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The error exponent of a discrete memoryless channel is expressed in twoforms. One is Gallager's expression with a positive slope parameter and theother is Csiszar and Korner's information-theoretic representation expressedusing the mutual information and the relative entropy. They differ inappearance, and existing methods to prove their agreement are not elementary,as they require an evaluation of the KKT conditions that the optimaldistribution must satisfy. Similarly, there are two types of expressions forthe strong converse exponent. They are Arimoto's expression with a negativeslope parameter and Dueck and Korner's information-theoretic expression. Thepurpose of this paper is to clarify the relation between two ways ofrepresenting exponents, i.e., representations using slope parameters and thoseusing information-theoretic quantities, from the viewpoint of algorithms forcomputing exponents. Arimoto's algorithm is based on expression using slopeparameters, while the authors' and Tridenski and Zamir's algorithms are basedon Dueck and Korner's information-theoretic expression. An algorithm familythat includes the above two algorithms as special cases was recently proposed.This paper clarifies that the convergence of Tridenski and Zamir's algorithmproves the match of Arimoto's and Dueck and Korner's exponents. We discussanother family of algorithms and, using the surrogate objective function usedtherein, prove that the two expressions of the error exponent coincide.Evaluation of the KKT condition is not needed in this proof. We then discussthe computation of the error and correct decoding probability exponents inlossy source coding. A new algorithm family for computing the source codingstrong converse exponent is defined. The convergence of a member of thealgorithm family implies the match of the two expressions of the strongconverse exponent.

Algorithm Families for Computing Information-Theoretic Forms of Strong Converse Exponents in Channel Coding and Lossy Source Coding