Research On Trapping Sets Constrained Root-LDPC Codes For Block Fading Channels

With the continuous development of wireless mobile communication technology, people’s requirement of communication transmission technology with better reliability and validity is increasing. In real life, due to the effect of multipath propagation and mobility, the wireless channel often be abstracted into a slowly time varyng channel model-the block fading channel. The construction of full diversity Root-LDPC codes with better code performance for block fading channels is an attractive research hot spot recently.Based on the progressive edge-growth (PEG) algorithm, this thesis analyes some main factors that can affect the performance of Root-LDPC codes and introduces the graphical structure of trapping sets and related concepts in detail. Then we focus on analysing the effects of trapping sets for the error floor and the frame error rate (FER) of Root-LDPC codes. Numerous studies have shown that the elementary trapping sets are the trapping sets which is most hamful to the error correction performance of Root-LDPC codes. Among these ETS, those trapping sets which have small sizes are called dominant elementary trapping sets, and have more effect on the error floor performance of Root-LDPC codes. Well, it’s unlikely to find the check node which has degree larger than 2 in the Tanner graph of dominant elementary trapping sets, i.e. almost all of the dominant trapping sets of Root-LDPC code are elementary trapping sets.In order to solve this problem, this thesis presents a trapping sets constrained PEG algorithm for block fading channels to construct Root-LDPC codes. This algorithm combines an efficient elementary trapping sets (ETS) enlarging algorithm with the original PEG algorithm. At first, the proposed algorithm constructs the edges one column at a time by using PEG algorithm. Then elementary trapping sets (ETS) enlarging algorithm is applied to find the small dominant ETS in Tanner graph, and enlarge the ETS, which avoid the influence of dominant ETS on the coding performance. Simulation results demonstrate that codes generated by the proposed algorithm have lower error floor compared with codes constructed by the original and other modifications of the PEG algorithm. Meanwhile, with the decrease of code length, its FER performance also decreases. However, in the simulation process, we observe that the proposed algorithm is a kind of greedy algorithm. With the increasing of code length, the encoding/decoding complexity also increases. Quasi-Cyclic (QC) algorithm is a kind of structure construction algorithm which has lower encoding/decoding complexity. Therefore, based on the trapping sets constrained PEG algorithm, a modified algorithm which combines the proposed ETS-constrained PEG algorithm with QC algorithm is proposed in this thesis. Simulations show that the modified algorithm and the ETS-constrained PEG algorithm have the closed code performance, and they have lower error floor than the PEG algorithm and the other modified PEG algorithm. The proposed algorithm has shorter running time and achieves a tradeoff between the frame error rate performance and the encoding/decoding complexity.