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，區塊碼有在編碼及解碼的複雜度過高的缺點。
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迴旋碼相同。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。
目前的文獻所提出的低密度偶繳迴旋碼之建構方式十分的有限，主要都是運用類訊環低密度偶校碼(Quasi-Cyclic Low-Density Parity-Check Codes)來建造。但是，在之前所提出的這種代數建構方式中，有可能會建造出含有長度6的循環的碼。所以在這篇論文中，我們將提出推廣的建構方式並且確保這種建構方式所造出來的碼，一定不會有長度4的循環。在我們所提出的建構方式中，我們運用循環的條件，找出了確保不會有長度6的循環的建構方式。
模擬結果顯示我們所提出的建構方式可以造出表現和過去建構方式一樣好的碼。然而，在過去的建構方式中，必須要運用電腦模擬來找參數，以確保不會含有長度6的循環。我們所提出的建構方式可確保我們的碼所包含的循環長度一定大於或等於8。

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,
block codes have the disadvantages in the respect of encoding and decoding complexity.
LDPC convolutional codes (LDPC-CCs) are convolutional codes with sparse parity check
matrices. They can encode and decode arbitrary lengths of data and can be encoded using
shift registers with small complexity. Previous algebraic constructions of LDPC-CCs are all
based on their quasi-cyclic LDPC (QC-LDPC) block code counterparts. However, codes of
girth 6 may be obtained by previous methods. Therefore, in this thesis, we develop a general-
ized construction of LDPC-CCs and girth of the constructed codes is at least 6. Within this
set of codes, we propose constructions for LDPC-CCs of girth at least 8. Simulation results
show that codes of girth 8 by our construction have performance similar to codes constructed
by the previous method. However, computer search is needed for ‾nding codes of girth 8
in previous constructions, while the codes obtained by our constructions are guaranteed to
have a girth at least 8.
i

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