Error floor analysis of left-regular LDPC codes

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Error correcting codes (ECC) are an essential part of any communication system to ensure the reliability of communication at the presence of noise and interference. Iterative coding schemes including low-density parity-check (LDPC) codes are prime candidates for future generations of ECC. One of the main challenges for the application of LDPC codes in optical communications is the very low error rate requirement in such systems (in the oder of $10^{-15}$ to $10^{-17}$). Currently, in the absence of analytical results, evaluating a given code and reliably estimating its error floor at such low error rates would require months of Monte Carlo simulations even on the fastest computers. Hardware emulations would also take weeks to reach such error rates. There exist a variety of estimation techniques, mostly based on the theory of Importance Sampling, that can speed up the process of error floor estimation, but those techniques all rely on having reliable information about certain problematic structures in the code, referred to as trapping sets. Not surprisingly, attaining such information is in general a very hard problem. Threfore, even if one uses such techniques to estimate the error floor faster, there is no guarantee that the estimate is accurate. As a result, the common practice in the literature is to verify the accuracy of the estimates by Monte Carlo simulations. This defeats the whole purpose of devising estimation techniques that are faster than Monte Carlo simulations. In this project, the goal is to devise a fast technique that can reliably estimate the error floor of regular LDPC codes. Regular codes are of particular interest in optical communications as they are known to have lower error floors compared to their irregular counterparts. The proposed technique will allow our industrial partner, Infinera, to efficiently evaluate different LDPC code candidates currently considered for possible adoption in future optical systems. This will save Infinera a tremendous amount of time and computational resources. It also provides the company with an analytical tool for rigorous evaluation of LDPC codes in the error floor region, something that is currently missing in the industry.