论文标题
用于计算频道编码和有损源编码中强匡威指数的信息理论形式的算法家族
Algorithm Families for Computing Information-Theoretic Forms of Strong Converse Exponents in Channel Coding and Lossy Source Coding
论文作者
论文摘要
离散无内存通道的误差指数以两种形式表示。一个是Gallager的表达式具有正斜率参数，另一个是使用共同信息和相对熵表示的Csiszar和Korner的信息理论表示。它们的外观有所不同，现有的证明其协议的方法不是基本的，因为它们需要评估最佳分布必须满足的KKT条件。同样，强逆变指数有两种类型的表达式。它们是Arimoto的表达，具有负斜率参数，Dueck和Korner的信息理论表达。本文的目的是阐明从算法的角度来计算指数的角度来阐明两种表示指数的方式，即使用斜率参数和使用信息理论数量的表示之间的关系。 Arimoto的算法基于使用斜率参数的表达式，而作者和Tridenski和Zamir的算法基于Dueck和Korner的信息理论表达。最近提出了一种包括上述两种算法的算法家族，该算法最近提出了。本文阐明了Tridenski和Zamir的算法的融合证明了Arimoto和Dueck和Korner的指数的匹配。我们讨论了另一个算法家族，并使用其中使用的替代目标函数证明了误差指数的两个表达式重合。在此证明中，不需要评估KKT条件。然后，我们讨论错误源编码中误差的计算并纠正解码概率指数。定义了用于计算源编码强匡威指数的新算法家族。算法家族成员的融合意味着强匡威指数的两个表达式的匹配。
The error exponent of a discrete memoryless channel is expressed in two forms. One is Gallager's expression with a positive slope parameter and the other is Csiszar and Korner's information-theoretic representation expressed using the mutual information and the relative entropy. They differ in appearance, and existing methods to prove their agreement are not elementary, as they require an evaluation of the KKT conditions that the optimal distribution must satisfy. Similarly, there are two types of expressions for the strong converse exponent. They are Arimoto's expression with a negative slope parameter and Dueck and Korner's information-theoretic expression. The purpose of this paper is to clarify the relation between two ways of representing exponents, i.e., representations using slope parameters and those using information-theoretic quantities, from the viewpoint of algorithms for computing exponents. Arimoto's algorithm is based on expression using slope parameters, while the authors' and Tridenski and Zamir's algorithms are based on Dueck and Korner's information-theoretic expression. An algorithm family that includes the above two algorithms as special cases was recently proposed. This paper clarifies that the convergence of Tridenski and Zamir's algorithm proves the match of Arimoto's and Dueck and Korner's exponents. We discuss another family of algorithms and, using the surrogate objective function used therein, prove that the two expressions of the error exponent coincide. Evaluation of the KKT condition is not needed in this proof. We then discuss the computation of the error and correct decoding probability exponents in lossy source coding. A new algorithm family for computing the source coding strong converse exponent is defined. The convergence of a member of the algorithm family implies the match of the two expressions of the strong converse exponent.
