|LDPC code design for cooperative communications
|Coding theory -- Mathematics.
Error-correcting codes (Information theory)
Hong Kong Polytechnic University -- Dissertations
|Department of Electronic and Information Engineering
|60 leaves : ill. ; 30 cm.
|The low-density parity-check code (LDPC) is one potential error correction code that can achieve the Shannon capacity with belief propagation (BP) decoding. In order to design a good LDPC code with low bit error rate (BER), two numerical methods called density evolution (DE) and Gaussian approximation (GA) are developed. These two methods are powerful in analyzing the performance of an LDPC code ensemble. Since they are effective in finding the threshold of an LDPC code ensemble with certain degree distribution, DE and GA are widely used in the optimization of the LDPC code. Besides, recent research of the relay channel system includes employing distributed LDPC codes on the relay channels. So we first review the relay system and focus on one coding scheme - the LDPC coded relay scheme. Compared to optimization of the LDPC code for a single link, the bilayer LDPC code optimization is more complex since the code should have good performance on two links at diferent signal-to-noise ratios (SNRs). In this thesis, we frst propose the stability condition (SC) method as a fast method to find the threshold of an LDPC ensemble. Then we propose to use a simple but efective optimization algorithm, called diferential evolution, combined with GA/DE/SC to optimize the LDPC code. As for the bilayer LDPC code, we derive the Gaussian approximation based on the bilayer density evolution. We also use the differential evolution to optimize the bilayer LDPC code. The results show that the optimized LDPC code and bilayer LDPC code have good performance with small gaps between their thresholds and the theoretical Shannon limit. Besides, it is proved that our method is effective and efficient.
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