| Summary: | 碩士 === 國立清華大學 === 通訊工程研究所 === 106 === Low-density parity-check (LDPC) codes have been demonstrated to approach the Shannon-limit with iterative message-passing decoding and long code lengths. Quasi-cyclic LDPC (QC-LDPC) codes with algebraic structures have attracted great interest because they can be encoded, decoded, and analyzed efficiently. For QC-LDPC codes with unequal error protection (UEP) properties, the codeword bits are divided into several parts, and each part possesses a different error-correcting capability. The asymptotic performance of LDPC codes under belief propagation decoding is usually analyzed by using density evolution, and Gaussian approximation for message densities under density evolution can be used to simplify the analysis. However, conventional analysis methods cannot be directly applied to LDPC codes with UEP properties.
In this thesis, we propose methods to analyze the behavior of UEP QC-LDPC codes by specifying the structures of parity-check matrices. Formulas for detailed representations are derived using density evolution with Gaussian approximation. Furthermore, we calculate the decoding thresholds for different protection levels and analyze the decoding convergence behavior by using the proposed analysis tool.
Simulation results verify that the proposed methods can well predict the UEP capability for various codes.
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