摘要
低密度偶校區塊碼(Low-Density Parity-Check Block Codes) 已經被證實當運用疊代訊號傳遞解碼(Iterative Message Passing Decoding)以及配合極長的碼長時，會有接近Shannon bound的表現。不過，大部分都是用隨機建構的方法去設計低密度偶校區塊碼，而這樣得到的結果並沒有特殊的建構，導致我們在做編碼跟解碼時會有很大的複雜度，這是很大的缺點。
在最近的研究上，發明了有代數結構的各種碼，其中類訊環低密度偶校碼(Quasi-Cyclic Low-Density Parity-Check Codes)是一種佔有非常重要的地位的區塊碼。低密度偶校迴旋碼(Low-Density Parity-Check Convolutional Codes)本身是一種迴旋碼，它的特性是具有低密度的偶校矩陣。它也可以運用疊代訊號傳遞來解碼，所以其解碼複雜度跟低密度偶校碼相同。低密度偶校迴旋碼之編碼器和解碼器都可以有連續的輸出並且可以編碼成任意長度。我們可以用位移暫存器來做編碼，因為其編碼複雜度會相對的低很多。我們可以將其應用在相當多的地方，像是封包交換網路(packet-switching networks)等。
在此篇論文中，我們對類訊環低密度偶校碼和低密度偶校迴旋碼提出了新的建構方式，使得有此結構的碼會比前人所提出的碼具有比較大的最小距離(minimum distance)。此外對於某些特定的碼，我們可以給定特定的參數，以確保不會有長度6的循環，所以可確保我們的碼所包含的循環長度一定大於或等於8。
由模擬結果顯示，在高訊號雜訊比(signal-to-noise ratio)時，我們所提出的建構方式所得到的碼，會比前人所建構出來的碼有著比較好的表現。

Abstract
Low-density parity-check (LDPC) block codes have been shown to have near-capacity perfor-
mance with iterative message-passing decoding and su±ciently long block length. However,
most methods for designing LDPC block codes are based on random constructions; 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 developed, among
which quasi-cyclic LDPC (QC-LDPC) codes are an important class. LDPC convolutional
codes (LDPC-CCs) are convolutional codes in nature but with sparse parity-check matri-
ces. They can be encoded and decoded for arbitrary lengths of data with low complexity,
suitable for applications such as packet-switching networks. In this thesis, we develop new
constructions of QC-LDPC codes and LDPC-CCs with enlarged minimum distance. Simula-
tion results show that codes by our construction can have better performance than previous
codes at high signal-to-noise ratios.

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