Re: Can we correct 2t errors in a BCH code?

On Sun, 20 Jul 2008 20:43:55 -0700 (PDT), Broken Arrow
<moon.zia@xxxxxxxxx> wrote:

First, Turbo Codes and LDPCs work best when soft information is
available, i.e., a confidence level on each bit as to whether it is a
one or a zero. Your application may lend itself to this, since the
measurement of the biometric may not be binary for each bit that was
originally quantized. In other words, if the biomeasure is made on
a scale rather than a hard binary decision for each bit, using that
"soft" scaling will significantly improve the performance of many
decoders and enable the efficient use of Turbo Codes or LDPCs.

Unfortunately, no soft information is available. The iris template is
binary having no systematic correlation.

Bummer. That'll hurt for many codes as even convolutional codes do
better with soft input information.

Second, would it not be possible to make just the information part of
C the same length as W? Then XORing W and K (assuming C is a
systematic code) will produce P, then P plus the parity bits from C
are stored together (or would that give away too much information
about the key?)

Thats true. Storing P in clear will leak too much information.

Okay, that helps narrow it down.

That's a quite bad error rate to try to overcome. Usually "very bad"
error rates are in the 10e-2 region, and 10e-1 would be "extremely
awful". I think correcting an error rate of one in three with a
codeword of only 2047 bits is going to be a tough nut to crack.

We may be able to increase the template size to 2 times (4094 bits)
but 32% error correction will still be needed. Will it help?

Moon

Larger codeword sizes help since it increases "bit diversity" and the
size of the code space. How much it helps in this case is hard to
quantify.

Also, I liked Glen's suggestion that since it isn't necessary to
correct *all* the errors that some sneaky tricks might be applied.
Leveraging the correlations that you'd mentioned earlier is probably
useful as well. Personally I'm not aware of an existing system that
would be obvious to apply to the problem, but what you've described
helps narrow things down a bit.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
.

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