On two strong converse theorems for discrete memoryless channels

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R >; C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Arimoto´s bound has been said to be equal to the bound of Dueck and Körner. However its rigorous proof has not been presented so far. In this paper we give a rigorous proof of the equivalence of Arimoto´s bound to that of Dueck and Körner.