广义Helberg码纠插入/删除错误的一个简单证明

Simple proof the generalized Helberg codes being capable of correcting insertion/deletion errors

针对广义Helberg码纠错能力的现有证明方法较为复杂的缺点,提出了广义Helberg码能够纠正多个插入/删除错误的一种简单证明方法。通过深入分析广义Helberg码的码字与权重之间內积的单调性,证明了任意两个不同码字与权重之间的內积之差的上下界。利用所得到的上下界,简化了广义Helberg码纠错能力的现有证明方法。所给出的简单证明方法有助于对广义Helberg码的理解和进一步深入研究。

Since the existing proof method of the error correction capability for generalized Helberg codes is complicated,a simple proof that generalized Helberg codes are capable of correcting multiple insertion/deletion errors is proposed.By making a detailed analysis of the monotonicity of the inner product between the codeword and the weights for the generalized Helberg codes,the upper and lower bounds of the difference of the inner product between any two different codewords and weights are proved.By using the upper and lower bounds,the existing proof method for the error correction capability for generalized Helberg codes is simplified.The proposed simple proof is helpful in understanding generalized Helberg codes and making a further study.