...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>IEEE Transactions on Communications >On the MacWilliams Identity for Classical and Quantum Convolutional Codes
【24h】

On the MacWilliams Identity for Classical and Quantum Convolutional Codes

机译：关于经典和量子卷积码的MacWilliams身份

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

The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing-Luerssen and Schneider in the case of minimal encoders, and generalized by Forney. We consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this MacWilliams identity in the case of minimal encoders. For our purpose, we choose a different representation for the exact weight generating function (EWGF) of a block code, by defining it as a linear combination of orthonormal vectors in Dirac bra–ket notation. This representation provides great flexibility so that general split weight generating functions and their MacWilliams identities can be easily obtained from the MacWilliams identity for EWGFs. As a result, we also obtain the MacWilliams identity for the input-parity WAMs of a systematic convolutional code and its dual. Finally, paralleling the development of the classical case, we establish the MacWilliams identity for quantum CCs.
机译：与卷积码（CC）关联的权重生成函数基于状态空间实现或权重邻接矩阵（WAM）。在最小编码器的情况下，Gluesing-Luerssen和Schneider首先建立了WAM上CC的MacWilliams身份，然后由Forney推广。我们从约束代码的角度考虑此问题，并在最小编码器的情况下获得此MacWilliams身份的简单直接证明。为了达到我们的目的，我们为分组代码的精确权重生成函数（EWGF）选择了一个不同的表示形式，方法是将其定义为Dirac braket表示法中正交向量的线性组合。这种表示提供了极大的灵活性，因此可以从EWGF的MacWilliams身份轻松获得常规的分割权重生成函数及其MacWilliams身份。结果，我们还获得了系统卷积码及其对偶的输入奇偶校验WAM的MacWilliams身份。最后，与经典案例的发展并行，我们为量子CC建立了MacWilliams身份。

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