce F (2014) Array convolutional low-density parity-check codes. IEEE Comm Lett 18:336–339CrossRefGoogle Scholar
  4. Bates S, Elliot DC, Swamy R (2006) Termination sequence generation circuits for low-density parity-check convolutional codes. IEEE Trans Circ Syst 53:1909CrossRefGoogle Scholar
  5. Bocharova IE, Kudryashov BD, Satyukov RV (2009) Graph-based convolutional and block LDPC codes. Prob Inf Transm 45:357–377CrossRefzbMATHMathSciNetGoogle Scholar
  6. (ETSI EN 301 790) Digital Video Broadcasting (DVB) Interaction Channel for Satellite Distribution Systems, ETSI EN 301 790, 2009Google Scholar
  7. (ETSI TS 136 212) Evolved Universal Terrestrial Radio Access (E-UTRA), Multiplexing and Channel Coding, 2013Google Scholar
  8. Hu XY, Eleftheriou E, Arnold DM (2001) Progressive edge-growth tanner graphs. Proc IEEE Globecom 01, San Antonio (TX): 995–1001Google Scholar
  9. (IEEE 802.16e) IEEE Standard for Air Interface for Broadband Wireless Access Systems, 802.16e, 2012Google Scholar
  10. (IEEE 802.3an) IEEE Standard for Ethernet, 802.3an, 2012Google Scholar
  11. Jimenez-Felstrom AJ, Zigangirov KS (1999) Time-varying periodic convolutional codes with low density parity-check matrix. IEEE Trans Inf Th 45:2181–2191CrossRefMathSciNetGoogle Scholar
  12. Kamiya N (2007) High-rate quasi-cyclic low-density parity-check codes derived from finite affine planes. IEEE Trans Inf Th 53:1444–1459CrossRefMathSciNetGoogle Scholar
  13. Kishigami T, Murakami Y, Yoshii I (2009) LDPC-convolutional codes for E-MBS FEC, proposal to IEEE 802.16 broadband wireless access working group, for 802.16 m discussion and adoptionGoogle Scholar
  14. Pusane AE, Smarandache R, Vontobel O, Costello DJ (2011) Deriving good LDPC convolutional codes from LDPC block codes. IEEE Trans Inf Th 57:835–857CrossRefMathSciNetGoogle Scholar
  15. Smarandache R, Vontobel PO (2012) Quasi-cyclic LDPC codes: influence of proto- and Tanner graph structure on minimum Hamming distance upper bounds. IEEE Trans Inf Theory 58:585–607Google Scholar
  16. Tanner RM, Sridhara D, Sridharan A et al (2004) LDPC block and convolutional codes based on circulant matrices. IEEE Trans Inf Th 50:2966–2984CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Information EngineeringPolytechnic University of MarcheAnconaItaly

Personalised recommendations