Prof. Dr.-Ing. Werner Henkel
April 4 – Sept 3, 2005
In this work, we have proposed a method to optimize the unequal error protection properties of LDPC Codes. We have shown that it is possible to adapt the two kinds of irregularities in order to speed up the local convergence. We first discussed the definition of UEP properties, and highlighted the fact that an LDPC code can have UEP properties if decoded by maximum-likelihood, but none if decoded by belief propagation. UEP properties must then be defined depending on the used decoding. We have adopted a detailed representation of LDPC codes allowing to describe subsets of possible interleavers that fit the UEP requirements, to define local convergence and to find a cost function. Since the irregularities of the bit node profile have already been studied, we especially focused on the check node profile optimization, keeping the bit node profile set regular. We found that the irregularities over check nodes does not only influence the speed of a local convergence, but also generates different behaviors at different parts of the codeword at high number of iterations, in contrast to irregularities over bit nodes; we tried to explain these two behaviors formally. This fact that UEP properties remain at high number of iterations is very interesting if we consider recent work in  which reduces the complexity of decoding, and then allows a higher number of iterations with the same resources. However, acting on check irregularities implied sub-optimality of the overall code in the case when the maximum degree of bit nodes is not adapted, and we then had to define a validity domain for our optimization, that then can be considered and achieved whether as a second stage in the optimization of the whole code, i.e. after bit nodes optimization, or as a first stage that would add a constraint on the following optimization. We would then have to keep all the parameters in the cost function, and optimize the check node profile in terms of the fixed bit nodes profile. On a practical point of view, we tried to optimize a so-called mother code by pruning, i.e. by making some bits deterministic, in order to construct a subcode, with lower code rate, that fulfills the UEP requirements, and that can be decoded by the same decoder as the mother code, or a better one according to the available memory of the receiver. Finally we tried to briefly analyze what the optimal puncturing of such UEP codes should be, still using the detailed representation of LDPC codes, in order to compensate the code rate loss due to pruning. Such an optimization provides flexibility in selecting the appropriate scheme from performance, computational-complexity and memory-requirements perspectives. As further tasks, testing the robustness to variations of proportions of classes should be useful considering practical applications of such codes. Another work would be to optimize both kinds of irregularities in a joint way, and not sequentially anymore, by properly describing the cost function, and still considering the required performance and the constraints of the target system. The difficulty of such an approach would lie in the non-linearity of the optimization.
[Thesis] Unequal Error Protection LDPC Codes