On the stopping distance and the stopping redundancy of codes
On the stopping distance and the stopping redundancy of codes
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关于停车距离和代码的停车冗余
DOI：
10.1109/isit.2005.1523483
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Vardy
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文献类型：
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作者：
Moshe Schwartz;A. Vardy
现在众所周知，在二进制擦除通道（和其他通道）上迭代解码下的线性代码COPF的性能取决于Tanner图中最小的停止设置的大小。最近的几篇论文将此参数称为Copf的停止距离。这在某种程度上是错误的，因为Copf的Tanner图中最小的停止设置的大小取决于相应的奇偶校验检查矩阵的选择。很容易看到S Les D，其中D是COPF的最小锤距，我们表明可以为COPF选择一个奇偶校验检查矩阵（有足够多的依赖行），以便s = d。因此，我们引入了一个新参数，称为COPF的停止冗余，定义为COPF平均检查矩阵H中的最小行数，以使相应的停止距离S（H）达到其最大的可能值，即H（H ）= d。然后，我们在线性代码的停止冗余上得出一般边界。我们还研究了几种从其他代码构建代码的简单方法，并研究了这些结构对停止冗余的影响。具体来说，对于二元芦苇毛刺法规（在所有订单中）的家族，我们证明它们的停止冗余最多是他们常规的冗余。我们表明，二进制和三元扩展的Golay代码的裁员最多分别为34和22。最后，我们在MDS代码的停止冗余上提供上限和下限
It is now well known that the performance of a linear code Copf under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for Copf. Several recent papers refer to this parameter as the stopping distance s of Copf. This is somewhat of a misnomer since the size of the smallest stopping set in the Tanner graph for Copf depends on the corresponding choice of a parity-check matrix. It is easy to see that s les d, where d is the minimum Hamming distance of Copf, and we show that it is always possible to choose a parity-check matrix for Copf (with sufficiently many dependent rows) such that s = d. We thus introduce a new parameter, termed the stopping redundancy of Copf, defined as the minimum number of rows in a parity-check matrix H for Copf such that the corresponding stopping distance s(H) attains its largest possible value, namely s(H) = d. We then derive general bounds on the stopping redundancy of linear codes. We also examine several simple ways of constructing codes from other codes, and study the effect of these constructions on the stopping redundancy. Specifically, for the family of binary Reed-Muller codes (of all orders), we prove that their stopping redundancy is at most a constant times their conventional redundancy. We show that the stopping redundancies of the binary and ternary extended Golay codes are at most 34 and 22, respectively. Finally, we provide upper and lower bounds on the stopping redundancy of MDS codes
Eiichi Bannai：“汉明关联方案 H(d,q) 的字符表的模不变性”J.of Number Theory。
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