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Wed, 22 Aug 2007
LDPC codes.
Ok, I've completed hard-decision decoding algorithm,
with randomly generated matrix (if we are lucky) it can safely decode small
words with multiple bits errors - for example word of 16 bit with
3-bit weight of the random matrix it is possible to decode at leat two bits of
errors even if one of them is in transferred checksum itself.
Unfortunately random matrix generation for larger word sizes
does not work (at all). LDPC generation matrices must obey at least
one rule - it must be invertible. Number of 1's in each column depends on
number of 1's in each row, which is known as weight.
So, to correctly decode damaged message one needs
to have correct matrix, so I need to think about a good algorithm of
creating it. In the regular (simpler) case, matrix has
the same number of 1's in each row and column. The simplest case
is wrapping sequence of bits, like this matrix with weight 3:
1 1 1 0 0 0 0 0
0 1 1 1 0 0 0 0
0 0 1 1 1 0 0 0
0 0 0 1 1 1 0 0
0 0 0 0 1 1 1 0
0 0 0 0 0 1 1 1
1 0 0 0 0 0 1 1
1 1 0 0 0 0 0 1
And so on, I will check if it works good.
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