论文标题
通用不对称通道的最佳误差检测代码通过Sperner理论
Optimal Error-Detecting Codes for General Asymmetric Channels via Sperner Theory
论文作者
论文摘要
实际上，几种与之相关的通信模型在它们对传输的“对象”的作用方式不对称。示例包括渠道，其中只能减少传输脉冲的幅度，符号只能删除的频道，非零符号只能将非零符号转移到右侧（例如定时频道）（例如定时频道）（例如，定时频道），只有在该频道中只能在该频道中仅列为储存量的子空间，并且可以恢复量的储存量，以置换量的范围，以下均可用来订购的范围。减少等等。我们引入了一个不对称通道作为通道的正式定义，其动作在所有可能的输入的集合上诱导了部分顺序，并证明此定义捕获了上述所有示例。这样的一般方法允许人们以统一的方式对待所有这些不同的模型，并通过使用Sperner理论来获得许多有趣的不对称通道的最佳误差检测代码的表征。
Several communication models that are of relevance in practice are asymmetric in the way they act on the transmitted "objects". Examples include channels in which the amplitudes of the transmitted pulses can only be decreased, channels in which the symbols can only be deleted, channels in which non-zero symbols can only be shifted to the right (e.g., timing channels), subspace channels in which the dimension of the transmitted vector space can only be reduced, unordered storage channels in which the cardinality of the stored (multi)set can only be reduced, etc. We introduce a formal definition of an asymmetric channel as a channel whose action induces a partial order on the set of all possible inputs, and show that this definition captures all the above examples. Such a general approach allows one to treat all these different models in a unified way, and to obtain a characterization of optimal error-detecting codes for many interesting asymmetric channels by using Sperner theory.
