...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Information Theory, IEEE Transactions on >Stopping Set Distributions of Some Reed–Muller Codes
【24h】

Stopping Set Distributions of Some Reed–Muller Codes

机译：停止某些里德穆勒码的集合分布

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Stopping sets and stopping set distribution of a linear code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let $C$ be a binary $[n,k]$ linear code with parity-check matrix $H$, where the rows of $H$ may be dependent. A stopping set $S$ of $C$ with parity-check matrix $H$ is a subset of column indices of $H$ such that the restriction of $H$ to $S$ does not contain a row of weight one. The stopping set distribution ${T_i(H)}_{i=0}^n$ enumerates the number of stopping sets with size $i$ of $C$ with parity-check matrix $H$. Note that stopping sets and stopping set distribution are related to the parity-check matrix $H$ of $C$. Let $H^{*}$ be the parity-check matrix of $C$ which is formed by all the nonzero codewords of its dual co-n-nde $C^{perp}$. A parity-check matrix $H$ is called BEC-optimal if $T_i(H)=T_i(H^*), i=0,1,ldots, n$ and $H$ has the smallest number of rows. In this paper, we study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics, we obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed–Muller codes, and the extended Hamming codes, which are some Reed–Muller codes or their shortening or puncturing versions.
机译：线性码的停止集和停止集分布用于确定在二进制擦除信道（BEC）上进行迭代解码时此代码的性能。假设$ C $是带有奇偶校验矩阵$ H $的二进制$ [n，k] $线性代码，其中$ H $的行可能是相关的。具有奇偶校验矩阵$ H $的停止集$ S $ $ C $是$ H $列索引的子集，因此$ H $对$ S $的限制不包含一行权重。停止集分布$ {T_i（H）} _ {i = 0} ^ n $用奇偶校验矩阵$ H $枚举大小为$ i $的停止集的数量。注意，停止集和停止集分布与$ C $的奇偶校验矩阵$ H $有关。令$ H ^ {*} $为$ C $的奇偶校验矩阵，该矩阵由其双对数$ C ^ {perp} $的所有非零码字组成。如果$ T_i（H）= T_i（H ^ *），i = 0,1，ldots，n $和$ H $的行数最少，则奇偶校验矩阵$ H $被称为BEC最优。在本文中，我们研究了二进制线性码的停止集，停止集分布和BEC最优奇偶校验矩阵。在组合算术中使用有限几何，我们获得BEC最优奇偶校验矩阵，然后确定单纯形码，汉明码，一阶里德-穆勒码和扩展汉明码的停止集分布，其中一些是里德-穆勒码或其缩短或删截版本。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号