The objectives of the project are to study iterative decoding convergence and the dynamical structures near the fixed point of the belief propagation decoding of low-density parity-check codes. This will result in development of an effective method of error correcting code performance analysis based on the idea of instantons or most probable message distortions causing the decoding error. The motivation for the dynamics of iterations study comes from an observational fact: nonconvergence of the iterations and the consequent decoding error is because the iterations circle around the fixed point. In contrast to the currently available method, the newly developed instanton search method is applicable to the case of an infinite (or very large in practice) number of iterations in decoding.
During our everyday activities we send and receive a huge amount of information. In many situations it is important that the information is transmitted without the slightest error. To decrease the probability of the transmission error people for ages have introduced some redundancy in their messages, e.g. repeating the message several times or using a phonetic alphabet. Practically all modern electronic devices would not operate properly without that kind of error correction. Recently it was shown that a certain class of error correcting codes (low-density parity-check codes) is extremely effective in suppressing errors. These codes have a problem, though. We can not guarantee their good performance in applications that demand a very small probability of error, e.g. computer hard disk drives. A careful analysis of the problem source is needed before we can adopt this type of code in demanding industrial applications and enjoy the benefits these codes provide. In this project the investigator studies ways to achieve good performance of these codes in practical applications.
