On Two Strong Converse Theorems for Stationary Discrete Memoryless Channels

TL;DR

This paper provides a rigorous proof demonstrating the equivalence between two strong converse theorems for stationary discrete memoryless channels, clarifying the relationship between Arimoto's and Dueck-Körner's bounds on error exponents.

Contribution

The paper offers the first rigorous proof establishing the equivalence of Arimoto's and Dueck-Körner's bounds for the strong converse theorem in discrete memoryless channels.

Findings

Proves the equivalence of Arimoto's and Dueck-Körner's bounds

Clarifies the relationship between different error exponent bounds

Strengthens the theoretical foundation of the strong converse theorem

Abstract

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 K\"orner determined the optimal exponent of correct decoding. Arimoto's bound has been said to be equal to the bound of Dueck and K\"orner. 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 K\"orner.