A Method for Evaluating the Decoding Performance of LDPC Convolutional Codes and its Application to Code Constructions

低密度奇偶校验（LDPC）卷积码是由卷积码的稀疏奇偶校验矩阵构造的纠错码。用迭代算法对编码进行译码，显示出良好的译码性能。在本研究中，我们提出了一种有效的LDPC卷积码权谱低部分的计算方法。最小自由距离和权谱是评价LDPC卷积码误差性能的重要因素。研究了稀疏奇偶校验矩阵的结构和卷积码的性质，以减少枚举低权码字的计算量。此外，我们将所提出的方法应用于若干LDPC卷积码，并评估其编码的性能。

Low-density parity-check(LDPC) convolutional codes are error correcting codes constructed by sparse parity-check matrices of convolutional codes. The codes show good performance when they are decoded by iterative algorithms. In this research, we propose an efficient method for computing the low part of weight spectrum of LDPC convolutional codes. The minimum free distance and the weight spectrum are important factors to evaluate the error performance of LDPC convolutional codes. We focus on the structure of sparse parity-check matrices and the property of convolutional codes in order to reduce the computational cost for enumerate the low-weight codewords. Furthermore, we apply the proposed method to several LDPC convolutional codes, and evaluate the performance of their codes.