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。该码在迭代译码中表现出良好的性能。在本研究中，我们提出一种计算低密度奇偶校验卷积码低重量频谱的有效方法。最小自由距离和权谱是评价LDPC卷积码误码性能的重要指标。为了减少计算量，我们重点研究了稀疏校验矩阵的结构和卷积码的性质。此外，我们将所提出的方法应用到几个LDPC卷积码，并评估其代码的性能。

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.