Some years back I designed a low-density parity-check (LDPC) code ($n=816, k=408$) and I was able to verify the performance of the code (probability of error in an AWGN channel) down to $10^{-10}$, using a multicore computer with a heavily optimized program running about 3 days. The code did not present any error floor.
Recently I was asked if I can validate the code even further (at least $10^{-12}$). One might be able to run the program at a high-performance computing center but I do not access to such a facility at the moment and I feel that I'd need a cluster of 100 or more computers running for few days, if not weeks.
It's been a while that I studied the subject, but are there analytical tools/methods so I can use for the purpose of this validation?
Thanks!
Some backgrounds and notes:
a regular binary parity check matrix $\mbox{H}_{408\times816}$ without girths of size 4 and 6 was constructed
the source bits from binary field $\mathbb{F}_2$ were mapped to $\left\{-1,+1\right\}$.
For an Additive White Gaussian Noise (AWGN) channel, the data received at each time is equal to the data sent plus Gaussian noise with zero-mean and some standard deviation, $s$, independently for each bit.
the Belief Propagation algorithm was used at the decoder
I have studied the same problem around a month ago. A really good method along with good citations of the literature in this area, is given in the following paper by Cole, et al. http://arxiv.org/pdf/cs/0605051v1.pdf
I hope it comes as a help to you.
Good luck!