Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Information Theory

arXiv:0904.0768 (cs)
[Submitted on 5 Apr 2009 (v1), last revised 15 May 2009 (this version, v2)]

Title:Codes on Planar Graphs

Authors:Srimathy Srinivasan, Andrew Thangaraj
View PDF
Abstract: Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several intriguing problems in the intersection of coding theory and graph theory. In this paper, we study codes defined by planar Tanner graphs. We derive an upper bound on minimum distance $d$ of such codes as a function of the code rate $R$ for $R \ge 5/8$. The bound is given by $$d\le \lceil \frac{7-8R}{2(2R-1)} \rceil + 3\le 7.$$ Among the interesting conclusions of this result are the following: (1) planar graphs do not support asymptotically good codes, and (2) finite-length, high-rate codes on graphs with high minimum distance will necessarily be non-planar.
Comments: several improvements in presentation; more figures for illustration
Subjects: Information Theory (cs.IT)
Cite as: arXiv:0904.0768 [cs.IT]
  (or arXiv:0904.0768v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.0904.0768

Submission history

From: Andrew Thangaraj [view email]
[v1] Sun, 5 Apr 2009 12:43:37 UTC (97 KB)
[v2] Fri, 15 May 2009 06:42:29 UTC (155 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.IT
< prev   |   next >
new | recent | 2009-04
Change to browse by:
cs
math
math.IT

References & Citations

DBLP - CS Bibliography

listing | bibtex
Srimathy Srinivasan
Andrew Thangaraj
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)