低密度偶校碼 (Low-Density Parity-Check Codes) 已被證實當運用疊代訊號傳遞解碼 (Iterative Message Passing Decoding) 及配合極長的碼長時，會有接近薛農極限 (Shannon limit) 的表現。但大部分低密度偶校區塊碼是由隨機建構方式去設計，因其沒有特殊建構，導致在編碼與解碼時有很大的複雜度。因此在最近研究中發明了有代數結構的類循環低密度偶校碼 (Quasi-Cyclic Low-Density Parity-Check Codes)，這是一種編碼複雜度相對低很多的低密度偶校碼。我們可以將其應用在許多系統上，像是封包交換網路等。
在此論文中，我們首先對類循環低密度偶校碼提出了具有良好距離與循環特性的新建構方式，模擬結果顯示，在高訊號雜訊比時，透由我們提出的建構方式所得到的碼，會比前人建構出來的碼有較好的表現。第二部分，我們藉由屏蔽方法提出了新式非均等錯誤保護類循環低密度偶校碼的建構方式，這些建構出來的碼由模擬結果顯示具有非均等錯誤保護的效果存在，且效能會比傳統分時系統為佳。此外，這些建構方式可以因應不同應用而建構出具不同區塊長度及碼率的碼。最後，我們提出了由屏蔽方法去建造可變碼率的非均等錯誤保護類循環低密度偶校碼。藉由此結果可設計出具有合適長度與多樣碼率的非均等錯誤保護類循環低密度偶校碼給實際系統使用。模擬結果顯示這些建造出來的碼具有優異的錯誤保護能力。

Low-density parity-check (LDPC) block codes have been shown to have near-capacity perfor- mance with iterative message-passing decoding and sufficiently long block length. However, quite a number of methods for designing LDPC block codes are based on random construc- tions; the lack of structures leads to serious disadvantages of high complexity in encoding and decoding. Therefore, in recent researches, codes with algebraic structures have been devel- oped, among which quasi-cyclic LDPC (QC-LDPC) codes are an important class. They can be encoded and decoded with low complexity, suitable for many applications such as packet- switching networks. In this dissertation, we first develop new constructions of QC-LDPC codes with good distance and girth properties. Simulation results show that the constructed codes can have better error performance than previous codes at high signal-to-noise ratios.
Constructions of unequal error protection (UEP) QC-LDPC codes are also provided in this dissertation. A criterion for constructing UEP QC-LDPC codes via the masking technique is given, based on which explicit conditions on the base parity-check matrices and masking matrices are provided. Three specific constructions of UEP QC-LDPC codes are also presented. Furthermore, a sufficient condition to ensure strict UEP is developed. Simulation results show that the constructed UEP codes can indeed provide coded bits with different protection levels and perform better than traditional time-sharing schemes.
Finally constructions of variable-rate UEP QC-LDPC codes are developed. The criteria which guarantee that a higher-rate QC-LDPC code can be obtained by adding column-blocks to or removing row-blocks from the parity-check matrix of a given lower-rate QC-LDPC code are provided. Then the conditions on the base parity-check matrices and masking matrices are given. We also present specific constructions of variable-rate UEP QC-LDPC codes. Simulation results show that all the constructed codes can indeed provide coded bits with different error-correcting capabilities and have good error performance.

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