Binary weight distribution of non-binary LDPC codes
2009 (English)In: 2009 IEEE International Symposium on Information Theory, IEEE , 2009, 65-69 p.Conference paper (Refereed)
This paper is the first part of an investigation if the capacity of a binary-input memoryless symmetric channel under ML decoding can be achieved asymptotically by using non-binary LDPC codes. We consider (l.r)-regular LDPC codes both over finite fields and over the general linear group and compute their asymptotic binary weight distributions in the limit of large blocklength and of large alphabet size. A surprising fact, the average binary weight distributions that we obtain do not tend to the binomial one for values of normalized binary weights ω smaller than 1-2-l/r. However, it does not mean that non-binary codes do not achieve the capacity asymptotically, but rather that there exists some exponentially small fraction of codes in the ensemble, which contains an exponentially large number of codewords of poor weight. The justification of this fact is beyond the scope of this paper and will be given in .
Place, publisher, year, edition, pages
IEEE , 2009. 65-69 p.
, IEEE International Symposium on Information Theory - Proceedings, ISSN 2157-8102
Binary weight distribution, Error probability, Galois fields, General linear groups, LDPC codes, ML decoding
Other Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-153535DOI: 10.1109/ISIT.2009.5205662ISI: 000280141400014ScopusID: 2-s2.0-70449473657ISBN: 978-142444313-0OAI: oai:DiVA.org:kth-153535DiVA: diva2:754345
2009 IEEE International Symposium on Information Theory, ISIT 2009, 28 June 2009 through 3 July 2009, Seoul, South Korea
QC 201410102014-10-102014-10-062014-10-10Bibliographically approved