Parity-Check Matrices Separating Erasures From Errors
Parity-Check Matrices Separating Erasures From Errors
复制标题
将擦除与错误分开的奇偶校验矩阵
DOI：
10.1109/tit.2013.2245939
复制
发表时间：
2013
影响因子：
2.5
通讯作者：
J. Weber
中科院分区：
文献类型：
--
作者：
K. Abdel;J. Weber
通常，线性代码的大多数解码算法旨在纠正或检测错误。但是，除错误外，许多渠道还会引起擦除。原则上，可以通过删除删除的符号并相对于刺破的代码解码所得向量来实现对此类渠道的解码。对于任何给定的线性代码和任何给定最大数量的可更正擦除，引入了奇偶校验检查矩阵，该矩阵产生了不选中任何删除符号的平等检查方程擦除。这些矩阵允许将擦除与误差分开以促进解码。提出了这种分离的平价检查矩阵的几种结构。为了降低解码的复杂性，首选将奇偶校验检查矩阵分开。分隔给定最大擦除数量的平等检查矩阵中的最小行数称为分离冗余。分离裁员的上限和下限是得出的。特别是表明，分离的冗余倾向于与代码的全等级检查矩阵中的行数线性生长。确定一些最大擦除数量的某些代码的分离冗余。
Most decoding algorithms of linear codes, in general, are designed to correct or detect errors. However, many channels cause erasures in addition to errors. In principle, decoding over such channels can be accomplished by deleting the erased symbols and decoding the resulting vector with respect to a punctured code. For any given linear code and any given maximum number of correctable erasures, parity-check matrices are introduced that yield parity-check equations which do not check any of the erased symbols and which are sufficient to characterize all punctured codes corresponding to this maximum number of erasures. These matrices allow for the separation of erasures from errors to facilitate decoding. Several constructions of such separating parity-check matrices are presented. To reduce decoding complexity, separating parity-check matrices with small number of rows are preferred. The minimum number of rows in a parity-check matrix separating a given maximum number of erasures is called the separating redundancy. Upper and lower bounds on the separating redundancies are derived. In particular, it is shown that the separating redundancies tend to grow linearly with the number of rows in full-rank parity-check matrices of codes. The separating redundancies of some classes of codes are determined for some maximum numbers of erasures.