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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

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  • $\begingroup$ It might help if you elaborate what your LPDC code is and what you mean by probability of error in an "AWGN" channel. It seems at the very least people can help you more if they know exactly what your code is, but also, someone really good on here might be able to help you with no background if you give them all the relevant references and definitions. $\endgroup$
    – user2566092
    Sep 16, 2015 at 18:14
  • $\begingroup$ @user2566092: sure, I'll add more details. $\endgroup$
    – Ali
    Sep 16, 2015 at 18:19
  • $\begingroup$ Good luck with this. My experience is limited here, because I only reached the ball park of $10^{-8}$ overnight with a sim running on my (this was in 2008) single processor laptop. That was good enough for comparisons, but not for verification down to $10^{-12}$. The buzzword Importance sampling was suggested to me to get things done faster. Alas, I did not have the time to study that, but the paper Santosh Emmadi refers to (+1) seems to be using the idea. $\endgroup$
    – Jyrki Lahtonen
    Sep 16, 2015 at 19:38
  • $\begingroup$ (cont'd) Luckily at that time Nokia and BBC were collaborating on a new DVB standard, and the English colleagues had built dedicated hardware to go deeper. We managed to get rid of some persistent error floors by partly redesigning the parity checks, and removing a number of smallish trapping sets. BTW $10^{-12}$ is absolutely needed for reliable delivery of an HD-TV service. Your code is surprisingly short. $\endgroup$
    – Jyrki Lahtonen
    Sep 16, 2015 at 19:41
  • $\begingroup$ @JyrkiLahtonen: Thanks for the information. This was work was not for DVB. $\endgroup$
    – Ali
    Sep 16, 2015 at 19:44

2 Answers 2

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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!

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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. $\endgroup$
    – daw
    Sep 16, 2015 at 19:45
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    $\begingroup$ The link I provided is from the archives, so the citation should be valid for much time. While I appreciate and agree, in some times, with your suggestion of expanding the answer, the paper may not be summarized in a short passage without explaining the concepts provided in it. More over, the paper is self sufficient and very long, so the interested and focused people will read it. $\endgroup$
    – Santosh Emmadi
    Sep 17, 2015 at 22:15
  • $\begingroup$ In general we have a tendency to be unhappy with link only answers, but I am certainly willing to make an exception in this case - at least for the time being. The reference is to a research paper - not to a Wikipage, PlanetMath or to somebody's course notes, and we should not expect anyone to be able to give a useful summary in under six pages. However, link rot may still happen, when the paper gets published. Therefore it would be desirable to give a link to a published version (when/if such a thing becomes available). $\endgroup$
    – Jyrki Lahtonen
    Sep 18, 2015 at 19:52
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A LDPC validation service is available here: http://www.avaliant.com/ldpc-validation-service/

One can simulate bit error rate and block error rate to very low error rates to ensure error floor free performance. The LDPC Validator has quick turnaround time because it was designed to seamlessly take advantage of a massively parallel General Purpose Graphics Processor (GPU) architecture. It has been validated using standard IEEE LDPC codes including 802.11ad and 802.16.

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