On Coset Leader Graphs of LDPC Codes

Eran Iceland, Alex Samorodnitsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Our main technical result is that, in the coset leader graph of a linear binary code of block length n , the metric balls spanned by constant-weight vectors grow exponentially slower than those in \{0,1\}^{n}. Following the approach of Friedman and Tillich, we use this fact to improve on the first linear programming bound on the rate of low-density parity check (LDPC) codes, as the function of their minimal relative distance. This improvement, combined with the techniques of Ben-Haim and Litsyn, improves the rate versus distance bounds for LDPC codes in a significant subrange of relative distances.

Original languageEnglish
Article number7114293
Pages (from-to)4158-4163
Number of pages6
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Hamming weight
  • Indexes
  • Linear codes
  • Measurement
  • Parity check codes
  • Probability
  • Upper bound


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