在本論文中，我們專注在設計一組短碼長的同時為好的源編碼與通道編碼(SSC)。其主要目的是應用在Wyner-Ziv編碼當中可做為雲端網路或是分佈資訊編碼上。在魏的文獻中，提出了一組長碼長的SSC設計是基於低密度奇偶檢測碼(LDPC)作為源編碼與通道編碼，然而長碼長的設計會造成系統上過大的延遲所以並不適合在即時的應用上面。在短碼長的設計中，我們採用了一種奇偶檢查矩陣的設計可降低LDPC碼的Tanner圖內的短迴圈造成的錯誤底限(error-floor)的問題。而在相應的通道解碼演算法中，一個新的演算法稱為增強型信任傳遞(RBP)被提出，藉由在原始的信任傳遞演算法(BP)中加入一增強的項次可明顯的改善原始信任傳遞的解碼效能。在資訊源編碼演算法中，增強型信任傳遞在短碼長的設計上也是能有不錯的表現。其中我們也計算了在短碼長的區域中的理論表現的邊界，並藉由這個理論邊界與我們的模擬結果相比，得知我們所提出的LDPC碼設計在短碼長中可以為好的SSC。

In this thesis, we focus on designing a simultaneously good for source and channel coding (SSC) with short codeword length. The main application of SSC is the Wyner-Ziv coding, which is the key technique for cloud network and distributed source coding. In Wei e.t. a.l., a long length SSC code was proposed based on low-density parity-check code (LDPC) as the source and channel code. However, a long codeword length code design prohibits real-time applications due to the intolerable latency. Aim for the short codeword length regime, a new parity check matrix, which reduces the short circles of the Tanner graph of LDPC code, is adopted. For the corresponding channel decoding algorithm, a new algorithm called as reinforced belief propagation (RBP) is proposed. By adding a reinforced term in the celebrated BP algorithm, the RBP can improve the channel decoding performance of BP significantly. As for the source encoding algorithm, the RBP also performs well with short codeword length. We also calculate the theoretical performance bounds in short length regimes. Compared with these bounds, the proposed LDPC code can serve as a good SSC in short length regime.

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