具有緊密自由距離範圍之低密度奇偶檢查迴旋碼

Abstract

由一具有短限制長度的迴旋編碼器串接額外處理器可建構出一具有長限制長度的籬柵碼．在西元1993年Hellstern提出一種具有延遲處理器及信號點對應器的籬柵碼架構，此編碼架構可建構出具有大自由距離的籬柵碼和獲得緊密的自由距離的界限． 在此篇論文裡面我們採用具有大自由距離的籬柵碼的架構建構出其低密度奇偶檢查迴旋碼(LDPC-CCs)．其中最主要的問題為所建構出之奇偶檢查矩陣，在解碼時的泰納圖中出現許多四個週期的循環．因此，我們提出兩種建構方式來解決四個週期的循環問題．第一種方式，我們利用增加額外的位元消除四個週期的循環問題．第二種方式，我們沿用原模圖(Protograph)的概念延展出更大的奇偶檢查矩陣，因而消除四個週期循環的問題．兩種方式都可採用並行解碼方式(Pipeline decoding)作為解碼器，模擬結果顯示出提出的方法比具有四個週期的循環在錯誤解碼的能力上有明顯的改進． 我們也提出另外兩種疊帶解碼演算法為了幫助增加額外位元的架構方式執行更有效的解碼．第一種疊帶解碼演算法，其疊帶的迴圈是介於具有短限制長度的迴旋編碼器及信號對應器之間;第二種疊帶解碼演算法，是一種二個步驟的疊帶演算法方式，第一個步驟我們採用第一種提出的疊帶解碼演算法，先求出額外位元的軟式資料然後再與接收訊號一起送至並行解碼器做第二個步驟的解碼動作．

A trellis code, which is constructed by using the encoder of a basic convolutional code with a short constraint length followed by a delay processor and a signal mapper, is equivalent to a trellis code with a large constraint length. In addition, for such a code, tight lower and upper bounds on the free distance can be obtained. In this thesis, we use this code structure to construct low density parity check convolutional codes (LDPC-CCs). The undesired 4-cycles that exist in the Tanner graph for the proposed LDPC convolutional codes are as a result of the inherited properties of the code structure. To remove these undesired cycles, two unique schemes are employed. For the first scheme, denoted as auxiliary-nodes construction (ANC), we employ additional auxiliary nodes to remove 4-cycles. For the second, denoted as the protograph based construction (PGC), we use the concept of protograph to obtain a derived code which extends the size of parity-check matrix so as to increase the girth. Both schemes can be efficiently decoded by the iterative message-passing algorithm which is also called the pipeline decoder. Simulation results show that the newly constructed codes can obtain satisfactory error performances as compared to code that has 4-cycles. We also propose two additional iterative decoding algorithms, denoted as IDEC 1 and IDEC 2 respectively for the ANC construction. For IDEC 1, a loop of the iteration between the trellis of the basic convolutional code and the signal mapper is employed. For IDEC 2, a two-stage decoding is employed, where in the first stage IDEC 1 is implemented, and the derived soft information for auxiliary nodes is sent to the pipeline decoder of the ANC to enable the second-stage decoding to be performed.