Study On Application Of Low Density Parity Check Codes Over Fading Channel

Low density parity check code (LDPC) is a kind of capacity approaching codes.It has linear complexity of iterative decoding based on graph models and arouses muchinterest in the coding community. Study on combining LDPC codes with other tech-nologies such as synchronization and equalization is important for raising spectrumefficiency and channel capacity of the system. Based on the previous related researchachievements, the dissertation will focus on application of LDPC codes in frame syn-chronization and SC-FDE system.First, we present detailed analysis of blind synchronization performance of LD-PC coded system based on hard constraints. Previous estimation relied on numericalsimulation and used coarse model based on discrete pdf computation. It is far awayfrom the simulation results for codes having large column weight. We deduce the the-oretical value of FSER by using gaussian approximation of continuous pdf. We showthat FSER only depends on the row and column weight distribution of the code. Simu-lation results verify the good prediction of the theoretical estimation. We proved that:irregular LDPC codes have better synchronization performance than regular codeswith the same rate, length and row weight; synchronization based on multiple shortframes is better than that based on one long frame;the error floor only depends on thedimensions of the parity check matrix and almost disappears with longer code. Pre-vious frame synchronization methods did not utilize the inner structure of QC-LDPCcodes, while we propose a fast algorithm which is efficient in reducing computationalcomplexity and it is suitable for both hard and soft synchronizers.Second, we present detailed analysis of blind synchronization performance ofLDPC coded system based on soft constraints. We prove that the improved Sun algo-rithm is equal to the simplified MAP algorithm proposed by Imad. We use the weight method to improve the Imad simplified algorithm at high SNR region without increas-ing any complexity. The estimation of FSER proposed by Imad is based on numericalsimulation and independence of the syndromes. It is far away from the simulation re-sults for codes having large column weight. We deduce the theoretical value of FSERby using gaussian approximation of continuous pdf for minimum decoding. It is closeto the simulation results at low SNR region and becomes a tight upper bound at highSNR region. It can be easily applied to the case of convolutional codes and fadingchannels. We use the theoretical FSER to compute the suitable thresold for thresholdbased synchronizer and estimate the FSER of hybrid synchronizer. Both of the twomethods can decrease the complexity of synchronization. We combine decoding withcorrelation to improve the synchronizer based on decoding. It shows much better per-formance for one iterative decoding. We propose a phase estimator based on minimumsquare distance which can be combined with the phase estimator based on high orderstatics. The method can eliminate uncorrect phase ambiguity. The π phased ambiguitycan be eliminated together with blind frame synchronization for some codes.Last, we applied LPDC codes in SC-FDE system. In contrast to the tractional re-moval of CP (Cyclic prefix) in frequency domain processing, we show that CP can becombined in non ISI (Inter symbol interference) channel to achieve more capacity andlower error rate and the SNR loss can also be compensated. Simulation results showthat more coding gain is achieved over fading channel than AWGN channel. For ISIchannels, we treat CP as part of the expanded parity check matrix which is transformedto improve the degree distribution of variable nodes and the cycle distribution of theTanner graph. Simulation result shows that TDE (Time domain equalizer) based onBCJR algorithm has better performance than linear FDE (Frequency domain equal-izer) over frequency selective channels. We propose two methods combining CP overimpulsive channels. One method uses EGC (Equal gain combining) and the otheruses LLR (Log likelihood addition). Simulations shows that the former method cannot improve the degrading by impulsive noise, while the latter one can achieve theperformance as well as the system with no CP.