Jump to content

Group code

From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by Matthiaspaul (talk | contribs) at 00:45, 1 May 2017 (Further reading: improved ref). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In computer science, group codes are a type of code. Group codes consist of linear block codes which are subgroups of , where is a finite abelian group.

A systematic group code is a code over of order defined by homomorphisms which determine the parity check bits. The remaining bits are the information bits themselves.

Construction

Group codes can be constructed by special generator matrices which resemble generator matrices of linear block codes except that the elements of those matrices are endomorphisms of the group instead of symbols from the code's alphabet. For example, consider the generator matrix

The elements of this matrix are matrices which are endomorphisms. In this scenario, each codeword can be represented as where are the generators of .

See also

References

Further reading

  • Watkinson, John (1990). "3.4. Group codes". Coding for Digital Recording. Stoneham, MA, USA: Focal Press. pp. 51–61. ISBN 0-240-51293-6. ISBN 978-0-240-51293-8.
  • Biglieri, Ezio; Elia, Michele (1993-01-17). "Construction of Linear Block Codes Over Groups". Proceedings. IEEE International Symposium on Information Theory (ISIT). p. 360. doi:10.1109/ISIT.1993.748676. ISBN 0-7803-0878-6.
  • Forney, G. David; Trott, Mitch D. (1993). "The dynamics of group codes: State spaces, trellis diagrams and canonical encoders". IEEE Transactions on Information Theory. 39: 1491–1593. doi:10.1109/18.259635.
  • Vazirani, Vijay Virkumar; Saran, Huzur; Rajan, B. Sundar (1996). "An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups". IEEE Transactions on Information Theory. 42 (6): 1839–1854. doi:10.1109/18.556679.
  • Zain, Adnan Abdulla; Rajan, B. Sundar (1996). "Dual codes of Systematic Group Codes over Abelian Groups". Applicable Algebra in Engineering, Communication and Computing (AAECC). 8 (1): 71–83.