Evaluation of Gallager Codes for Short Block Length and High Rate
Applications
David J C MacKay and and Matthew C. Davey
Gallager codes with large block length and low rate (\eg,
N ~= 10,000-40,000, R ~= 0.25-0.5)
have been shown to have record-breaking performance
for low signal-to-noise applications.
In this paper we study Gallager codes
at the other end of the spectrum.
We first explore the theoretical properties
of binary Gallager codes
with very high rates and observe that Gallager codes of any rate offer
runlength-limiting properties
at no additional cost.
We then report the empirical performance
of high rate binary and non-binary Gallager codes on three channels:
the binary input Gaussian channel, the binary symmetric
channel, and the 16-ary symmetric channel.
We find that Gallager codes with rate
R=8/9 and block length N=1998 bits outperform
comparable BCH and Reed-Solomon codes (decoded by
a hard input decoder) by more than a decibel
on the Gaussian channel.
postscript (Cambridge UK).
postscript (Canada mirror).
Bibtex entry
@InCollection{MacKayHighRate98,
KEY ="",
AUTHOR ="D. J. C. MacKay and M. C. Davey",
TITLE ="Evaluation of {G}allager Codes for Short Block Length and High Rate
Applications",
booktitle = {Codes, Systems and Graphical Models},
volume={123},
series = {IMA Volumes in Mathematics and its Applications},
publisher = {Springer},
year = 2000,
pages={113-130},
editor = {B. Marcus and J. Rosenthal},
address = {New York},
url={http://www.inference.phy.cam.ac.uk/mackay/CodesRegular.html}
}
David MacKay's:
home page,
publications.
bibtex file.
Canadian mirrors:
home page,
publications.
bibtex file.